{"id":1183,"date":"2024-10-09T17:09:32","date_gmt":"2024-10-09T09:09:32","guid":{"rendered":"http:\/\/blog.chxzking.cn\/?p=1183"},"modified":"2025-09-22T11:39:42","modified_gmt":"2025-09-22T03:39:42","slug":"%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84-%e6%a0%91","status":"publish","type":"post","link":"http:\/\/blog.chxzking.cn\/index.php\/2024\/10\/09\/%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84-%e6%a0%91\/","title":{"rendered":"\u6570\u636e\u7ed3\u6784\u2014\u2014\u6811"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\"><kbd>\u524d\u8a00<\/kbd><\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u94fe\u8868\u8131\u79bb\u4e86\u6570\u7ec4\u7684\u7a7a\u95f4\u9650\u5236\uff0c\u7406\u8bba\u4e0a\u53ef\u4ee5\u65e0\u9650\u5ef6\u4f38\uff0c\u5177\u6709\u9ad8\u6548\u7684\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\uff0c\u4f46\u662f\u4e0e\u4e4b\u4ed8\u51fa\u7684\u4ee3\u4ef7\u662f\u2014\u2014\u94fe\u8868\u7684\u67e5\u627e\u6548\u7387\u4f4e\u4e0b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u6811\u7ed3\u6784\u7684\u51fa\u73b0\u4fbf\u662f\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u6587\u63d0\u4f9b\u4e00\u4e2a\u57fa\u4e8ec\u8bed\u8a00\u7684\u901a\u7528\u578b\u7ea2\u9ed1\u6811\u6a21\u677f\u5e93\uff0c\u60a8\u53ef\u4ee5\u901a\u8fc7\u8bbf\u95eeGitHub\u8fde\u63a5\u4e0b\u8f7d\u6e90\u7801\uff1a<a href=\"https:\/\/github.com\/chxzking\/Red-Black-Tree\/tree\/master\">https:\/\/github.com\/chxzking\/Red-Black-Tree\/tree\/master<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5e38\u7528\u6027\u8d28<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5ea6\u662f\u4ec0\u4e48\uff1f<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5ea6\u6709\u4e24\u4e2a\u6982\u5ff5\u2014\u2014\u8282\u70b9\u5ea6\u6570\u4e0e\u6811\u7684\u5ea6\u6570\uff0c<mark style=\"background-color:#00d084\" class=\"has-inline-color\">\u8282\u70b9\u7684\u5ea6\u6307\u7684\u662f\u8282\u70b9\u5177\u6709\u591a\u5c11\u5b50\u8282\u70b9<\/mark>\u3002<mark style=\"background-color:#8ed1fc\" class=\"has-inline-color\">\u6811\u7684\u5ea6\u5219\u662f\u6307\u8fd9\u4e2a\u6574\u4e2a\u6811\u4e2d\u7684\u6700\u5927\u8282\u70b9\u5ea6<\/mark>\u3002\u8fd8\u6709\u4e00\u4e2a\u7c7b\u4f3c\u5ea6\u662f\u6811\u7684\u603b\u5ea6\u6570\uff0c\u603b\u5ea6\u6570\u6307\u6240\u6709\u8282\u70b9\u7684\u5ea6\u6570\u4e4b\u548c\u3002\u800c\u603b\u5ea6\u6570\u548c\u8282\u70b9\u6570\u5b58\u5728\u4e00\u4e2a\u5173\u7cfb\uff1a<code>\u8282\u70b9\u6570=\u603b\u5ea6\u6570+1<\/code>\u3002\u8fd9\u4e2a\u6bd4\u8f83\u597d\u7406\u89e3\uff0c\u56e0\u4e3a\u8282\u70b9\u7684\u5ea6\u6570\u5c31\u662f\u8bb0\u8f7d\u4e86\u4e00\u4e2a\u8282\u70b9\u5b69\u5b50\u8282\u70b9\u7684\u4e2a\u6570\uff0c\u800c\u6839\u8282\u70b9\u662f\u6ca1\u6709\u8282\u70b9\u6307\u5411\u5b83\u7684\uff0c\u6240\u4ee5\u7f3a\u4e86\u4e00\u4e2a\u5ea6\uff0c\u52a0\u4e0a\u7f3a\u7684\u5c31\u548c\u603b\u7ed3\u70b9\u6811\u76f8\u7b49\u4e86\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8282\u70b9\u548c\u9ad8\u5ea6\u7684\u5173\u7cfb<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\u8981\u610f\u8bc6\u5230\u6811\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a<code>a<sub>1<\/sub>=1<\/code>\u7684\u7b49\u6bd4\u6570\u5217\uff0c<code>m<\/code>\u53c9\u6811\u6bcf\u4e00\u5c42\u6700\u5927\u8282\u70b9\u6811\u662f\u4e0a\u4e00\u5c42\u6700\u5927\u8282\u70b9\u6570\u7684<code>m<\/code>\u500d\uff0c\u90a3\u4e48\u7b49\u6bd4\u6570\u5217\u7684<code>q=m<\/code>\uff0c\u7531\u6b64\u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">1\u3001<\/mark><code>m<\/code>\u53c9\u6811\u7b2c<code>n<\/code>\u5c42\u6700\u591a\u6709<code> m<sup>n-1<\/sup>(i\u22651)<\/code>\u4e2a\u8282\u70b9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">2\u3001<\/mark>\u9ad8\u5ea6\u4e3ah\u7684m\u53c9\u6811\u6700\u591a\u6709<img loading=\"lazy\" decoding=\"async\" width=\"63\" height=\"61\" class=\"wp-image-1192\" style=\"width: 63px;\" src=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/S7C1WRG1NMMO_WIY7INB.png\" alt=\"\">\u4e2a\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">3\u3001<\/mark>\u9ad8\u5ea6\u4e3a<code>n<\/code>\u7684<code>m<\/code>\u53c9\u6811\u6700\u5c11\u6709\u591a\u5c11<code>n<\/code>\u4e2a\u8282\u70b9\u3002\u53ea\u9700\u8981\u4fdd\u8bc1\u6bcf\u5c42\u81f3\u5c11\u4e00\u4e2a\u8282\u70b9\u4fbf\u53ef\uff0c\u56e0\u6b64\u5728\u4e00\u4e2a\u6811\u4f1a\u9000\u5316\u6210\u4e00\u4e2a\u94fe\u8868\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">4\u3001<\/mark>\u9ad8\u5ea6\u4e3a<code>n<\/code>\u7684\u5ea6\u4e3a<code>m<\/code>\u7684\u6811\u81f3\u5c11\u6709<code>n+m-1<\/code>\u4e2a\u8282\u70b9\u3002\u56e0\u4e3a\u6570\u7684\u5ea6\u4e3a<code>m<\/code>\uff0c\u90a3\u4e48\u5c31\u610f\u5473\u7740\u6811\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u8282\u70b9\u5b58\u5728<code>m<\/code>\u4e2a\u5b50\u8282\u70b9\uff0c\u90a3\u4e48\u6700\u5c11\u60c5\u51b5\u4e0b\uff0c\u9664\u4e86\u8fd9\u4e2a\u8282\u70b9\u5916\u5176\u4ed6\u8282\u70b9\u5168\u90e8\u5ea6\u4e3a<code>1<\/code>\uff0c\u90a3\u4e48\u603b\u6570\u5c31\u662f<code>\uff08n-1\uff09*1+1*m <\/code>\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c<code>n<\/code>\u5c42\u4e2d\uff0c\u6709<code>n-1<\/code>\u5c42\u7684\u90fd\u53ea\u6709\u4e00\u4e2a\u8282\u70b9\uff0c\u800c\u5b58\u5728<code>1<\/code>\u5c42\u5177\u6709<code>m<\/code>\u4e2a\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">5\u3001<\/mark>\u5177\u6709<code>n<\/code>\u4e2a\u8282\u70b9\u7684<code>m<\/code>\u53c9\u6811\u6700\u5c0f\u7684\u9ad8\u5ea6\u4e3a <code>h = log<sub>m<\/sub>n(m-1)+1 <\/code>\u3002\u4e3a\u4e86\u6c42\u53d6\u6700\u5c0f\u9ad8\u5ea6\uff0c\u5c31\u9700\u8981\u8ba9\u6570\u5728\u6a2a\u5411\u6269\u5f20\uff0c\u6bcf\u4e00\u5c42\u90fd\u6dfb\u52a0\u5230\u6700\u5927\u7684\u8282\u70b9\u6570\uff0c\u6b64\u65f6\u53ef\u4ee5\u8054\u7acb\u8282\u70b9<code>n<\/code>\u7b49\u4e8e<code>\u7b2c2\u6761<\/code>\u6027\u8d28\u7684\u7ed3\u8bba\u89e3\u51fa<code>h<\/code>\u3002<\/p>\n\n\n\n<h1 class=\"wp-block-heading\"><kbd>\u4e8c\u53c9\u6811<\/kbd><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u6982\u5ff5<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u53c9\u6811\uff08Binary Tree\uff09\u662f\u4e00\u79cd\u6811\u5f62\u6570\u636e\u7ed3\u6784\uff0c\u5176\u4e2d\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\uff0c\u5206\u522b\u79f0\u4e3a\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u53c9\u6811\u884d\u751f\u51fa\u4e86\u6ee1\u4e8c\u53c9\u6811\u548c\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u6982\u5ff5\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6ee1\u4e8c\u53c9\u6811<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6ee1\u4e8c\u53c9\u6811<\/strong>\u6307\u7684\u662f\uff1a\u5982\u679c\u4e00\u68f5\u4e8c\u53c9\u6811\u7684\u6240\u6709\u5c42\u90fd\u8fbe\u5230\u6700\u5927\u8282\u70b9\u6570\uff0c\u5219\u79f0\u4e3a\u6ee1\u4e8c\u53c9\u6811\uff08\u5373\u6811\u4e2d\u4e0d\u5b58\u5728\u5ea6\u4e3a<code>1<\/code>\u7684\u8282\u70b9\uff0c\u9664\u53f6\u5b50\u8282\u70b9\u5916\u6240\u6709\u7684\u8282\u70b9\u5ea6\u5747\u4e3a<code>2<\/code>\uff09\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='\/wp-content\/uploads\/2024\/09\/1094457-20170225183610632-1388959691.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"\/wp-content\/uploads\/2024\/09\/1094457-20170225183610632-1388959691.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u76f4\u89c2\u7684\u611f\u53d7\u5c31\u662f\u6700\u5e95\u5c42\u7684\u4e00\u884c\u90fd\u662f\u5e73\u5e73\u6574\u6574\u7684\uff0c\u6ca1\u6709\u7f3a\u4e00\u4e2a\u5c11\u4e00\u4e2a\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u6ee1\u4e8c\u53c9\u6570\u7684\u7279\u6027<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">1\u3001<\/mark>\u9ad8\u5ea6\u4e3a<code>h<\/code>\u7684\u6811\u5177\u6709<code>2<sup>h<\/sup>-1<\/code>\u4e2a\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">2\u3001<\/mark>\u7b2cn\u5c42\u7684\u7ed3\u70b9\u6570\u4e3a<code>2<sup>i\u22121<\/sup><\/code>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">3\u3001<\/mark>\u5982\u679c\u7ed9\u6ee1\u4e8c\u53c9\u6811\u4ece<code>1<\/code>\u5f00\u59cb\u4ee5\u4ece\u4e0a\u5230\u4e0b\u4ece\u5de6\u81f3\u53f3\u8fdb\u884c\u7f16\u53f7\uff0c\u90a3\u4e48\u8282\u70b9i\u7684\u5de6\u5b69\u5b50\u4e00\u5b9a\u662f<code>2i<\/code>\uff0c\u800c\u6709\u5b69\u5b50\u662f<code>2i+1<\/code>\u3002\u8bc1\u660e\uff1a<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u8bc1\u660e\u8fc7\u7a0b<\/summary>\n<p class=\"wp-block-paragraph\">\u7236\u8282\u70b9\uff1a\u7b2c<code>n<\/code>\u884c\u7684\u7b2c<code>i<\/code>\u4e2a\u8282\u70b9\uff0c\u90a3\u4e48\u5b83\u7684\u7f16\u53f7\u4e3a<code>2<sup>n-1<\/sup>-1+i<\/code>\u3002\u516c\u5f0f\u610f\u4e49\u4e3a\uff0c<code>n-1<\/code>\u884c\u7684\u8282\u70b9\u603b\u6570\u52a0\u4e0a\u672c\u884c\u7684\u504f\u79fb\u91cf\u5c31\u662f\u5f53\u524d\u7684\u7f16\u53f7\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5de6\u5b69\u5b50\u8282\u70b9\uff1a\u7f16\u53f7\u4e3a<code>2<sup>n<\/sup>-1+I<\/code>\u3002\u516c\u5f0f\u7684\u542b\u4e49\u662f\uff0c<code>n<\/code>\u884c\u8282\u70b9\u603b\u6570\u52a0\u4e0a\u672c\u884c\u504f\u79fb\u91cf\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7531\u4e8e\u6bcf\u4e00\u4e2a\u8282\u70b9\u5fc5\u5b9a\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\uff0c\u6240\u4ee5\u504f\u79fb\u91cf<code>I = (i-1)*2+1<\/code>\u3002\u8054\u7acb\u53ef\u5f97\u5de6\u5b69\u5b50\u8282\u70b9\u7684\u7f16\u53f7\u4e3a<code>2<sup>n<\/sup>-1+(i-1)*2+1<\/code>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5de6\u5b69\u5b50\u7f16\u53f7\u9664\u4ee5\u7236\u4eb2\u8282\u70b9\u7f16\u53f7\uff1a<code>(2<sup>n<\/sup>-1+(i-1)*2+1)\u00f7(2<sup>n-1<\/sup>-1+i) = 2<\/code><\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\">\u540c\u6837\u7684\uff0c\u5982\u679c\u4e00\u4e2a\u8282\u70b9<code>i<\/code>\u5b58\u5728\u7236\u8282\u70b9\uff0c\u90a3\u4e48\u7236\u8282\u70b9\u7684\u7f16\u53f7\u662f<code>i\/2<\/code>\u53d6\u6574\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b8c\u5168\u4e8c\u53c9\u6811<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5b8c\u5168\u4e8c\u53c9\u6811<\/strong>\u6307\u7684\u662f\uff1a\u5982\u679c\u4e00\u68f5\u4e8c\u53c9\u6811\u9664\u4e86\u6700\u540e\u4e00\u5c42\u5916\uff0c\u6240\u6709\u5c42\u90fd\u662f\u6ee1\u7684\uff0c\u5e76\u4e14\u6700\u540e\u4e00\u5c42\u7684\u8282\u70b9\u4ece\u5de6\u5230\u53f3\u8fde\u7eed\u6392\u5217\uff0c\u5219\u79f0\u4e3a\u5b8c\u5168\u4e8c\u53c9\u6811\u3002\u5982\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/E8K8EFTDY_6_F807G92L.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"284\" height=\"223\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/E8K8EFTDY_6_F807G92L.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1187\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u901a\u4fd7\u7684\u8bb2\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u5176\u5b9e\u53ea\u9700\u8981\u89c2\u5bdf\u6700\u540e\u4e00\u5c42\uff0c\u5c06\u6ee1\u4e8c\u53c9\u6811\u7684\u6700\u5927\u7f16\u53f7\u5f80\u6700\u5c0f\u7f16\u53f7\u5f00\u59cb\u5220\u9664\uff0c\u9057\u7559\u4e0b\u6765\u7684\u5c31\u662f\u5b8c\u5168\u4e8c\u53c9\u6811\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8865\u5145\u4e00\u4e2a\u5c0f\u70b9\uff0c\u6ee1\u4e8c\u53c9\u6811\u5c5e\u4e8e\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u4f46\u662f\u5b8c\u5168\u4e8c\u53c9\u6811\u4e0d\u5c5e\u4e8e\u6ee1\u4e8c\u53c9\u6811\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u7279\u6027<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">1\u3001<\/mark>\u5b8c\u5168\u4e8c\u53c9\u6811\u6700\u591a\u53ea\u80fd\u5b58\u5728\u4e00\u4e2a\u5ea6\u4e3a<code>1<\/code>\u7684\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">2\u3001<\/mark>\u7531\u4e8e\u5b8c\u5168\u4e8c\u53c9\u6811\u53ef\u4ee5\u7531\u6ee1\u4e8c\u53c9\u6811\u51cf\u679d\u800c\u6765\uff0c\u6240\u4ee5\u5b83\u7684\u7f16\u53f7\u4e5f\u5b58\u5728\u5de6\u5b69\u5b50\u4e3a<code>2i<\/code>\uff0c\u53f3\u5b69\u5b50<code>2i+1<\/code>\u7684\u89c4\u5f8b\uff0c\u540c\u65f6\u4e5f\u652f\u6301i\u7684\u7236\u8282\u70b9\u4e3a<code>i\/2<\/code>\u7684\u6027\u8d28\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">3\u3001<\/mark>\u5047\u8bbe\u4e00\u68f5\u5b8c\u5168\u4e8c\u53c9\u6811\u5b58\u5728<code>m<\/code>\u4e2a\u8282\u70b9\uff0c\u90a3\u4e48\u7f16\u53f7<code>i\u2264\u230am\/2\u230b<\/code>\u7684\u4e3a\u5206\u652f\u8282\u70b9\uff0c\u5982\u679c\u7f16\u53f7<code>i\uff1e\u230am\/2\u230b<\/code>\u5219\u4e3a\u53f6\u5b50\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">4\u3001<\/mark>\u5177\u6709<code>n(n &gt; 0)<\/code>\u4e2a\u8282\u70b9\u7684\u5b8c\u5168\u4e8c\u53c9\u6811\u9ad8\u5ea6\u4e3a<code>\u2308log<sub>2<\/sub>(n+1)\u2309<\/code>\u6216\u8005<code>\u230alog<sub>2<\/sub>n\u230b+1<\/code><\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u8bc1\u660e\u8fc7\u7a0b<\/summary>\n<p class=\"wp-block-paragraph\"><\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#8ed1fc\" class=\"has-inline-color\">\u7b2c\u4e00\u79cd\u8868\u8fbe\u5f0f\u5199\u6cd5\u7684\u8bc1\u660e<\/mark>\uff1a<br>\u7531\u4e8e\u4e00\u5c42\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u6700\u5927\u53ef\u80fd\u662f\u6ee1\u4e8c\u53c9\u6811\uff0c\u800c\u6700\u5c0f\u53ef\u80fd\u662f\u8fd9\u4e00\u5c42\u5177\u6709\u4e00\u4e2a\u8282\u70b9\uff0c\u90a3\u4e48\u4e5f\u5c31\u662f\u610f\u5473\u7740\u8282\u70b9\u6570\u76ee\u6ee1\u8db3\u533a\u95f4\uff1a<code>2<sup>h-1<\/sup>-1&lt; n \u22642<sup>h<\/sup>-1<\/code><br><code>2<sup>h-1<\/sup>&lt; n+1 \u22642<sup>h<\/sup><\/code><br><code>h-1&lt;log<sub>2<\/sub>(n+1)\u2264h<\/code><br>\u5373<code>log<sub>2<\/sub>(n+1) \u2264 h &lt; log<sub>2<\/sub>(n+1)+1<\/code><br>\u7531\u4e8e\u9ad8\u5ea6\u4e00\u5b9a\u662f\u4e00\u4e2a\u6574\u6570\uff0c\u4e3a\u4e86\u786e\u4fdd\u7b49\u521a\u597d\u5927\u4e8e\u7b49\u4e8e\uff0c\u6240\u4ee5\u8981\u5411\u4e0a\u53d6\u6574\uff0c\u5373\uff1a<code>\u2308log<sub>2<\/sub>(n+1)\u2309<\/code><br><br><mark style=\"background-color:#8ed1fc\" class=\"has-inline-color\">\u7b2c\u4e8c\u79cd\u8868\u8fbe\u5f0f\u5199\u6cd5\u7684\u8bc1\u660e\uff1a<\/mark><br>\u548c\u7b2c\u4e00\u79cd\u4e00\u6837\uff0c\u4e0d\u8fc7\u662f\u9650\u5236\u533a\u95f4\u6709\u4e00\u70b9\u70b9\u53d8\u5316\uff1a<code>2<sup>h-1<\/sup>-1+1\u2264 n &lt;2<sup>h<\/sup><\/code><br><code>h-1\u2264 log<sub>2<\/sub>n &lt;h<br>log<sub>2<\/sub>n&lt; h \u2264log<sub>2<\/sub>n+1<\/code><br>\u4e3a\u4e86\u80fd\u6070\u597d\u5c0f\u4e8e\u7b49\u4e8e\u8fd9\u4e2a\u8fb9\u754c\uff0c\u6240\u4ee5\u9700\u8981\u5411\u4e0b\u53d6\u6574\uff0c\u5373\uff1a<code>\u230alog<sub>2<\/sub>n\u230b+1<\/code><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u53c9\u6811\u7684\u904d\u5386\u65b9\u5f0f<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u6df1\u5ea6\u641c\u7d22<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6df1\u5ea6\u641c\u7d22\u6709\u4e09\u79cd\u904d\u5386\u65b9\u5f0f\uff0c\u5206\u522b\u662f\u524d\u3001\u4e2d\u3001\u540e\u5e8f\u4e09\u79cd\u3002\u4e00\u4e2a\u4e8c\u53c9\u6811\u53ef\u4ee5\u770b\u4f5c\u5de6\u8282\u70b9\u3001\u5f53\u524d\u8282\u70b9\u3001\u53f3\u8282\u70b9\u4e09\u90e8\u5206\u7ec4\u6210\uff0c\u800c\u4e09\u79cd\u904d\u5386\u65b9\u5f0f\u5c31\u662f\u4ee5\u8fd9\u4e09\u90e8\u5206\u7684\u904d\u5386\u987a\u5e8f\u8fdb\u884c\u5212\u5206\uff0c\u4ee5\u5f53\u524d\u8282\u70b9\u4e3a\u4e2d\u5fc3\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u524d\u5e8f\u904d\u5386\uff1a\u5148\u904d\u5386\u5f53\u524d\u8282\u70b9\uff0c\u518d\u904d\u5386\u5de6\u8282\u70b9\uff0c\u6700\u540e\u904d\u5386\u53f3\u8282\u70b9<\/li>\n\n\n\n<li>\u4e2d\u5e8f\u904d\u5386\uff1a\u5148\u904d\u5386\u5de6\u8282\u70b9\uff0c\u518d\u904d\u5386\u5f53\u524d\u8282\u70b9\uff0c\u6700\u540e\u904d\u5386\u53f3\u8282\u70b9<\/li>\n\n\n\n<li>\u540e\u5e8f\u904d\u5386\uff1a\u5148\u904d\u5386\u5de6\u8282\u70b9\uff0c\u518d\u904d\u5386\u53f3\u8282\u70b9\uff0c\u6700\u540e\u904d\u5386\u5f53\u524d\u8282\u70b9<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6838\u5fc3\u70b91<\/strong>\uff1a\u4e3a\u4ec0\u4e48\u80fd\u4f7f\u7528\u8fd9\u4e9b\u65b9\u6cd5\u4fdd\u8bc1\u5b8c\u6574\u904d\u5386\u6574\u4e2a\u6811\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6839\u672c\u539f\u56e0\u662f\u4e8c\u53c9\u6811\u5177\u6709\u9012\u5f52\u5d4c\u5957\u6027\uff0c\u4e00\u4e2a\u5e9e\u5927\u7684\u4e8c\u53c9\u6811\u53ef\u4ee5\u4e0d\u65ad\u88ab\u770b\u4f5c\u4e09\u4e2a\u8282\u70b9\u7684\u4e8c\u53c9\u6811\uff0c\u6bd4\u5982\u4e0b\u56fe\uff0c\u5728\u5de6\u5b50\u6811\u4e2d\u62c6\u5206\u4e3a\u4e86\u4e00\u4e2a\u6807\u51c6\u4e09\u8282\u70b9\u4e8c\u53c9\u6811\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8fdb\u884c\u904d\u5386\u64cd\u4f5c\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/8@K61@G70E_WGXH@Z@RH.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"479\" height=\"424\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/8@K61@G70E_WGXH@Z@RH.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1202\"  sizes=\"auto, (max-width: 479px) 100vw, 479px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\u5de6\u5b50\u6811\u904d\u5386\u5b8c\u6210\u540e\uff0c\u5bf9\u4e8e\u6574\u4f53\u6765\u8bf4\uff0c\u521a\u624d\u76f8\u5f53\u4e8e\u904d\u5386\u5b8c\u6210\u4e86\u4e09\u8282\u70b9\u4e2d\u7684\u5de6\u8282\u70b9\uff0c\u90a3\u4e48\u63a5\u4e0b\u6765\u518d\u904d\u5386\u5269\u4e0b\u4e24\u4e2a\u8282\u70b9\u5c31\u53ef\u4ee5\u5b8c\u6210\u6574\u68f5\u6811\u4e86<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/UKNHE_Y7LD7YNZA9EP.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"337\" height=\"305\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/UKNHE_Y7LD7YNZA9EP.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1201\"  sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u524d\u5e8f\u904d\u5386<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u524d\u5e8f\u904d\u5386\u987a\u5e8f\u662f\u5f53\u524d\u8282\u70b9\u3001\u5de6\u8282\u70b9\u3001\u53f3\u8282\u70b9\uff0c\u6216\u8005\u8bf4\u53ef\u4ee5\u5199\u4e3a\u201c<strong>\u6839\u5de6\u53f3<\/strong>\u201d\uff0c\u4e5f\u5c31\u662f\u5148\u904d\u5386\u6839\u8282\u70b9\uff0c\u518d\u904d\u5386\u5de6\u8282\u70b9\uff0c\u6700\u540e\u904d\u5386\u53f3\u8282\u70b9\u3002\u4ee5\u4e0b\u56fe\u4e3a\u4f8b\u5b50\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/4P9D7NXDK_CX0FD.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"549\" height=\"557\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/4P9D7NXDK_CX0FD.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1203\"  sizes=\"auto, (max-width: 549px) 100vw, 549px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u56fe\u7684\u904d\u5386\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4ece\u6700\u9ad8\u89c6\u89d2\u770b\uff0c\u8fd9\u4e2a\u6570\u7684\u5de6\u4e2d\u53f3\u5206\u522b\u662f<code>2\u30011\u30013<\/code>\u8282\u70b9\u3002\u90a3\u4e48\u6839\u636e\u524d\u5e8f\u904d\u5386\u89c4\u5219\uff0c\u90a3\u4e48\u5148\u6253\u5370\u51fa<strong><code>1<\/code><\/strong><\/li>\n\n\n\n<li>\u63a5\u4e0b\u6765\u51c6\u5907\u6253\u5370<code>2<\/code>\u7684\u65f6\u5019\uff0c\u53d1\u73b02\u53ef\u4ee5\u5c55\u5f00\u4e3a<code>4\u30012\u30015<\/code>\uff0c\u5728\u8fd9\u4e2a\u6811\u7684\u89c6\u89d2\u4e2d\u6839\u636e\u89c4\u5219\u8981\u6253\u5370\u6839\u8282\u70b9<code>2<\/code><\/li>\n\n\n\n<li>\u63a5\u4e0b\u6765\u51c6\u5907\u6253\u5370<code>4<\/code>\uff0c\u53d1\u73b0<code>4<\/code>\u5230\u4e86\u5e95\u90e8\uff0c\u90a3\u4e48\u65e0\u9700\u518d\u6b21\u5c55\u5f00\uff0c\u76f4\u63a5\u6253\u5370<code>4<\/code><\/li>\n\n\n\n<li>\u4e4b\u540e\u518d\u51c6\u5907\u6253\u5370<code>5<\/code>\uff0c\u6b64\u65f6\u53d1\u73b05\u53ef\u4ee5\u5c55\u5f00\u4e3a<code>8\u30015\u3001\u7a7a<\/code>\uff0c\u4f9d\u65e7\u66f4\u5177\u89c4\u5219\u5148\u6253\u5370<code>5<\/code><\/li>\n\n\n\n<li>\u7136\u540e\u6253\u5370<code>8<\/code>\uff0c<code>8<\/code>\u65e0\u6cd5\u5c55\u5f00\uff0c\u90a3\u4e48\u63a5\u4e0b\u6765\u6253\u5370\u7a7a\uff0c\u7a7a\u4e0d\u5b58\u5728\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u5ffd\u7565\u3002<\/li>\n\n\n\n<li>\u5de6\u5b50\u6811\u6253\u5370\u5b8c\u6210\uff0c\u90a3\u4e48\u6839\u636e\u89c4\u5219\u662f\u6839\u5de6\u53f3\uff0c\u90a3\u4e48\u63a5\u4e0b\u6765\u770b\u53f3\u8fb9\uff0c\u53f3\u8fb9\u7684\u503c\u53ef\u4ee5\u5c55\u5f00\u4e3a<code>6\u30013\u30017<\/code>\uff0c\u53ef\u4ee5\u770b\u5230\u8fd9\u4e2a\u662f\u6700\u5e95\u90e8\u7684\u6807\u51c6\u4e09\u8282\u70b9\uff0c\u90a3\u4e48\u6309\u7167\u89c4\u5219\u76f4\u63a5\u8f93\u51fa<code>3\u30016\u30017<\/code><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u6700\u7ec8\u7684\u8f93\u51fa\u4e3a <strong>1\u30012\u30014\u30015\u30018\u30013\u30016\u30017<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">\u4ee3\u7801\u5b9e\u73b0\u5982\u4e0b\uff1a<\/mark><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u6811\u7684\u5b9a\u4e49\ntypedef struct Node\n{\n    int data;\n    struct Node* left;\n    struct Node* right;\n}Node;\n\/\/\u524d\u5e8f\u904d\u5386\nvoid PreorderTraversal(Node* root){\n    \/\/\u9012\u5f52\u51fa\u53e3\uff0c\u9047\u5230\u7a7a\u8282\u70b9\u8fd4\u56de\n    if(root == NULL) return;\n    \/\/\u5148\u6253\u5370\u5f53\u524d\u8282\u70b9\u7684\u503c\n    printf(\"%d \",root-&gt;data);\n    \/\/\u6253\u5370\u5de6\u8282\u70b9\u7684\u503c\n    PreorderTraversal(root-&gt;left);\n    \/\/\u6253\u5370\u53f3\u8282\u70b9\u7684\u503c\n    PreorderTraversal(root-&gt;right);\n    return;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u904d\u5386\u65b9\u5f0f\u6700\u663e\u8457\u7684\u7279\u70b9\u662f\u7b2c\u4e00\u4e2a\u6253\u5370\u7684\u662f\u6574\u68f5\u6811\u7684\u6839\u8282\u70b9\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e2d\u5e8f\u904d\u5386<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e2d\u5e8f\u904d\u5386\u987a\u5e8f\u662f\u5de6\u8282\u70b9\u3001\u5f53\u524d\u8282\u70b9\u3001\u53f3\u8282\u70b9\uff0c\u6216\u8005\u8bf4\u53ef\u4ee5\u5199\u4e3a\u201c<strong>\u5de6\u6839\u53f3<\/strong>\u201d\uff0c\u4ee5\u4e0b\u56fe\u4e3a\u4f8b\u5b50\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/4P9D7NXDK_CX0FD.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"549\" height=\"557\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/4P9D7NXDK_CX0FD.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1203\"  sizes=\"auto, (max-width: 549px) 100vw, 549px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4ece\u6700\u9ad8\u89c6\u89d2\u770b\uff0c\u8fd9\u4e2a\u6570\u7684\u5de6\u4e2d\u53f3\u5206\u522b\u662f<code>2\u30011\u30013<\/code>\u8282\u70b9\u3002\u90a3\u4e48\u6839\u636e\u4e2d\u5e8f\u904d\u5386\u89c4\u5219\uff0c\u90a3\u4e48\u5148\u6253\u5370\u51fa<code>2<\/code>\uff0c\u4f46\u662f\u800c\u53ef\u4ee5\u5c55\u5f00\uff0c\u90a3\u4e48\u5c31\u6682\u65f6\u4e0d\u80fd\u6253\u5370\u5b83\uff0c\u5c55\u5f00\u540e\u53d1\u73b0\u8282\u70b9\u4e3a<code>4\u30012\u30015<\/code>\uff0c\u6b64\u65f6\u6253\u5370\u8282\u70b94<\/li>\n\n\n\n<li>\u7136\u540e\u6309\u7167\u89c4\u5219\u6253\u5370<code>2<\/code>\u3002<\/li>\n\n\n\n<li>\u63a5\u7740\u6253\u5370<code>5<\/code>\uff0c\u4f46\u662f\u7531\u4e8e<code>5<\/code>\u80fd\u5c55\u5f00\uff0c\u6240\u4ee5\u5c55\u5f00\u540e\u662f<code>8\u30015\u3001\u7a7a<\/code>\uff0c\u90a3\u4e48\u6700\u7ec8\u6253\u5370\u7684\u662f<code>8<\/code><\/li>\n\n\n\n<li>\u6309\u7167\u89c4\u5219\uff0c\u63a5\u4e0b\u6765\u6253\u5370<code>5<\/code><\/li>\n\n\n\n<li>\u5de6\u5b50\u6811\u6253\u5370\u5b8c\u6210\u540e\uff0c\u6253\u5370\u6839\u8282\u70b9<code>1<\/code>\u3002<\/li>\n\n\n\n<li>\u63a5\u4e0b\u6765\u627e\u53f3\u8282\u70b9\uff0c\u7531\u4e8e\u53f3\u8282\u70b9\u80fd\u5c55\u5f00\u4e3a<code>6\u30013\u30017<\/code>\uff0c\u90a3\u4e48\u6309\u7167\u89c4\u5219\u5c31\u662f\u4f9d\u6b21\u6253\u5370<code>6\u30013\u30017<\/code><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u7ec8\u7684\u7ed3\u679c\u662f\uff1a<strong>4\u30012\u30018\u30015\u30011\u30016\u30013\u30017<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">\u4ee3\u7801\u5b9e\u73b0\u4e3a\uff1a<\/mark><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u6811\u7684\u5b9a\u4e49\ntypedef struct Node\n{\n    int data;\n    struct Node* left;\n    struct Node* right;\n}Node;\n\/\/\u4e2d\u5e8f\u904d\u5386\nvoid InorderTraversal(Node* root){\n    \/\/\u9012\u5f52\u51fa\u53e3\uff0c\u9047\u5230\u7a7a\u8282\u70b9\u8fd4\u56de\n    if(root == NULL) return;\n    \/\/\u6253\u5370\u5de6\u8282\u70b9\u7684\u503c\n    InorderTraversal(root-&gt;left);\n    \/\/\u6253\u5370\u5f53\u524d\u8282\u70b9\u7684\u503c\n    printf(\"%d \",root-&gt;data);\n    \/\/\u6253\u5370\u53f3\u8282\u70b9\u7684\u503c\n    InorderTraversal(root-&gt;right);\n    return;\n}<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">\u540e\u5e8f\u904d\u5386<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u540e\u5e8f\u904d\u5386\u987a\u5e8f\u662f\u5de6\u8282\u70b9\u3001\u53f3\u8282\u70b9\u3001\u5f53\u524d\u8282\u70b9\uff0c\u6216\u8005\u8bf4\u53ef\u4ee5\u5199\u4e3a\u201c<strong>\u5de6\u53f3\u6839<\/strong>\u201d\uff0c\u4ee5\u4e0b\u56fe\u4e3a\u4f8b\u5b50\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/4P9D7NXDK_CX0FD.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"549\" height=\"557\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/4P9D7NXDK_CX0FD.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1203\"  sizes=\"auto, (max-width: 549px) 100vw, 549px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u548c\u4e4b\u524d\u7684\u904d\u5386\u601d\u8def\u4e00\u6837\uff0c\u5728<code>2\u30011\u30013<\/code>\u7684\u65f6\u5019\u6309\u7167\u89c4\u5219\u5c55\u5f00\u5de6\u8282\u70b9\uff0c\u53d1\u73b0\u662f<code>4\u30012\u30015<\/code>\uff0c\u6240\u4ee5\u5148\u6253\u5370\u51fa<code>4<\/code>\uff0c\u5728<code>5<\/code>\u7684\u4f4d\u7f6e\u5c55\u5f00\u4e3a<code>8\u30015\u3001\u7a7a<\/code>\uff0c\u90a3\u4e48\u5c31\u6253\u5370<code>8\u30015<\/code>\uff0c\u6700\u540e\u6253\u5370<code>2<\/code><\/li>\n\n\n\n<li>\u5de6\u5b50\u6811\u7684\u8f93\u51fa\u5b8c\u6210\u540e\u63a5\u4e0b\u6765\u904d\u5386\u53f3\u5b50\u6811\uff0c\u6309\u7167\u89c4\u5219\u662f<code>6\u30017\u30013<\/code><\/li>\n\n\n\n<li>\u5de6\u53f3\u5b50\u6811\u8f93\u51fa\u540e\uff0c\u6700\u540e\u6253\u5370<code>1<\/code><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u7ec8\u7684\u8f93\u51fa\u7ed3\u679c\u662f<strong>4\u30018\u30015\u30012\u30016\u30017\u30013\u30011<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">\u4ee3\u7801\u5b9e\u73b0\u4e3a<\/mark><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u6811\u7684\u5b9a\u4e49\ntypedef struct Node\n{\n    int data;\n    struct Node* left;\n    struct Node* right;\n}Node;\n\/\/\u540e\u5e8f\u904d\u5386\nvoid PostorderTraversal(Node* root){\n    \/\/\u9012\u5f52\u51fa\u53e3\uff0c\u9047\u5230\u7a7a\u8282\u70b9\u8fd4\u56de\n    if(root == NULL) return;\n    \/\/\u6253\u5370\u5de6\u8282\u70b9\u7684\u503c\n    PostorderTraversal(root-&gt;left);\n    \/\/\u6253\u5370\u53f3\u8282\u70b9\u7684\u503c\n    PostorderTraversal(root-&gt;right);\n    \/\/\u6253\u5370\u5f53\u524d\u8282\u70b9\u7684\u503c\n    printf(\"%d \",root-&gt;data);\n    return;\n}<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">\u975e\u9012\u5f52\u6df1\u5ea6\u641c\u7d22\uff08\u8fed\u4ee3\u6cd5\uff09<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u9012\u5f52\u7c7b\u578b\u7684\u6df1\u5ea6\u641c\u7d22\u5b58\u5728\u4e00\u4e2a\u660e\u663e\u7684\u7f3a\u9677\u5c31\u662f\u53ef\u80fd\u9020\u6210\u6808\u6ea2\u51fa\uff0c\u5982\u679c\u6811\u7684\u6df1\u5ea6\u8fc7\u6df1\u6216\u8005\u6808\u5c0f\u5c31\u975e\u5e38\u5bb9\u6613\u5f15\u53d1\u6808\u6ea2\u51fa\u5bfc\u81f4\u7a0b\u5e8f\u5d29\u6e83\uff0c\u6240\u4ee5\u9700\u8981\u4e00\u79cd\u975e\u9012\u5f52\u7c7b\u578b\u7684\u7b97\u6cd5\u8fdb\u884c\u641c\u7d22\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ed4\u7ec6\u5206\u6790\u4e3a\u4ec0\u4e48\u4f7f\u7528\u9012\u5f52\u540e\uff0c\u4f1a\u5f97\u51fa\u4e00\u4e2a\u7ed3\u8bba\uff1a\u9700\u8981\u5229\u7528\u9012\u5f52\u540e\u8fdb\u5148\u51fa\u7684\u7279\u6027\uff0c\u800c\u8fd9\u4e2a\u5177\u6709\u8fd9\u4e2a\u7279\u6027\u7684\u4e00\u79cd\u6570\u636e\u7ed3\u6784\u662f\u201c\u6808\u201d\uff0c\u5176\u5b9e\u9012\u5f52\u4e5f\u5229\u7528\u4e86\u6808\uff0c\u4e0d\u8fc7\u662f\u4f7f\u7528\u4e86\u7cfb\u7edf\u6808\u3002\u6240\u4ee5\u9700\u8981\u624b\u52a8\u5b9e\u73b0\u4e00\u4e2a\u5806\u533a\u6808\uff0c\u7528\u4e8e\u8fdb\u884c\u641c\u7d22\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e2d\u5e8f\u904d\u5386<\/h5>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u975e\u9012\u5f52\u7c7b\u578b\u7684\u4e2d\u5e8f\u904d\u5386\ntypedef struct myStack\n{\n    Node* node;\/\/\u8282\u70b9\u5730\u5740\n    struct myStack* next;\n}myStack;\n\/\/\u538b\u6808\nvoid push(myStack** top,Node* node){\n     if(node==NULL) return;\n    \/\/\u751f\u6210\u4e00\u4e2a\u6808\u8282\u70b9\n    myStack *stackNode = (myStack*)malloc(sizeof(myStack));\n    stackNode-&gt;node = node;\n    stackNode-&gt;next = *top;\n    \/\/\u66f4\u65b0\u6808\u9876\n    *top = stackNode; \n}\n\/\/\u51fa\u6808\nNode* pop(myStack** top){\n    if((*top) == NULL) return NULL;\n\n    myStack* temp = *top;\n    *top = (*top)-&gt;next;\n    Node* node = temp-&gt;node;\n    free(temp);\n    return node;\n}\n\/\/\u68c0\u67e5\u662f\u5426\u4e3a\u7a7a\nbool isEmpty(myStack* top){\n    if(!top) return true;\n    return false;\n}\n\/\/\u4e2d\u5e8f\u904d\u5386\nvoid InorderTraversal(Node* root){\n    if(root == NULL) return;\n    \/\/\u5b9a\u4e49\u6808\u9876\n    myStack* top = NULL;\n    \/\/\u5b9a\u4e49\u4e00\u4e2a\u626b\u63cf\u8282\u70b9\n    Node* current = root;\n\n    while((current != NULL) || !isEmpty(top)){\n        \/\/\u5faa\u73af\u904d\u5386\u4e00\u6761\u8def\u5de6\u5b69\u5b50\u5165\u6808\n        while(current != NULL){\n            push(&amp;top,current);\n            current = current-&gt;left;\n        }\n        \/\/\u5f39\u51fa\u4e00\u4e2a\u8282\u70b9\uff0c\u8bfb\u53d6\u8be5\u8282\u70b9\u7684\u503c\n        current = pop(&amp;top);\n        printf(\"%d \",current-&gt;data);\n        \/\/\u83b7\u53d6\u53f3\u5b69\u5b50\n        current = current-&gt;right;\n    }\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6574\u4e2a\u4ee3\u7801\u5176\u5b9e\u5e76\u4e0d\u96be\uff0c\u9996\u5148\u662f\u6808\u51fd\u6570\uff0c\u5165\u6808\u4e0e\u51fa\u6808\u9053\u4ee3\u7801\u5f88\u597d\u7406\u89e3\uff0c\u800c\u4e2d\u5e8f\u904d\u5386\u4ee3\u7801\u603b\u4f53\u7684\u903b\u8f91\u5f88\u6e05\u6670\uff0c\u4e0d\u8fc7\u6700\u96be\u7684\u90e8\u5206\u662f\u5916\u5c42<code>while<\/code>\u7684\u6761\u4ef6\u3002<code>\u6761\u4ef61<\/code>\u7684<code>isEmpty<\/code>\u5224\u65ad\u6bd4\u8f83\u597d\u7406\u89e3\uff0c\u5b83\u7684\u4f5c\u7528\u662f\u4e3a\u4e86\u5224\u65ad\u6808\u662f\u5426\u7a7a\u4e86\uff0c\u5982\u679c\u7a7a\u4e86\u5219\u610f\u5473\u7740\u904d\u5386\u5b8c\u6210\u3002\u4f46\u662f\u53e6\u5916\u4e00\u4e2a<code>\u6761\u4ef62<\/code>\u7684<code>current != NULL<\/code>\u662f\u4e00\u4e2a\u96be\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6574\u4e2a<code>while<\/code>\u5faa\u73af\u7684\u903b\u8f91\u5f88\u660e\u786e\uff0c\u9996\u5148\u5f80\u5de6\u5b69\u5b50\u7684\u65b9\u5411\u5165\u6808\uff0c\u4e00\u76f4\u5230\u538b\u5230<code>NULL<\/code>\uff0c\u8fd9\u4e2a\u65f6\u5019\u518d\u5f39\u51fa\u4e00\u4e2a\u8282\u70b9\u7528\u4e8e\u8bfb\u53d6\uff0c\u800c\u5728\u6df1\u5ea6\u904d\u5386\u4e2d\uff0c\u5176\u5b9e\u6bcf\u5c42\u7684\u6839\u8282\u70b9\u90fd\u662f\u4f5c\u4e3a\u4e0a\u4e00\u4e2a\u8282\u70b9\u7684\u5de6\u5b69\u5b50\u4fdd\u5b58\u7684\uff0c\u6240\u4ee5\u6574\u4e2a\u903b\u8f91\u5c31\u53ea\u5305\u542b\u4e86\u5de6\u5b69\u5b50\u548c\u53f3\u5b69\u5b50\uff0c\u800c<code>current<\/code>\u4e0d\u4ec5\u4f5c\u4e3a\u4e86\u8bfb\u53d6\u8282\u70b9\uff0c\u540c\u65f6\u4e5f\u8d1f\u8d23\u627f\u63a5\u56de\u6eaf\u7684\u4f4d\u7f6e\uff0c\u800c\u56de\u6eaf\u4e5f\u662f\u6808\u672c\u8eab\u5b8c\u6210\u7684\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u524d\u5e8f\u904d\u5386<\/h5>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u524d\u5e8f\u904d\u5386\nvoid PreorderTraversal(Node* root){\n    if(root == NULL) return;\n    myStack* top = NULL;\n    Node* current = root;\n\n    while(!isEmpty(top) || current != NULL){\n        \/\/\u5165\u6808\n        while(current != NULL){\n            printf(\"%d \",current-&gt;data);\n            push(&amp;top,current);\n            current = current-&gt;left;\n        }\n        \/\/\u51fa\u6808,\u83b7\u53d6\u53f3\u5b50\u6811\n        current = pop(&amp;top);\n        current = current-&gt;right;\n    }\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e00\u79cd\u65b9\u6848\u7684\u524d\u5e8f\u904d\u5386\u548c\u4e2d\u5e8f\u904d\u5386\u5f88\u76f8\u4f3c\uff0c\u4e0d\u8fc7\u5b83\u662f\u5148\u8fdb\u884c\u4e86\u6253\u5370\u8f93\u51fa\u7136\u540e\u518d\u8fdb\u884c\u538b\u6808\u64cd\u4f5c<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u540e\u5e8f\u904d\u5386<\/h5>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u540e\u5e8f\u904d\u5386\nvoid PostorderTraversal(Node* root){\n    if(root == NULL) return;\n    myStack* top = NULL;\n    Node* current = root;\n    Node* last = NULL;\/\/\u7528\u4e8e\u8bb0\u5f55\u4e0a\u4e00\u6b21\u904d\u5386\u7684\u8282\u70b9\uff0c\u4f5c\u7528\u662f\u786e\u8ba4\u53f3\u5b50\u6811\u662f\u5426\u88ab\u904d\u5386\u8fc7\n\n    while(!isEmpty(top) || current != NULL){\n        \n       while (current != NULL){\n            push(&amp;top,current);\n            current = current-&gt;left;\n       }\n       current = pop(&amp;top);\n       \/\/\u5224\u65ad\u662f\u5426\u904d\u5386\u4e86\u53f3\u5b50\u6811\n       if(current-&gt;right == last || current-&gt;right == NULL){\n            printf(\"%d \",current-&gt;data);\n            last = current;\n            current = NULL;\n       }\n       \/\/\u5982\u679c\u6ca1\u6709\u904d\u5386\u53f3\u5b50\u6811\uff0c\u5219\u5f80\u53f3\u5b50\u6811\u5f00\u59cb\u904d\u5386\n       else{\n           push(&amp;top,current);\/\/\u91cd\u65b0\u538b\u6808\n           current = current-&gt;right;\/\/\u5e76\u4e14\u51c6\u5907\u5c06\u53f3\u5b50\u6811\u538b\u6808\n       }        \n    }\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u79cd\u65b9\u6848\u4e2d\u7684\u540e\u5e8f\u904d\u5386\u6bd4\u8f83\u590d\u6742\uff0c\u5982\u679c\u76f4\u63a5\u56de\u6eaf\u4f1a\u6253\u5370\u6839\u8282\u70b9\uff0c\u6240\u4ee5\u5728\u6253\u5370\u6839\u8282\u70b9\u4e4b\u524d\u5224\u65ad\u662f\u5426\u5df2\u7ecf\u6253\u5370\u4e86\u53f3\u5b69\u5b50\uff0c\u4e8e\u662f\u4f7f\u7528\u4e86last\u6307\u9488\u8bb0\u5f55\u4e0a\u4e00\u6b21\u6253\u5370\u7684\u7ed3\u679c\uff0c\u7528\u4e8e\u5224\u65ad\u662f\u5426\u6253\u5370\u4e86\u53f3\u5b69\u5b50\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0a\u65b9\u6848\u7684\u601d\u7ef4\u903b\u8f91\u5e94\u8be5\u662f\u548c\u4e0b\u56fe\u7c7b\u4f3c\uff0c\u548c\u6811\u672c\u8eab\u7684\u903b\u8f91\u5e76\u4e0d\u5b8c\u5168\u5bf9\u7b49\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/J7OW6K18KZIB6FQ.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"537\" height=\"532\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/J7OW6K18KZIB6FQ.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1251\"  sizes=\"auto, (max-width: 537px) 100vw, 537px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u904d\u5386\u903b\u8f91<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b83\u66f4\u50cf\u662f\u4ee5\u4e00\u6761\u56de\u6eaf\u8def\u7ebf\u4e3a\u4e3b\uff0c\u4e0d\u65ad\u4f9d\u6b21\u5f80\u53f3\u53d1\u6563\u76f4\u81f3<code>NULL<\/code>\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0d\u8fc7\u6811\u7684\u904d\u5386\u8fd8\u6709\u5176\u4ed6\u7684\u601d\u8def\uff0c\u4f46\u662f\u5927\u5dee\u4e0d\u5dee\u90fd\u662f\u5229\u7528\u6808\u5b9e\u73b0\u7684\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\u8fd9\u4e2a\u524d\u5e8f\u904d\u5386\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>void PreorderTraversal(Node* root){\n    if(root == NULL) return;\n    myStack* top = NULL;\n    Node* current = root;\n    \/\/\u6839\u8282\u70b9\u5165\u6808\n    push(&amp;top,current);\n\n    while(!isEmpty(top)){\n        \/\/\u53d6\u51fa\u6808\u9876\u8282\u70b9\n        current = pop(&amp;top);\n        \/\/\u6808\u7a7a\u5219\u9000\u51fa\n        if(current == NULL){\n            return;\n        }\n        \/\/\u6253\u5370\u6808\u9876\n        printf(\"%d \",current-&gt;data);\n        \/\/\u8be5\u8282\u70b9\u53f3\u5b69\u5b50\u5165\u6808\n        push(&amp;top,current-&gt;right);\n        \/\/\u8be5\u8282\u70b9\u5de6\u5b69\u5b50\u5165\u6808\n        push(&amp;top,current-&gt;left);\n    }\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u904d\u5386\u65b9\u5f0f\u975e\u5e38\u590d\u5408\u6811\u7684\u672c\u8eab\u7684\u903b\u8f91\uff0c\u4f46\u662f\u524d\u4e2d\u540e\u4e09\u79cd\u904d\u5386\u7684\u5199\u6cd5\u5dee\u522b\u6bd4\u8f83\u5927\uff0c\u800c\u8fd9\u4e2a\u903b\u8f91\u6700\u7b80\u5355\u7684\u5c31\u662f\u524d\u5e8f\u904d\u5386\u5199\u6cd5\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5e7f\u5ea6\u641c\u7d22<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e7f\u5ea6\u641c\u7d22\u4e5f\u662f\u6811\u7684\u4e00\u79cd\u904d\u5386\u65b9\u5f0f\uff0c\u7531\u4e8e\u662f\u4e00\u5c42\u5c42\u641c\u7d22\uff0c\u6240\u4ee5\u5b83\u80fd\u6bd4\u8f83\u6e05\u6670\u7684\u770b\u5230\u6811\u7684\u7ed3\u6784\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e7f\u5ea6\u641c\u7d22\u7684\u4e5f\u53eb\u5c42\u6b21\u904d\u5386\uff0c\u5b83\u7684\u57fa\u672c\u601d\u8def\u662f\u5148\u8bfb\u53d6\u4e00\u5c42\uff0c\u7136\u540e\u4ece\u5de6\u5230\u53f3\u9010\u6b65\u8bbf\u95ee\u6570\u636e\uff0c\u8bbf\u95ee\u7ed3\u675f\u540e\u63a8\u8fdb\u5230\u4e0b\u4e00\u5c42\u3002\u800c\u961f\u5217\u7684\u5148\u8fdb\u5148\u51fa\u7684\u7279\u6027\u975e\u5e38\u590d\u5408\u5c42\u6b21\u904d\u5386\u3002\u6240\u4ee5\u5c42\u6b21\u904d\u5386\u7684\u4ee3\u7801\u5b9e\u73b0\u4e2d\u9700\u8981\u989d\u5916\u4f7f\u7528\u4e00\u4e2a\u961f\u5217\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\u4e00\u5c42\u8fdb\u5165\u5230\u961f\u5217\u540e\uff0c\u4ece\u961f\u5217\u5934\u90e8\u53d6\u51fa\u4e00\u4e2a\u8282\u70b9\u7684\u540c\u65f6\u9700\u8981\u5c06\u5176\u5de6\u53f3\u5b69\u5b50\u5165\u961f\u3002\u6240\u4ee5\u5f53\u4e00\u5c42\u904d\u5386\u5b8c\u6210\u540e\uff0c\u6b64\u65f6\u4e0b\u4e00\u5c42\u7684\u8282\u70b9\u4e5f\u5165\u961f\u5b8c\u6210\u7b49\u5f85\u51fa\u961f\u3002\u4ee5\u4e0b\u662f\u4ee3\u7801\u5b9e\u73b0\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>typedef struct QueueNode{\n    Node* node;\/\/\u8282\u70b9\u5730\u5740\n    struct QueueNode* next;\n}QueueNode;\n\ntypedef struct Queue{\n    QueueNode* QueueHeader;\n    QueueNode* QueueTail;\n}Queue;\n\n\/\/\u5165\u961f\nvoid enQueue(Queue* queue, Node* node){\n    if(node == NULL) return;\n    \/\/\u521b\u5efa\u961f\u5217\u8282\u70b9\n    QueueNode* queueNode = (QueueNode*)malloc(sizeof(QueueNode));\n    queueNode-&gt;node = node;\n    queueNode-&gt;next = NULL;\n    \/\/\u52a0\u5165\u961f\u5217\n\n    \/\/\u5982\u679c\u961f\u5217\u4e3a\u7a7a\n    if (queue-&gt;QueueHeader == NULL){\n        queue-&gt;QueueHeader = queueNode;\n        queue-&gt;QueueTail = queueNode;\n    }\n    \/\/\u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a\n    else{\n        queue-&gt;QueueTail-&gt;next = queueNode;\n        queue-&gt;QueueTail = queueNode;\n    }\n    return;\n}\n\/\/\u51fa\u961f\nNode* deQueue(Queue* queue){\n    \/\/\u5982\u679c\u961f\u5217\u4e3a\u7a7a\u5219\u8fd4\u56de\n    if(queue-&gt;QueueHeader == NULL) return NULL;\n    \/\/\u83b7\u53d6\u961f\u9996\u7684\u6811\u8282\u70b9\n    Node* node = queue-&gt;QueueHeader-&gt;node;\n    \/\/\u83b7\u53d6\u961f\u5217\u4e0b\u4e00\u4e2a\u8282\u70b9\u7684\u503c\n    QueueNode* temp = queue-&gt;QueueHeader;\n    queue-&gt;QueueHeader = queue-&gt;QueueHeader-&gt;next;\n    if(queue-&gt;QueueHeader == NULL){\/\/\u5982\u679c\u961f\u5217\u4e3a\u7a7a\u4e86\u5219\u7f6e\u7a7a\n        queue-&gt;QueueTail = NULL;\n    }\n    free(temp);\n    return node;\n}\n\/\/\u961f\u5217\u5224\u7a7a\nbool queueIsEmpty(Queue* queue){\n    return queue-&gt;QueueHeader == NULL;\n}\n\/\/\u5c42\u6b21\u904d\u5386\nvoid Hierarchical_traversal(Node* root){\n    if(root == NULL) return;\n    \/\/\u521b\u5efa\u4e00\u4e2a\u961f\u5217\n    Queue queue;\n    queue.QueueHeader = NULL;\n    queue.QueueTail = NULL;\n    \n    Node* current = root;\n    enQueue(&amp;queue,current);\n    \n    while (!queueIsEmpty(&amp;queue)){\n       \/\/\u51fa\u961f\n       current = deQueue(&amp;queue);\n       if(current == NULL){\n            return;\n       }\n       \/\/\u8f93\u51fa\u8282\u70b9\u6570\u636e     \n       printf(\"%d \",current-&gt;data);\n       \/\/\u5165\u961f\n       enQueue(&amp;queue,current-&gt;left);\n       enQueue(&amp;queue,current-&gt;right);\n    }\n}<\/code><\/pre>\n\n\n\n<h1 class=\"wp-block-heading\"><kbd>\u4e8c\u53c9\u641c\u7d22\u6811<\/kbd><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u6982\u5ff5<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u53c9\u641c\u7d22\u6811\u76f8\u5bf9\u666e\u901a\u5728\u4e8c\u53c9\u6811\u8fdb\u884c\u4e86\u6539\u8fdb\uff0c\u6216\u8005\u8bf4\uff0c\u4ece\u4e8c\u53c9\u641c\u7d22\u6811\u5f00\u59cb\u624d\u662f\u771f\u6b63\u8fdb\u5165\u4e86\u4e8c\u53c9\u6811\u7684\u4f18\u52bf\u9886\u57df\u3002\u5728\u666e\u901a\u7684\u4e8c\u53c9\u6811\u4e2d\uff0c\u53ef\u4ee5\u6e05\u695a\u7684\u770b\u5230\uff0c\u8981\u60f3\u67e5\u627e\u4e00\u4e2a\u503c\uff0c\u6700\u574f\u7684\u60c5\u51b5\u4f9d\u65e7\u9700\u8981\u904d\u5386\u6574\u4e2a\u6811\uff0c\u5c31\u548c\u94fe\u8868\u7684\u6548\u7387\u4e00\u6837\uff0c\u800c\u4e8c\u53c9\u641c\u7d22\u6811\u5219\u662f\u5728\u5143\u7d20\u6dfb\u52a0\u9636\u6bb5\u5c31\u5bf9\u5143\u7d20\u8fdb\u884c\u4e86\u6392\u5e8f\uff0c\u4ece\u800c\u63d0\u4f9b\u4e86\u66f4\u52a0\u9ad8\u6548\u7684\u641c\u7d22\u65b9\u6848\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u53c9\u641c\u7d22\u6811\u5177\u6709\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8282\u70b9\u7684\u5de6\u5b50\u6811<\/strong>\uff1a\u6bcf\u4e2a\u8282\u70b9\u7684\u5de6\u5b50\u6811\u4e2d\u7684\u6240\u6709\u8282\u70b9\u7684\u503c\u90fd\u5c0f\u4e8e\u8be5\u8282\u70b9\u7684\u503c\u3002<\/li>\n\n\n\n<li><strong>\u8282\u70b9\u7684\u53f3\u5b50\u6811<\/strong>\uff1a\u6bcf\u4e2a\u8282\u70b9\u7684\u53f3\u5b50\u6811\u4e2d\u7684\u6240\u6709\u8282\u70b9\u7684\u503c\u90fd\u5927\u4e8e\u8be5\u8282\u70b9\u7684\u503c\u3002<\/li>\n\n\n\n<li><strong>\u5de6\u53f3\u5b50\u6811<\/strong>\uff1a\u6bcf\u4e2a\u8282\u70b9\u7684\u5de6\u53f3\u5b50\u6811\u4e5f\u90fd\u662f\u4e8c\u53c9\u641c\u7d22\u6811\u3002<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/SLY7PBUL22E9R9EG_7.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"665\" height=\"464\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/SLY7PBUL22E9R9EG_7.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1206\"  sizes=\"auto, (max-width: 665px) 100vw, 665px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e9b\u7279\u70b9\u4f7f\u5f97\u4e8c\u53c9\u641c\u7d22\u6811\u5728\u67e5\u627e\u3001\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u4e0a\u5177\u6709\u8f83\u9ad8\u7684\u6548\u7387\u3002\u5e73\u5747\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e9b\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a<code>O(log n)<\/code>\uff0c\u6700\u574f\u60c5\u51b5\u4e0b\u4e3a<code>O(n)<\/code>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u63d2\u5165<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u7531\u4e8e\u4e8c\u53c9\u6811\u5177\u6709\u9012\u5f52\u6027\uff0c\u6240\u4ee5\u63d2\u5165\u64cd\u4f5c\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u7684\u601d\u60f3\uff0c\u800c\u4e8c\u53c9\u641c\u7d22\u6811\u53ea\u9700\u8981\u7ef4\u6301\u5de6\u5b50\u6811\u5c0f\u4e8e\u53f3\u5b50\u6811\u7684\u57fa\u672c\u89c4\u5219\u5c31\u53ef\u4ee5\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">\u4ee3\u7801\u793a\u4f8b\uff1a<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u524d\u7f6e\u51c6\u5907<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include &lt;stdio.h&gt;\n#include &lt;malloc.h&gt;\n\/\/\u6811\u7684\u5b9a\u4e49\ntypedef struct Node\n{\n    int data;\n    struct Node* left;\n    struct Node* right;\n}Node;\n\/\/\u521b\u5efa\u8282\u70b9\nNode* createNode(int data){\n    Node* temp = (Node*)malloc(sizeof(Node));\n    temp-&gt;data = data;\n    temp-&gt;left = NULL;\n    temp-&gt;right = NULL;\n    return temp;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8282\u70b9\u63d2\u5165<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u63d2\u5165\u8282\u70b9\uff08\u5199\u6cd51\uff09\uff0c\u8be5\u51fd\u6570\u7684\u4f5c\u7528\u662f\u5c06\u4e00\u4e2a\u6839\u8282\u70b9\u7684\u5b50\u6811\u4e2d\u63d2\u5165\u4e00\u4e2a\u5143\u7d20\uff0c\u5e76\u8fd4\u56de\u8fd9\u4e2a\u53ef\u80fd\u88ab\u4fee\u6539\u7684\u6839\u8282\u70b9\nNode* insert(Node* root,int data){\n    if(root == NULL) return createNode(data);\n\n    if(data &lt;= root-&gt;data)\n        root-&gt;left = insert(root-&gt;left,data);\n    else\n        root-&gt;right = insert(root-&gt;right,data);\n    return root;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u5199\u6cd5\u8fd4\u56deNode\u6307\u9488\u7684\u539f\u56e0\u662f\uff0c\u5728\u9012\u5f52\u7684\u8fc7\u7a0b\u4e2d\u6bcf\u6b21\u4f20\u5165\u7684\u6839\u8282\u70b9\u5b58\u5728\u88ab\u4fee\u6539\u53ef\u80fd\uff0c\u800c\u4e00\u7ea7\u6307\u9488\u662f\u65e0\u6cd5\u8fd4\u56de\u88ab\u4fee\u6539\u7684\u6307\u9488\u7684\uff0c\u6240\u4ee5\u6362\u4e86\u4e00\u79cd\u601d\u8def\uff0c\u8fd4\u56de\u65b0\u7684\u5730\u5740\uff0c\u91cd\u65b0\u4fdd\u5b58\u5230\u6839\u8282\u70b9\u4e2d \u3002\u5f53\u7136\u4e5f\u53ef\u4ee5\u76f4\u63a5\u5728\u9012\u5f52\u7684\u8fc7\u7a0b\u4e2d\u4fee\u6539\u6839\u8282\u70b9\u7684\u6307\u9488\u7684\u503c\uff0c\u6bd4\u5982\u4e0b\u9762\u7684\u5199\u6cd52\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u63d2\u5165\u8282\u70b9\uff08\u5199\u6cd52\uff09\uff0c\u4f7f\u7528\u4e8c\u7ea7\u6307\u9488\nvoid insert(Node** root ,int data){\n    \/\/\u9000\u51fa\u6761\u4ef6\n    if(*root == NULL){\n        *root = createNode(data);\n        return;\n    }\n    \/\/\u53f6\u5b50\u7684\u9009\u62e9\n    if(data &lt;= (*root)-&gt;data){\n        insert(&amp;(*root)-&gt;left,data);\n    }else{\n        insert(&amp;(*root)-&gt;right,data);\n    }\n    return;\n}<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>int num&#91;]={10,7,20,6,8,18,23,16,19,21,24};\/\/\u6d4b\u8bd5\u6848\u4f8b\nint main(){\n    Node* root = NULL;\n    \/\/\u5199\u6cd51\n&nbsp;  for(int i = 0;i&lt;sizeof(num)\/sizeof(num&#91;0]);i++){\n&nbsp; &nbsp; &nbsp;root = insert(root,num&#91;i]);\n&nbsp;  }\n\n    \/\/\u5199\u6cd52\n&nbsp;  for(int i = 0;i&lt;sizeof(num)\/sizeof(num&#91;0]);i++){\n&nbsp; &nbsp; &nbsp;insert(&amp;root,num&#91;i]);\n&nbsp;  }\n}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u5220\u9664<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5220\u9664\u7684\u64cd\u4f5c\u6bd4\u8f83\u590d\u6742\u4e00\u70b9\uff0c\u56e0\u4e3a\u5220\u9664\u64cd\u4f5c\u9700\u8981\u540c\u65f6\u7ef4\u62a4\u6811\u7ed3\u6784\u4e0d\u88ab\u7834\u574f\u3002\u4f46\u662f\u6811\u7684\u8282\u70b9\u4e4b\u95f4\u7684\u5173\u7cfb\u9519\u7efc\u590d\u6742\uff0c\u6240\u4ee5\u9700\u8981\u5206\u7c7b\u8ba8\u8bba\u3002\u8fd9\u91cc\u5206\u4e3a\u4e09\u7c7b\uff0c\u4ee5\u8282\u70b9\u7684\u5ea6\u505a\u4e3a\u5212\u5206\u6761\u4ef6\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5ea6\u4e3a0\u65f6<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5ea6\u4e3a0\u7684\u8282\u70b9\u662f\u53f6\u5b50\u8282\u70b9\uff0c\u800c\u53f6\u5b50\u8282\u70b9\u662f\u6700\u597d\u5220\u9664\u7684\u8282\u70b9\uff0c\u56e0\u4e3a\u5b83\u4e0d\u4e0e\u6811\u7684\u7ed3\u6784\u6709\u76f4\u63a5\u7684\u5173\u7cfb\uff0c\u5b83\u53ea\u88ab\u7236\u4eb2\u8282\u70b9\u8fde\u63a5\uff0c\u6240\u4ee5\u53ef\u4ee5\u4e4b\u95f4\u5220\u9664\uff0c\u7136\u540e\u5c06\u7236\u4eb2\u8282\u70b9\u7684\u5bf9\u5e94\u6307\u9488\u7f6e\u7a7a\u4fbf\u53ef\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5ea6\u4e3a1\u65f6<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5ea6\u4e3a1\u7684\u8282\u70b9\u76f8\u5bf9\u96be\u4e00\u4e9b\uff0c\u5b83\u5f00\u59cb\u8bbe\u8ba1\u5230\u4e86\u6811\u7684\u7ed3\u6784\uff0c\u5e76\u4e14\u5206\u4e3a\u5de6\u53f3\u5b50\u6811\u4e24\u79cd\u60c5\u51b5\uff0c\u4e0d\u8fc7\u4e24\u79cd\u60c5\u51b5\u7684\u672c\u8d28\u90fd\u662f\u4e00\u6837\u7684\u3002\u4e0d\u7ba1\u5b83\u7684\u5de6\u5b50\u6811\u8fd8\u662f\u53f3\u5b50\u6811\u7684\u503c\u662f\u4ec0\u4e48\uff0c\u76f8\u5bf9\u4e8e\u88ab\u5220\u9664\u8282\u70b9\u7684\u7236\u4eb2\u8282\u70b9\u90fd\u6ca1\u6709\u5f71\u54cd\uff0c<mark style=\"background-color:#7bdcb5\" class=\"has-inline-color\">\u5982\u679c\u88ab\u5220\u9664\u8282\u70b9\u5728\u662f\u7236\u4eb2\u8282\u70b9\u7684\u5de6\u5b50\u6811\uff0c\u90a3\u4e48\u5b83\u7684\u5b50\u8282\u70b9\u4e00\u5b9a\u63a5\u66ff\u66f4\u65b0\u540e\u5de6\u5b50\u6811\u7684\u4f4d\u7f6e\uff0c\u5982\u679c\u88ab\u5220\u9664\u8282\u70b9\u5728\u662f\u7236\u4eb2\u8282\u70b9\u7684\u53f3\u5b50\u6811\uff0c\u90a3\u4e48\u5b83\u7684\u5b50\u8282\u70b9\u4e00\u5b9a\u63a5\u66ff\u66f4\u65b0\u540e\u53f3\u5b50\u6811\u7684\u4f4d\u7f6e\u3002<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/X1O1MG2HQYHJYC.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"544\" height=\"298\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/X1O1MG2HQYHJYC.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1209\"  sizes=\"auto, (max-width: 544px) 100vw, 544px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/H0SSNVCSHEQB5810N6N.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"451\" height=\"308\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/H0SSNVCSHEQB5810N6N.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1210\"  sizes=\"auto, (max-width: 451px) 100vw, 451px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5ea6\u4e3a2\u65f6<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5ea6\u4e3a2\u65f6\u6700\u590d\u6742\u7684\u4e00\u79cd\u60c5\u51b5\uff0c\u5b83\u540c\u65f6\u5177\u6709\u5de6\u53f3\u5b50\u6811\uff0c\u5982\u679c\u60f3\u8981\u5220\u9664\u8be5\u8282\u70b9\uff0c\u5fc5\u987b\u8981\u5904\u7406\u5b83\u7684\u5b50\u6811\u7684\u903b\u8f91\uff0c\u7ef4\u6301\u6811\u7684\u57fa\u672c\u89c4\u5219\u548c\u7ed3\u6784\uff0c\u4fdd\u6301\u53f3\u5b50\u6811\u5927\u4e8e\u5de6\u5b50\u6811\u7684\u89c4\u5219\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5904\u7406\u65b9\u6cd5\u4e3b\u8981\u6709\u4e24\u79cd\uff0c\u4e0d\u8fc7\u5b83\u4eec\u672c\u8d28\u4e0a\u662f\u4e00\u79cd\uff0c\u53ea\u662f\u5b58\u5728\u4e9b\u5fae\u7684\u533a\u522b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#f78da7\" class=\"has-inline-color\">\u7b2c\u4e00\u79cd<\/mark>\uff1a\u88ab\u5220\u9664\u8282\u70b9\u7684\u53f3\u5b50\u6811\u79fb\u52a8\u5230\u88ab\u5220\u9664\u8282\u70b9\u7684\u5de6\u5b50\u6811\u7684\u6700\u5927\u8282\u70b9\u7684\u53f3\u5b50\u6811\u4e0a\uff0c\u8fd4\u56de\u88ab\u5220\u9664\u8282\u70b9\u7684\u5de6\u8282\u70b9\u4f5c\u4e3a\u65b0\u6839\u8282\u70b9\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/74KLXMJS_Y8U41WKD@J-489x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"489\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/74KLXMJS_Y8U41WKD@J-489x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1213\"  sizes=\"auto, (max-width: 489px) 100vw, 489px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#f78da7\" class=\"has-inline-color\">\u7b2c\u4e8c\u79cd<\/mark>\uff1a\u88ab\u5220\u9664\u8282\u70b9\u7684\u5de6\u5b50\u6811\u79fb\u52a8\u5230\u88ab\u5220\u9664\u8282\u70b9\u7684\u53f3\u5b50\u6811\u7684\u6700\u5c0f\u8282\u70b9\u7684\u5de6\u5b50\u6811\u4e0a\uff0c\u8fd4\u56de\u88ab\u5220\u9664\u8282\u70b9\u7684\u53f3\u8282\u70b9\u4f5c\u4e3a\u65b0\u6839\u8282\u70b9\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/5_I9AACUSERK6RIH-466x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"466\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/5_I9AACUSERK6RIH-466x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1214\"  sizes=\"auto, (max-width: 466px) 100vw, 466px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6838\u5fc3\u70b91<\/strong>\uff1a\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u8fd9\u6837\u79fb\u52a8\uff0c\u96be\u9053\u4e0d\u4f1a\u7834\u574f\u5176\u4ed6\u8282\u70b9\u5417\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u95ee\u9898\u662f\u521d\u5b66\u8005\u6700\u5bb9\u6613\u51fa\u73b0\u7684\u95ee\u9898\uff0c\u800c\u4e14\u901a\u5e38\u770b\u5f97\u4e91\u91cc\u96fe\u91cc\uff0c\u60f3\u95ee\u4e5f\u65e0\u4ece\u4e0b\u624b\uff0c\u4e0d\u77e5\u9053\u81ea\u5df1\u4ec0\u4e48\u5730\u65b9\u6ca1\u660e\u767d\uff0c\u603b\u611f\u89c9\u54ea\u91cc\u90fd\u660e\u767d\uff0c\u4f46\u53c8\u597d\u50cf\u77e5\u9053\u67d0\u4e00\u56de\u4e8b\u513f\uff0c\u5176\u5b9e\u53ea\u9700\u8981\u6362\u4e00\u79cd\u601d\u8def\u5c31\u53ef\u4ee5\u4e86\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#8ed1fc\" class=\"has-inline-color\">\u9996\u5148\u8981\u8bb2\u8bb2\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u8fd9\u6837\u79fb\u52a8\u3002<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">       \u9996\u5148\u79fb\u52a8\u9700\u8981\u4e00\u4e2a\u5927\u524d\u63d0\uff0c\u90a3\u5c31\u662f\u6570\u636e\u662f\u6709\u89c4\u5f8b\u7684\uff0c\u800c\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u89c4\u5f8b\u662f\u53f3\u8fb9\u4e00\u5b9a\u6bd4\u5de6\u8fb9\u5927\uff0c\u4ee5\u56fe\u4f8b\u6765\u8bf4\uff0c\u8981\u5220\u9664\u7684\u8282\u70b9\u662f<code>10<\/code>\uff0c\u90a3\u4e48\u53f3\u5b50\u6811\u6700\u5c0f\u7684\u4e5f\u662f<code>15<\/code>\uff0c\u8fdc\u8fdc\u5927\u4e8e\u5de6\u5b50\u6811\u7684\u6700\u5927\u503c<code>8<\/code>\u3002<br> \u90a3\u4e48\u5c31\u4ee5\u7b2c\u4e00\u79cd\u79fb\u52a8\u65b9\u5f0f\u4e3a\u4f8b\uff0c\u53bb\u6389\u4e86<code>10<\/code>\uff0c\u53c8\u60f3\u6811\u4fdd\u6301\u7ed3\u6784\uff0c\u90a3\u4e48\u9700\u8981\u518d\u6b21\u9009\u51fa\u4e00\u4e2a\u6839\u8282\u70b9\uff0c\u800c\u6839\u8282\u70b9\u9700\u8981\u6ee1\u8db3\u5de6\u5c0f\u53f3\u5927\u7684\u539f\u5219\u3002<br>        \u5728\u4f8b\u5b50\u4e2d\u5de6\u5b50\u6811\u6709\u5f88\u591a\u53ef\u9009\u7684\u53ef\u4ee5\u9009<code>5\u30017\u30018<\/code>\uff0c\u4f46\u662f\u6700\u7ec8\u9009<code>7<\/code>\u7684\u539f\u56e0\u5728\u4e8e\u4ee3\u7801\u5b9e\u73b0\u6700\u7b80\u5355\u3002\u5982\u679c\u9009<code>5<\/code>\uff0c\u90a3\u4e48\u8fd4\u56de\u65b0\u6839\u8282\u70b9\u9700\u8981\u8fdb\u884c\u591a\u4f59\u7684\u4ee3\u7801\u4fdd\u5b58\u5b83\u7684\u5730\u5740\uff0c\u7136\u540e\u6539\u53d8\u5b83\u7684\u53f3\u8282\u70b9\u7684\u503c\uff0c\u6b64\u5916\u8fd8\u9700\u8981\u5ac1\u63a5\u53f3\u5b50\u6811\u3002<br>         \u5982\u679c\u9009<code>8<\/code>\u4e5f\u4e00\u6837\uff0c\u9700\u8981\u6539\u53d8\u5b83\u7684\u5de6\u5b50\u6811\u903b\u8f91\uff0c\u7136\u540e\u518d\u5904\u7406\u53f3\u5b50\u6811\u7684\u65b0\u52a0\u7684\u503c\u3002<br>         \u800c\u5982\u679c\u4f7f\u75287\u5219\u7b80\u5355\u5f88\u591a\uff0c\u56e0\u4e3a\u4ee5\u5b83\u4e3a\u6839\u7684\u8fd9\u68f5\u5b50\u6811\u903b\u8f91\u7ed3\u6784\u5df2\u7ecf\u5b8c\u6574\u4e86\uff0c\u53ea\u9700\u8981\u52a0\u4e0a\u53f3\u5b50\u6811\u4fbf\u53ef\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#8ed1fc\" class=\"has-inline-color\">\u5176\u6b21\u8bb2\u8bb2\u4e3a\u4ec0\u4e48\u4e0d\u4f1a\u5f71\u54cd\u5230\u5176\u4ed6\u7684\u8282\u70b9\u3002<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">        \u8fd9\u91cc\u9700\u8981\u4f7f\u7528\u6574\u4f53\u7684\u5927\u5c40\u89c2\uff0c\u4f9d\u65e7\u4f7f\u7528\u7b2c\u4e00\u79cd\u65b9\u5f0f\u4e3a\u4f8b\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u4e2d\u53d1\u751f\u6539\u53d8\u7684\u8282\u70b9\u53ea\u6709<code>8<\/code>\uff0c\u770b\u4f3c\u590d\u6742\u7684\u64cd\u4f5c\uff0c\u5b9e\u9645\u4e0a\u90fd\u662f\u5b83\u4eec\u7684\u7236\u8282\u70b9\u5728\u8fdb\u884c\u64cd\u4f5c\uff0c\u7236\u8282\u70b9\u6700\u7ec8\u662f\u8981\u5220\u9664\u7684\u3002\u9664\u4e86\u7236\u8282\u70b9\uff0c\u6811\u4e2d\u53ea\u6709<code>8<\/code>\u771f\u6b63\u51fa\u73b0\u4e86\u4fee\u6539\uff0c\u5e76\u4e14\u6240\u6709\u7684\u8282\u70b9\u5176\u5b9e\u672c\u8d28\u4e0a\u662f\u65e0\u6cd5\u5bdf\u89c9\u7236\u8282\u70b9\u662f\u5426\u51fa\u73b0\u4e86\u4ec0\u4e48\u64cd\u4f5c\u7684\uff0c\u56e0\u4e3a\u8fde\u63a5\u7684\u5355\u5411\u94fe\u8868\u3002<br>        \u5f53\u7136\uff0c\u8fd9\u68f5\u793a\u4f8b\u7684\u4e8c\u53c9\u6811\u770b\u8d77\u6765\u4f3c\u4e4e\u6ca1\u6709\u529e\u6cd5\u4ee3\u8868\u6240\u6709\u7684\uff0c\u4f46\u662f\u518d\u62d3\u5c55\u4e00\u4e0b\u601d\u8def\uff0c\u5982\u679c\u8fd9\u68f5\u6811\u53ea\u662f\u67d0\u4e00\u4e2a\u5de8\u5927\u7684\u4e8c\u53c9\u6811\u7684\u4e00\u68f5\u5b50\u6811\uff0c\u800c\u4e14\u5b58\u5728\u4e00\u4e2a\u8282\u70b9\u6307\u5411\u4e86\u8fd9\u68f5\u5c40\u90e8\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9<code>10<\/code>\uff0c\u90a3\u4e48\u7ecf\u8fc7\u5220\u9664\u7b97\u6cd5\u540e\uff0c\u4f1a\u8fd4\u56de\u4e00\u4e2a\u65b0\u8282\u70b9\u7684\u5730\u5740<code>7<\/code>\uff0c\u800c\u8fd9\u68f5\u5c40\u90e8\u4e8c\u53c9\u6811\u6811\u53c8\u7ecf\u8fc7\u8c03\u6574\u91cd\u65b0\u6ee1\u8db3\u4e86\u5de6\u5c0f\u53f3\u5927\u7684\u539f\u5219\uff0c\u90a3\u4e48\u6574\u68f5\u5de8\u5927\u7684\u4e8c\u53c9\u6811\u6811\u7ecf\u8fc7\u4e00\u6b21\u5c40\u90e8\u8c03\u6574\u4e5f\u4f9d\u65e7\u6ee1\u8db3\u89c4\u5219\u3002<br>        \u540c\u7406\uff0c\u7531\u4e8e\u4e8c\u53c9\u6811\u5177\u6709\u9012\u5f52\u6027\uff0c\u5b8c\u5168\u53ef\u4ee5\u5c06\u8fd9\u4e9b\u6ca1\u6709\u53d1\u751f\u6539\u53d8\u7684\u8282\u70b9\u770b\u6210\u4e00\u68f5\u68f5\u5b50\u6811\uff0c\u90a3\u4e48\u5c31\u8282\u70b9\u6ca1\u6709\u53d1\u751f\u6539\u53d8\uff0c\u5b50\u6811\u7684\u7ed3\u6784\u5c31\u4e0d\u4f1a\u6539\u53d8\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba\uff0c\u8fd9\u4e2a\u5220\u9664\u6cd5\u6ca1\u6709\u5bf9\u7ed3\u6784\u8fdb\u884c\u7834\u574f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">\u5b9e\u73b0\u4ee3\u7801\uff08\u4ee5\u7b2c\u4e00\u79cd\u65b9\u6cd5\u4e3a\u4f8b\uff09\uff1a<\/mark><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u51fd\u6570\u7684\u542b\u4e49\uff0c\u4f20\u5165\u4e00\u68f5\u6811\uff0c\u5220\u9664\u6307\u5b9a\u8282\u70b9\u540e\u518d\u8fd4\u56de\u8fd9\u68f5\u88ab\u8c03\u6574\u8fc7\u7684\u6811\u7684\u6839\u8282\u70b9\u5730\u5740\nNode* NodeDelete(Node* root,int data){\n    \/\/\u9012\u5f52\u51fa\u53e3\n    if(root == NULL) return NULL;\n    \/\/\u67e5\u627e\u65b9\u5411\n    if(data &lt; root-&gt;data){\/\/\u503c\u6bd4\u5f53\u524d\u8282\u70b9\u503c\u5c0f\uff0c\u5219\u5f80\u5de6\n        root-&gt;left = NodeDelete(root-&gt;left,data);\n    }else if(data &gt; root-&gt;data){\/\/\u503c\u6bd4\u5f53\u524d\u8282\u70b9\u5927\uff0c\u5219\u5f80\u53f3\n        root-&gt;right = NodeDelete(root-&gt;right,data);\n    }\n    \/\/\u5220\u9664\u64cd\u4f5c\n    else{\/\/\u627e\u5230\u4e86\u503c\n\n        \/\/\u60c5\u51b51\uff0c\u5ea6\u4e3a0\uff0c\n        if(root-&gt;left == NULL &amp;&amp; root-&gt;right == NULL){\n            free(root);\n            return NULL;\n        }\n        \/\/\u60c5\u51b52\uff0c\u5ea6\u4e3a1\uff0c\u5c0f\u7c7b\u60c5\u51b51\uff1a\u4e3a\u53f3\u5b69\u5b50\n        else if(root-&gt;left == NULL&amp;&amp; root-&gt;right != NULL){\n            Node* temp = root-&gt;right;\n            free(root);\n            return temp;\n        }\n        \/\/\u60c5\u51b52\uff0c\u5ea6\u4e3a1\uff0c\u5c0f\u7c7b\u60c5\u51b52\uff1a\u4e3a\u5de6\u5b69\u5b50\n        else if(root-&gt;left != NULL &amp;&amp; root-&gt;right == NULL){\n            Node* temp = root-&gt;left;\n            free(root);\n            return temp;\n        }\n        \/\/\u60c5\u51b53\uff0c\u5ea6\u4e3a2.\n        else{\n            \/\/\u83b7\u53d6\u5de6\u5b50\u6811\u6700\u5927\u7684\u8282\u70b9\n            Node* left_max = root-&gt;left;\n            while(left_max-&gt;right != NULL){\n                left_max = left_max-&gt;right;\n            }\n            \/\/\u79fb\u52a8\u53f3\u5b50\u6811\u5ac1\u63a5\u5230\u8be5\u8282\u70b9\u7684\u53f3\u5b50\u6811\u4e0a\n            left_max-&gt;right = root-&gt;right;\n            \/\/\u8fd4\u56de\u88ab\u5220\u9664\u8282\u70b9\u7684\u5de6\u5b50\u6811\n            Node* temp = root-&gt;left;\n            free(root);\n            \/\/\u5de6\u5b50\u6811\u8282\u70b9\u4f5c\u4e3a\u65b0\u6839\u8282\u70b9\n            return temp;\n        }\n    }\n    \/\/\u8fd4\u56de\u65b0\u6811\n    return root;\n}<\/code><\/pre>\n\n\n\n<h1 class=\"wp-block-heading\"><kbd>\u5e73\u8861\u4e8c\u53c9\u6811<\/kbd><\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u53c9\u641c\u7d22\u6570\u63d0\u4f9b\u4e86\u4e00\u4e2a\u9ad8\u6548\u7684\u641c\u7d22\u548c\u63d2\u5165\u7684\u6570\u636e\u7ed3\u6784\uff0c\u4f46\u662f\u5374\u5b58\u5728\u4e00\u4e2a\u7f3a\u9677\uff0c\u5728\u7279\u6b8a\u7684\u6392\u5217\u4e0b\uff0c\u4e8c\u53c9\u641c\u7d22\u6811\u53ef\u80fd\u9000\u5316\u4e3a\u94fe\u8868\uff0c\u4ece\u800c\u6548\u7387\u964d\u4e3a<code>O(n)<\/code><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\u6211\u6709\u4e00\u4e2a\u6570\u7ec4 1\u30012\u30013\u30014\uff0c\u5982\u679c\u4ece\u5de6\u5230\u53f3\u63d2\u5165\u6811\uff0c\u5219\u4f1a\u51fa\u73b0\u4ee5\u4e0b\u60c5\u51b5\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/IK3F78R1NYEZ2E08OIE.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"408\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/IK3F78R1NYEZ2E08OIE.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1216\"  sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ece\u56fe\u793a\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u8fd9\u4e2a\u6570\u7ec4\u7684\u503c\u63d2\u5165\u5230\u6811\u540e\uff0c\u76f4\u63a5\u8ba9\u6811\u9000\u5316\u6210\u4e86\u94fe\u8868\uff0c\u4ece\u800c\u5931\u53bb\u4e86\u6811\u539f\u672c\u7684\u9ad8\u6548\u67e5\u627e\u80fd\u529b\uff0c\u90a3\u4e48\u662f\u5426\u529e\u6cd5\u89e3\u51b3\u4e8c\u53c9\u641c\u7d22\u6811\u9000\u5316\u7684\u95ee\u9898\u5462\uff1f<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">AVL\u6811<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">AVL\u6811\u662f\u4e00\u79cd\u81ea\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5b83\u7684\u4e3b\u8981\u7279\u70b9\u662f\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5e73\u8861\u56e0\u5b50<\/strong>\uff1a\u6bcf\u4e2a\u8282\u70b9\u7684\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\uff08\u5373\u5e73\u8861\u56e0\u5b50\uff09\u6700\u591a\u4e3a1\u3002\u8fd9\u786e\u4fdd\u4e86\u6811\u7684\u9ad8\u5ea6\u4fdd\u6301\u5728\u5bf9\u6570\u7ea7\u522b\uff0c\u4ece\u800c\u4fdd\u8bc1\u4e86\u57fa\u672c\u64cd\u4f5c\uff08\u5982\u63d2\u5165\u3001\u5220\u9664\u548c\u67e5\u627e\uff09\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(log n)\u3002<\/li>\n\n\n\n<li><strong>\u65cb\u8f6c\u64cd\u4f5c<\/strong>\uff1a\u4e3a\u4e86\u7ef4\u6301\u5e73\u8861\uff0cAVL\u6811\u5728\u63d2\u5165\u6216\u5220\u9664\u8282\u70b9\u540e\u53ef\u80fd\u9700\u8981\u8fdb\u884c\u65cb\u8f6c\u64cd\u4f5c\u3002\u65cb\u8f6c\u5206\u4e3a\u56db\u79cd\u7c7b\u578b\uff1a\u5355\u53f3\u65cb\u3001\u5355\u5de6\u65cb\u3001\u53cc\u53f3\u65cb\u548c\u53cc\u5de6\u65cb\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u5e73\u8861\u56e0\u5b50<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b80\u5355\u6765\u8bf4\uff0c\u5c31\u662fAVL\u6811\u53ef\u4ee5\u5c06\u5de6\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\u7ef4\u6301\u5728<code>[0,1]<\/code>\u4e4b\u95f4\uff0c\u6216\u8005\u8bf4<code> |\u5de6\u5b50\u6811\u9ad8\u5ea6-\u53f3\u5b50\u6811\u9ad8\u5ea6| \u2264 1<\/code>\u3002\u4e3e\u51e0\u4e2a\u4f8b\u5b50\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/9T3YCRX6KG_NEM56@OL.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"509\" height=\"518\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/9T3YCRX6KG_NEM56@OL.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1217\"  sizes=\"auto, (max-width: 509px) 100vw, 509px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u8ff0\u56fe\u7684 \u5de6\u5b50\u6811\u9ad8\u5ea6\u4e3a3\uff0c\u53f3\u5b50\u6811\u9ad8\u5ea6\u4e3a4\uff0c\u6240\u4ee5\u5b83\u7684\u6839\u8282\u70b9\u9ad8\u5ea6\u5dee\uff08\u5e73\u8861\u56e0\u5b50\uff09\u4e3a <code>|3-4| = 1<\/code><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/Q_WHE9@XJ7SNWL_QXK.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"456\" height=\"528\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/Q_WHE9@XJ7SNWL_QXK.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1218\"  sizes=\"auto, (max-width: 456px) 100vw, 456px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u8ff0\u56fe\u7684 \u5de6\u5b50\u6811\u9ad8\u5ea6\u4e3a2\uff0c\u53f3\u5b50\u6811\u9ad8\u5ea6\u4e3a4\uff0c\u6240\u4ee5\u5b83\u7684\u6839\u8282\u70b9\u9ad8\u5ea6\u5dee\uff08\u5e73\u8861\u56e0\u5b50\uff09\u4e3a <code>|2-4| = 2<\/code><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/SLY7PBUL22E9R9EG_7.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"665\" height=\"464\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/SLY7PBUL22E9R9EG_7.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1206\"  sizes=\"auto, (max-width: 665px) 100vw, 665px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u8ff0\u56fe\u7684 \u5de6\u5b50\u6811\u9ad8\u5ea6\u4e3a3\uff0c\u53f3\u5b50\u6811\u9ad8\u5ea6\u4e3a3\uff0c\u6240\u4ee5\u5b83\u7684\u6839\u8282\u70b9\u9ad8\u5ea6\u5dee\uff08\u5e73\u8861\u56e0\u5b50\uff09\u4e3a <code>|3-3| = 0<\/code><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u56db\u79cd\u57fa\u7840\u65cb\u8f6c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">AVL\u6811\u4f7f\u7528\u4e86\u56db\u79cd\u65b9\u6cd5\u52a8\u6001\u5e73\u8861\u4e8c\u53c9\u6811\u6811\uff0c\u5176\u4e2dLL\u578b\u548cRR\u578b\u662f\u57fa\u7840\u65cb\u8f6c\u7c7b\u578b\uff0cLR\u578b\u4e0eRL\u578b\u5219\u662f\u5148\u53d8\u6362\u4e3aLL\u578b\u6216RR\u578b\u7136\u540e\u5904\u7406\uff0c\u5b83\u4eec\u76f8\u5bf9\u4e8e\u57fa\u7840\u578b\u66f4\u4e3a\u590d\u6742\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u56db\u79cd\u65cb\u8f6c\u7c7b\u578b\u7684\u5212\u5206\u4f9d\u636e\u6bd4\u8f83\u96be\u4ee5\u7406\u89e3\uff0c\u7b3c\u7edf\u7684\u8bf4\u662f\u5f15\u8d77AVL\u6811\u5931\u8861\u7684\u54ea\u4e2a\u5b50\u6811\u7684\u54ea\u4e2a\u5b69\u5b50\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u8fd9\u4e4b\u524d\uff0c\u9996\u5148\u8981\u660e\u767d\u4e00\u4e2a\u6982\u5ff5\u2014\u2014\u4ec0\u4e48\u662f\u9996\u4e2a\u5931\u8861\u70b9\uff0c\u6545\u540d\u601d\u610f\u5c31\u662f\u7531\u4e8e\u63d2\u5165\u4e86\u65b0\u8282\u70b9\uff0c\u4ece\u65b0\u8282\u70b9\u5f80\u6839\u8282\u70b9\u7684\u8def\u7ebf\u4e2d\uff0c\u9996\u4e2a\u5e73\u8861\u56e0\u5b50\u88ab\u6253\u7834\u7684\u8282\u70b9\u5c31\u662f\u9996\u4e2a\u5931\u8861\u70b9\u3002\u6bd4\u5982\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u6279\u6ce8-2024-09-13-113507.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"562\" height=\"426\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u6279\u6ce8-2024-09-13-113507.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1222\"  sizes=\"auto, (max-width: 562px) 100vw, 562px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u5931\u8861\u70b91<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u56fe\u7684\u9996\u4e2a\u5931\u8861\u70b9\u662f<code>10<\/code><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u6279\u6ce8-2024-09-13-113834.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"697\" height=\"544\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u6279\u6ce8-2024-09-13-113834.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1223\"  sizes=\"auto, (max-width: 697px) 100vw, 697px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u5931\u8861\u70b92<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u56fe\u7684\u9996\u4e2a\u5931\u8861\u70b9\u662f<code>5<\/code><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u56db\u79cd\u64cd\u4f5c\u90fd\u662f\u4ee5\u9996\u4e2a\u5931\u8861\u70b9\u4e3a\u57fa\u51c6\uff0c\u6839\u636e\u4e0d\u540c\u60c5\u51b5\u8fdb\u884c\u4e0d\u540c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u63a5\u4e0b\u6765\u5c55\u5f00\u8bb2\u8bb2\u5982\u4f55\u64cd\u4f5c\u4ee5\u53ca\u5982\u4f55\u6839\u636e\u5931\u8861\u70b9\u5224\u65ad\u91c7\u53d6\u54ea\u79cd\u65cb\u8f6c\u64cd\u4f5c\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">LL\u578b<strong>\uff08\u5355\u53f3\u65cb\uff09<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">LL\u578b\u7684\u7279\u70b9\u662f\uff1a\u6dfb\u52a0\u8282\u70b9\u7684\u4e8b\u4ef6\u53d1\u751f\u5728\u9996\u4e2a\u5931\u8861\u8282\u70b9\u7684\u5de6\u5b69\u5b50\u7684\u5de6\u5b50\u6811\u4e0a\uff0c\u4e5f\u5c31\u662f<code>\u5de6(left)-\u5de6(left)\u578b<\/code>\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u6279\u6ce8-2024-09-13-113507.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"562\" height=\"426\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u6279\u6ce8-2024-09-13-113507.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1222\"  sizes=\"auto, (max-width: 562px) 100vw, 562px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-LL\u578b1<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u6279\u6ce8-2024-09-13-114627.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"561\" height=\"457\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u6279\u6ce8-2024-09-13-114627.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1224\"  sizes=\"auto, (max-width: 561px) 100vw, 561px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-LL\u578b2<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u8ff0\u4e24\u4e2a\u56fe\u90fd\u662f\u5f88\u76f4\u89c2\u7684\u5c55\u73b0\u51fa\u5178\u578b\u7684\u4f8b\u5b50\uff0c\u5bf9\u4e8e\u8282\u70b9<code>7<\/code>\u800c\u8a00\uff0c\u4e0d\u7ba1\u662f\u8282\u70b9<code>6<\/code>\u8fd8\u662f\u8282\u70b9<code>3<\/code>\uff0c\u90fd\u662f\u63d2\u5165\u5728\u5b83\u7684\u5de6\u5b50\u6811\u4e0a\uff0c\u800c<code>7<\/code>\u53c8\u662f<code>10<\/code>\u7684\u5de6\u5b69\u5b50\uff0c\u6240\u4ee5\u8fd9\u662f<code>LL<\/code>\u578b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6309\u7167AVL\u6811\u7684\u89c4\u5219\uff0c\u8fd9\u4e2a\u6811\u5df2\u7ecf\u4e0d\u5e73\u8861\u4e86\u3002\u5b83\u4e0d\u5e73\u8861\u7684\u539f\u56e0\u5728\u4e8e\u5de6\u5b50\u6811\u51fa\u73b0\u4e86\u65b0\u7684\u8282\u70b9\u5bfc\u81f4\u6df1\u5ea6\u52a0\u5927\uff0c\u90a3\u4e48\u6309\u7167\u4e00\u4e2a\u5e38\u89c4\u601d\u8def\u6765\u8bf4\uff0c\u5c31\u50cf\u662f\u4e00\u6746\u5929\u5e73\uff0c\u79e4\u7684\u4e1c\u897f\u53d8\u91cd\u4e86\uff0c\u90a3\u4e48\u9700\u8981\u5f80\u53f3\u8fb9\u52a0\u70b9\u781d\u7801\uff0c\u4ee5\u56fe-LL\u578b2\u4e3a\u4f8b\uff0c\u539f\u672c\u7684\u6839\u8282\u70b9\u662f<code>10<\/code>\uff0c\u90a3\u4e48\u6211\u5c06\u6839\u8282\u70b9\u65b0\u9009\u4e3a<code>7<\/code>\uff0c\u90a3\u4e48\u8fd9\u4e2a\u5929\u5e73\u7684\u53f3\u8fb9\u5c31\u6709<code>2<\/code>\u7684\u6df1\u5ea6\uff0c\u4f46\u662f\u6811\u548c\u5929\u5e73\u4e0d\u540c\u7684\u662f\uff0c\u603b\u8282\u70b9\u6570\u662f\u56fa\u5b9a\u7684\uff0c\u5982\u679c\u53f3\u8fb9\u591a\u90a3\u4e48\u5de6\u8fb9\u5c31\u8981\u5c11\uff0c\u6240\u4ee5\u5de6\u8fb9\u7684\u6df1\u5ea6\u5c31\u8981\u964d\u4e00\u4e2a\uff0c\u6700\u540e\u5f62\u6210\u5e73\u8861\u56e0\u5b50\u4e3a<code>0<\/code>\u7684AVL\u6811\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e00\u4e2a\u6734\u7d20\u7684\u601d\u8def\u76f8\u540c\u4e86\u65cb\u8f6c\u7684\u903b\u8f91\u540e\uff0c\u63a5\u4e0b\u6765\u8981\u5904\u7406\u7ec6\u679d\u672b\u8282\u3002\u524d\u9762\u7684\u601d\u8def\u662f\u8ba97\u4f5c\u4e3a\u65b0\u7684\u6839\u8282\u70b9\uff0c\u90a3\u4e48\u5c31\u9700\u8981\u6539\u53d8\u6811\u7684\u903b\u8f91\u4e86\uff0c\u5982\u679c\u76f4\u63a5\u5c067\u7684\u53f3\u5b69\u5b50\u6307\u9488\u6307\u541110\u90a3\u4e48\u4f1a\u548c\u539f\u6765\u76848\u8282\u70b9\u51b2\u7a81\uff0c\u90a3\u4e48\u8be5\u5982\u4f55\u89e3\u51b3\u5462\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u7684\u601d\u8def\u662f\u7c7b\u4f3c\u7684\uff0c\u9996\u5148\u5982\u679c7\u4f5c\u4e3a\u6839\u8282\u70b9\uff0c\u90a3\u4e4810\u5c31\u4e00\u5b9a\u662f7\u7684\u53f3\u5b50\u6811\uff0c\u800c7\u539f\u672c\u7684\u53f3\u5b50\u6811\u4e00\u5b9a\u5c0f\u4e8e10\uff0c10\u5931\u53bb\u6839\u8282\u70b9\u540e\u5b83\u7684\u5de6\u5b69\u5b50\u8282\u70b9\u4e00\u5b9a\u662f\u7a7a\u51fa\u6765\u7684\uff0c\u6700\u7ec8\u5c31\u53ef\u4ee5\u5f62\u6210\u4e00\u4e2a\u903b\u8f91\uff1a<mark style=\"background-color:#f78da7\" class=\"has-inline-color\">\u5931\u8861\u70b9\u7684\u5de6\u5b69\u5b50\u7684\u53f3\u5b50\u6811\u53d8\u6210\u5931\u8861\u70b9\u7684\u5de6\u5b50\u6811\uff0c\u5931\u8861\u70b9\u6210\u4e3a\u539f\u5de6\u5b69\u5b50\u7684\u53f3\u5b69\u5b50\u3002<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5177\u4f53\u65cb\u8f6c\u6d41\u7a0b\u5982\u4e0b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/3c39a9a6f0fca29e4af75e58636654ce-474x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"474\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/3c39a9a6f0fca29e4af75e58636654ce-474x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1227\"  sizes=\"auto, (max-width: 474px) 100vw, 474px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-LL\u578b\u65cb\u8f6c\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u88ab\u79f0\u4e3a\u5355\u53f3\u65cb\uff0c\u662f\u56e0\u4e3a\u65cb\u8f6c\u64cd\u4f5c\u53d1\u751f\u5728\u5931\u8861\u70b9\u7684\u53f3\u8fb9\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">RR\u578b<strong>\uff08\u5355\u5de6\u65cb\uff09<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">RR\u578b\u7684\u7279\u70b9\u662f\uff1a\u6dfb\u52a0\u8282\u70b9\u7684\u4e8b\u4ef6\u53d1\u751f\u5728\u9996\u4e2a\u5931\u8861\u8282\u70b9\u7684\u53f3\u5b69\u5b50\u7684\u53f3\u5b50\u6811\u4e0a\uff0c\u4e5f\u5c31\u662f<code>\u53f3(right)-\u53f3(right)\u578b<\/code>\u3002\u4ee5\u4e0b\u662f\u5177\u6709\u4ee3\u8868\u6027\u7684\u793a\u4f8b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/a0a871ea-5ee6-4b20-8628-3bdcb06360ad.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"828\" height=\"693\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/a0a871ea-5ee6-4b20-8628-3bdcb06360ad.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1232\"  sizes=\"auto, (max-width: 828px) 100vw, 828px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-RR\u578b1<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/dfcd6a49-5db9-4ffa-9fe3-8fcceb1ccd22.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"697\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/dfcd6a49-5db9-4ffa-9fe3-8fcceb1ccd22.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1233\"  sizes=\"auto, (max-width: 859px) 100vw, 859px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-RR\u578b2<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u548cLL\u578b\u7c7b\u4f3c\uff0cRR\u578b\u7684\u64cd\u4f5c\u903b\u8f91\u6709\u4e00\u70b9\u70b9\u4e0d\u540c\uff0c\u5b83\u7684\u903b\u8f91\u662f<code>10<\/code>\u7684\u53f3\u5b69\u5b50\u6307\u5411<code>12<\/code>\uff0c\u7136\u540e<code>15<\/code>\u7684\u5de6\u5b69\u5b50\u6307\u5411<code>10<\/code>\uff0c\u7136\u540e<code>15<\/code>\u5c31\u6210\u4e3a\u4e86\u65b0\u7684\u6839\u8282\u70b9\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/H_YAR_WKNGOI1Y39__3-438x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/H_YAR_WKNGOI1Y39__3-438x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1234\"  sizes=\"auto, (max-width: 438px) 100vw, 438px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-RR\u578b\u65cb\u8f6c\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u4e3a\u65cb\u8f6c\u64cd\u4f5c\u53d1\u751f\u5728\u5931\u8861\u70b9\u7684\u5de6\u8fb9\u6240\u4ee5\u662f\u5de6\u65cb\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">LR\u578b<strong>\uff08\u53cc\u65cb\u8f6c\uff1a\u5148\u5de6\u540e\u53f3\uff09<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">LR\u578b\uff08<code>Left-Right<\/code>\uff09\u662f\u4e0e\u5176\u8bf4\u662f\u4e00\u79cd\u65cb\u8f6c\u7c7b\u578b\uff0c\u4e0d\u5982\u8bf4\u662f\u4e00\u79cd\u590d\u5408\u7c7b\u578b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/DGPQQU_7GQOE407JQ.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"589\" height=\"596\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/DGPQQU_7GQOE407JQ.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1237\"  sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-LR\u578b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5LL\u578b\u6765\u8bf4\uff0c\u63d2\u5165\u8282\u70b9\u5728\u5de6\u5b69\u5b50\u7684\u5de6\u5b50\u6811\u4e0a\uff0c\u90a3\u4e48\u53ef\u4ee5\u5c06\u5de6\u5b69\u5b50\u63d0\u9ad8\u53d8\u6210\u6839\u8282\u70b9\uff0c\u4f46\u662f\u51fa\u73b0\u4e86\u4e00\u4e2a\u95ee\u9898\uff0c\u539f\u6765\u7684\u5de6\u5b69\u5b50\u7684\u53f3\u5b50\u6811\u9700\u8981\u548c\u539f\u6839\u8282\u70b9\u5408\u5e76\u3002\u5982\u679c\u63d2\u5165\u8282\u70b9\u662f\u5de6\u5b69\u5b50\u7684\u53f3\u5b50\u6811\u5c31\u4f1a\u628a\u65b0\u63d2\u5165\u5230\u8282\u70b9\u79fb\u52a8\u5230\u65b0\u6811\u4e0a\uff0c\u8131\u79bb\u4e86\u6b63\u5728\u5e73\u8861\u8c03\u6574\u7684\u8fd9\u4e00\u68f5\u5b50\u6811\u7684\u8303\u56f4\uff0c\u5c31\u5931\u53bb\u4e86\u610f\u4e49\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6700\u7ec8\u7684\u89e3\u51b3\u65b9\u6cd5\u662f\u5148\u5de6\u65cb\u8282\u70b9<code>5<\/code>\uff0c\u7136\u540e\u518d\u53f3\u65cb\u8282\u70b9<code>10<\/code> \u3002\u4e5f\u5c31\u662f\u5c06\u8fd9\u68f5\u6811\u7ecf\u8fc7\u7b2c\u4e00\u6b21\u65cb\u8f6c\u53d8\u6210LL\u578b\uff0c\u7136\u540e\u518d\u5904\u7406LL\u578b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/5DV_2IAKBOMWI_W7VQM-449x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"449\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/5DV_2IAKBOMWI_W7VQM-449x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1238\"  sizes=\"auto, (max-width: 449px) 100vw, 449px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-LR\u578b\u65cb\u8f6c\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u800cLR\u578b\u56e0\u4e3a\u7ecf\u8fc7\u5148\u5de6\u518d\u53f3\u7684\u65cb\u8f6c\u8fc7\u7a0b\uff0c\u6545\u800c\u88ab\u6210\u4e3aLR\u578b\u53cc\u65cb<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">RL\u578b<strong>\uff08\u53cc\u65cb\u8f6c\uff1a\u5148\u53f3\u540e\u5de6\uff09<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">RL\u578b\uff08Right-Left\uff09\u548cLR\u578b\u7684\u601d\u60f3\u7c7b\u4f3c\uff0c\u4e5f\u662f\u7ec4\u5408\u65cb\u8f6c\uff0c\u4e0d\u8fc7\u662f\u65b9\u5411\u76f8\u53cd\u7f62\u4e86\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/P0JNUNWB6YR8PU7Z_W9Q.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"635\" height=\"560\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/P0JNUNWB6YR8PU7Z_W9Q.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1240\"  sizes=\"auto, (max-width: 635px) 100vw, 635px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-RL\u578b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd8\u662f\u4e00\u6837\u7684\u601d\u8def\uff0c\u5148\u53f3\u65cb\u8f6c<code>15<\/code>\uff0c\u7136\u540e\u5de6\u65cb<code>10<\/code><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/Y_V2_KTDDIOCLK3W7V-455x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"455\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/Y_V2_KTDDIOCLK3W7V-455x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1239\"  sizes=\"auto, (max-width: 455px) 100vw, 455px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-RL\u578b\u65cb\u8f6c\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u63d2\u5165<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ecb\u7ecd\u4e86\u56db\u79cd\u65cb\u8f6c\u4e4b\u540e\uff0c\u5c31\u9700\u8981\u5c06\u5176\u8f6c\u6362\u4e3a\u4ee3\u7801\uff0c\u4f9d\u65e7\u662f\u5229\u7528\u5176\u9012\u5f52\u6027\u3002\u5148\u5c06\u6574\u4e2a\u63d2\u5165\u8fc7\u7a0b\u5206\u4e3a\u51e0\u4e2a\u90e8\u5206\uff0c<code>\u67e5\u627e\u5408\u9002\u70b9\u2014\u2014\u65cb\u8f6c\u8c03\u6574<\/code>\u3002\u5728\u65cb\u8f6c\u8c03\u6574\u8fd9\u4e2a\u90e8\u5206\u9700\u8981\u8be6\u7ec6\u5206\u6790\u8fc7\u7a0b\uff0c\u5927\u81f4\u4e3a<code>\u5224\u65ad\u5e73\u8861\u56e0\u5b50\u2014\u2014\u5224\u65ad\u65cb\u8f6c\u7c7b\u578b\u2014\u2014\u65cb\u8f6c<\/code>\u3002\u4e0d\u8fc7\u5728\u65cb\u8f6c\u7684\u8fc7\u7a0b\u4e2d\u8fd8\u9700\u8981\u52a8\u6001\u66f4\u65b0\u8282\u70b9\u7684\u9ad8\u5ea6\uff0c\u4e3a\u4e86\u7b80\u5316\u4ee3\u7801\u540c\u65f6\u63d0\u9ad8\u4ee3\u7801\u6267\u884c\u6548\u7387\uff0c\u901a\u5e38\u60c5\u51b5\u4e0b\u4f1a\u5c06\u5229\u7528\u9012\u5f52\u7684\u7279\u6027\uff0c\u9012\u5f52\u5206\u4e3a\u4e24\u4e2a\u8fc7\u7a0b\u2014\u2014\u63a8\u8fdb\u548c\u56de\u6eaf\uff0c\u63a8\u8fdb\u88ab\u7528\u6765\u662f\u6765\u67e5\u627e\u63d2\u5165\u4f4d\u7f6e\uff0c\u800c\u56de\u6eaf\u5219\u662f\u8c03\u6574\u7684\u4e3b\u8981\u6218\u573a\uff0c\u6bcf\u6b21\u56de\u6eaf\u610f\u5473\u7740\u4e0b\u4e00\u5c42\u7684\u6811\u5df2\u7ecf\u5904\u7406\u5b8c\u6210\uff0c\u90a3\u4e48\u5c31\u9700\u8981\u5728\u8fd9\u6b21\u56de\u6eaf\u4e2d\u66f4\u65b0\u8282\u70b9\u9ad8\u5ea6\uff0c\u4ee5\u53ca\u5224\u65ad\u5e73\u8861\u56e0\u5b50\uff0c\u5982\u679c\u5e73\u8861\u56e0\u5b50\u51fa\u73b0\u4e86\u5931\u8861\uff0c\u90a3\u4e48\u540c\u65f6\u9700\u8981\u5728\u6b64\u6b21\u56de\u6eaf\u4e2d\u8c03\u6574\u5e73\u8861\uff0c\u8c03\u6574\u5b8c\u6210\u540e\u518d\u6b21\u8fdb\u5165\u4e0b\u4e00\u8f6e\u56de\u6eaf\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">\u4ee3\u7801\u793a\u4f8b<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u57fa\u7840\u5b9a\u4e49\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include &lt;stdio.h&gt;\n#include &lt;malloc.h&gt;\n\/\/\u6811\u7684\u5b9a\u4e49\ntypedef struct Node\n{\n    int data;\/\/\u5b58\u50a8\u6570\u636e\n    int height;\/\/\u8bb0\u5f55\u5f53\u524d\u8282\u70b9\u7684\u9ad8\u5ea6\n    struct Node* left;\n    struct Node* right;\n}Node;\n\n\/\/\u521b\u5efa\u8282\u70b9\nNode* createNode(int data){\n    Node* temp = (Node*)malloc(sizeof(Node));\n    temp-&gt;data = data;\n    temp-&gt;left = NULL;\n    temp-&gt;right = NULL;\n    temp-&gt;height = 1;\n    return temp;\n}\n\/\/\u83b7\u53d6\u6307\u5b9a\u8282\u70b9\u7684\u9ad8\u5ea6\nint getHeight(Node* root){\n    return root ? root-&gt;height : 0;\n}\n\/\/\u83b7\u53d6\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\nint getBalaceFactor(Node* root){\n    return getHeight(root-&gt;left) - getHeight(root-&gt;right);\n}\n\/\/\u83b7\u53d6\u4e24\u4e2a\u503c\u5f97\u6700\u5927\u9ad8\u5ea6\nint max(int d1,int d2){\n    return d1&gt;d2 ? d1 : d2;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u57fa\u7840\u65cb\u8f6c\u2014\u2014LL\u578b\u548cRR\u578b\u65cb\u8f6c<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u5904\u7406\u65cb\u8f6c\uff08\u53f3\u65cbLL\u578b\uff09\nNode* rotateRight(Node* root){\n    \/\/\u5c06\u5de6\u5b69\u5b50\u4f5c\u4e3a\u65b0\u6839\u8282\u70b9\n    Node* newroot = root-&gt;left;\n    \/\/\u539f\u6839\u8282\u70b9\u4e0b\u6c89\u4e3anewroot\u7684\u53f3\u5b69\u5b50\n    root-&gt;left = newroot-&gt;right;\n    newroot-&gt;right = root;\n    \/\/\u91cd\u65b0\u8bb0\u5f55\u8fd9\u4e24\u4e2a\u8282\u70b9\u4e2d\u7684\u9ad8\u5ea6\n    root-&gt;height = max(getHeight(root-&gt;left),getHeight(root-&gt;right))+1;\n    newroot-&gt;height = max(getHeight(newroot-&gt;left),getHeight(newroot-&gt;right))+1;\n    return newroot;\n}\n\/\/\u5904\u7406\u65cb\u8f6c\uff08\u5de6\u65cbRR\u578b\uff09\nNode* rotateLeft(Node* root){\n    \/\/\u5c06\u53f3\u5b69\u5b50\u4f5c\u4e3a\u65b0\u6839\u8282\u70b9\n    Node* newroot = root-&gt;right;\n    \/\/\u539f\u6839\u8282\u70b9\u4e0b\u6c89\u4e3anewroot\u7684\u5de6\u5b69\u5b50\n    root-&gt;right = newroot-&gt;left;\n    newroot-&gt;left = root;\n    \/\/\u91cd\u65b0\u8bb0\u5f55\u8fd9\u4e24\u4e2a\u8282\u70b9\u4e2d\u7684\u9ad8\u5ea6\n    root-&gt;height = max(getHeight(root-&gt;left),getHeight(root-&gt;right))+1;\n    newroot-&gt;height = max(getHeight(newroot-&gt;left),getHeight(newroot-&gt;right))+1;\n    return newroot;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6838\u5fc3\u63d2\u5165\u4ee3\u7801<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Node* insert(Node* root,int data){\n    if(root == NULL){\n        root = createNode(data);\n        return root;\n    }\n\n    \/\/\u8f93\u5165\u7684\u503c\u5c0f\u4e8e\u6839\u8282\u70b9\n    if(data &lt; root-&gt;data){\n        root-&gt;left = insert(root-&gt;left,data);\/\/\u63d2\u5165\u5de6\u5b50\u6811\n    }\n    \/\/\u8f93\u5165\u7684\u503c\u5982\u679c\u5927\u4e8e\u6839\u8282\u70b9\n    else if(data &gt; root-&gt;data){\n        root-&gt;right = insert(root-&gt;right,data);\/\/\u63d2\u5165\u53f3\u5b50\u6811\n    }\n    \/\/\u5982\u679c\u503c\u76f8\u7b49\n    else{\n        return root;\n    }\n \n    \/\/\u7531\u4e8e\u5b50\u6811\u7684\u9ad8\u5ea6\u53d1\u751f\u4e86\u53d8\u5316\uff0c\u6240\u4ee5\u9700\u8981\u66f4\u65b0\u5f53\u524d\u8282\u70b9\u7684\u9ad8\u5ea6\n    root-&gt;height = max(getHeight(root-&gt;left),getHeight(root-&gt;right))+1;\n\n    \/\/\u83b7\u53d6\u5e73\u8861\u56e0\u5b50\n    int bf = getBalaceFactor(root);\n\n    \/\/\u5de6\u5b69\u5b50\u63d2\u5165\n    if(bf &gt; 1){\n        \/\/\u83b7\u53d6\u5de6\u5b69\u5b50\u7684\u5e73\u8861\u56e0\u5b50\n        int Lbf = getBalaceFactor(root-&gt;left);\n        \/\/\u5de6\u5b50\u6811\u63d2\u5165\n        if(Lbf &gt; 0){\/\/LL\u578b\n            root = rotateRight(root);\n        }\n        \/\/\u53f3\u5b50\u6811\u63d2\u5165\n        else{\/\/LR\u578b\n            \/\/\u5148\u5de6\u65cb\u5de6\u5b50\u6811\n            root-&gt;left = rotateLeft(root-&gt;left);\n            \/\/\u518d\u53f3\u65cb\u6574\u4e2a\u6811\n            root = rotateRight(root);\n        }\n    }\n    \/\/\u53f3\u5b69\u5b50\u63d2\u5165\n    else if(bf &lt; -1){\n        \/\/\u83b7\u53d6\u53f3\u5b69\u5b50\u7684\u5e73\u8861\u56e0\u5b50\n        int Rbf = getBalaceFactor(root-&gt;right);\n        \/\/\u5de6\u5b50\u6811\u63d2\u5165\n        if(Rbf &gt; 0){\/\/RL\u578b\n            \/\/\u5148\u53f3\u65cb\u53f3\u5b50\u6811\n            root-&gt;right = rotateRight(root-&gt;right);\n            \/\/\u518d\u5de6\u65cb\u6574\u4e2a\u6811\n            root = rotateLeft(root);\n        }\n        \/\/\u53f3\u5b50\u6811\u63d2\u5165\n        else{\/\/RR\u578b\n            root = rotateLeft(root);\n        }\n    }\n    return root;\n}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u5220\u9664<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5220\u9664\u662fAVL\u4e2d\u6700\u590d\u6742\u7684\u64cd\u4f5c\uff0c\u5b83\u76f8\u5f53\u4e8e\u5c06\u6574\u4e2aAVL\u7684\u64cd\u4f5c\u7ed3\u5408\u3002\u4ed4\u7ec6\u950a\u4e00\u950a\u601d\u8def\u4f1a\u53d1\u73b0\u4e00\u4e2a\u7279\u70b9\uff0c\u4e4b\u524d\u8bb2\u8fc7\u666e\u901a\u7684\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5220\u9664\uff0c\u53ef\u4ee5\u6839\u636e\u5ea6\u5206\u4e3a\u4e09\u7c7b\u60c5\u51b5\u5904\u7406\uff0cAVL\u4f5c\u4e3a\u4f18\u5316\u7248\u672c\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u4e5f\u9075\u5faa\u8fd9\u4e2a\u5904\u7406\u65b9\u5f0f\uff0c\u4f46\u662f\u8fd8\u6709\u589e\u52a0\u4e00\u9879\u7ef4\u6301\u6811\u5e73\u8861\u7684\u64cd\u4f5c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ef4\u6301\u6811\u7684\u5e73\u8861\u548c\u63d2\u5165\u5230\u64cd\u4f5c\u7c7b\u4f3c\uff0c\u4e5f\u662f\u5728\u9012\u5f52\u9636\u6bb5\u901a\u8fc7\u5e73\u8861\u56e0\u5b50\u4f7f\u7528LL\u3001RR\u3001LR\u3001RL\u56db\u79cd\u7c7b\u578b\u8fdb\u884c\u65cb\u8f6c\uff0c\u4e0d\u8fc7\u9700\u8981\u8865\u5145\u4e00\u70b9\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/NO3M78T23QG50UH_J.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"752\" height=\"759\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/NO3M78T23QG50UH_J.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1241\"  sizes=\"auto, (max-width: 752px) 100vw, 752px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u7279\u6b8a\u60c5\u51b5<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e24\u79cd\u60c5\u51b5\u6216\u8005\u8bf4\u662f\u4e00\u79cd\u7c7b\u578b\uff0c\u5b83\u5c5e\u4e8e\u5e73\u8861\u56e0\u5b50\u51fa\u73b0\u4e86\u5931\u8861\uff0c\u4f46\u662f\u56db\u79cd\u65cb\u8f6c\u7c7b\u578b\u4e0d\u4f1a\u51fa\u73b0\u8fd9\u79cd\u60c5\u51b5\u3002\u56e0\u4e3a\u5728\u5b50\u6811\u5f62\u6210\u5206\u652f\u4e4b\u524d\uff0c\u6811\u5c31\u5df2\u7ecf\u8c03\u6574\u4e86\u3002\u4f46\u662f\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e24\u79cd\u60c5\u51b5\u4f1a\u5728\u5220\u9664\u4e2d\u7ecf\u5e38\u51fa\u73b0\uff0c\u4e0d\u8fc7\u597d\u5728\u5b83\u4eec\u53ef\u4ee5\u4f7f\u7528\u6700\u57fa\u7840\u7684\u4e24\u79cd\u65cb\u8f6c\u89e3\u51b3\u3002\u5de6\u8fb9\u7684\u56fe\u53ef\u4ee5\u4f7f\u7528LL\u578b\uff0c\u53f3\u8fb9\u7684\u56fe\u53ef\u4ee5\u4f7f\u7528RR\u578b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5220\u9664\u903b\u8f91\u4e5f\u5229\u7528\u4e86\u6811\u7684\u9012\u5f52\u6027\uff0c\u5728\u63a8\u8fdb\u8fc7\u7a0b\u8d1f\u8d23\u5bfb\u627e\u5220\u9664\u8282\u70b9\uff0c\u7136\u540e\u5728\u627e\u5230\u540e\u8fdb\u884c\u5220\u9664\u64cd\u4f5c\u3002\u800c\u56de\u6eaf\u7684\u8fc7\u7a0b\u5219\u662f\u8d1f\u8d23\u8fdb\u884c\u8c03\u6574\uff0c\u5305\u62ec\u9ad8\u5ea6\u91cd\u7f6e\u548c\u8282\u70b9\u65cb\u8f6c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee3\u7801\u793a\u4f8b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Node* NodeDelete(Node* root, int data) {\n    \/\/\u6811\u7684\u7ec8\u70b9\n    if(root == NULL) return NULL;\n\n    \/*\u5220\u9664\u8282\u70b9*\/\n    \/\/\u5982\u679c\u5c0f\u4e8e\u8282\u70b9\n    if(data &lt; root-&gt;data){\n        root-&gt;left = NodeDelete(root-&gt;left,data);\n    }\n    \/\/\u5982\u679c\u5927\u4e8e\u8282\u70b9\n    else if(data &gt; root-&gt;data){\n        root-&gt;right = NodeDelete(root-&gt;right,data);\n    }\n    \/\/\u5982\u679c\u7b49\u4e8e\u8282\u70b9\n    else{\n        \/*\u4e09\u79cd\u5220\u9664\u7c7b\u578b*\/\n        \/\/\u5ea6\u4e3a0\u548c1\u7684\u60c5\u51b5\n        if( (root-&gt;left == NULL) || (root-&gt;right == NULL) ){\n            \/\/\u83b7\u53d6\u4e00\u4e2a\u5b50\u8282\u70b9\u7684\u6307\u9488\n            Node* temp = root-&gt;left ? root-&gt;left : root-&gt;right;\n            free(root);\n            return temp;\n        }\n        \/\/\u5904\u7406\u5ea6\u4e3a2\u7684\u70b9\n        else{\n            \/\/\u83b7\u53d6\u53f3\u5b50\u6811\u503c\u6700\u5c0f\u7684\u8282\u70b9\n            Node* temp = root-&gt;right;\n            while(temp-&gt;left != NULL){\n                temp = temp-&gt;left;\n            }\n            \/\/\u5c06\u8fd9\u4e2a\u8282\u70b9\u7684\u503c\u66ff\u6362\u5230\u6839\u8282\u70b9\u4e0a\n            root-&gt;data = temp-&gt;data;\n            \/\/\u4ece\u53f3\u5b50\u6811\u4e2d\u5220\u9664\u8fd9\u4e2a\u8282\u70b9\n            root-&gt;right = NodeDelete(root-&gt;right,temp-&gt;data);\n            return root;\n        }\n    }\n\n    \/*\u6811\u7684\u8c03\u6574*\/\n    \/\/\u7531\u4e8e\u5b50\u8282\u70b9\u53d1\u751f\u4e86\u6539\u53d8\uff0c\u6240\u4ee5\u66f4\u65b0\u5f53\u524d\u8282\u70b9\u7684\u9ad8\u5ea6\n    root-&gt;height = max(getHeight(root-&gt;left),getHeight(root-&gt;right))+1;\n    \/\/\u68c0\u67e5\u5e73\u8861\u56e0\u5b50\u662f\u5426\u51fa\u73b0\u4e86\u5931\u8861\n    int bf = getBalaceFactor(root);\n    \/\/LL\u578b\u5224\u5b9a\uff0c\u4ee5\u53ca\u7279\u6b8a\u60c5\u51b5\uff08\u5de6\uff09\n    if(bf &gt; 1 &amp;&amp; getBalaceFactor(root-&gt;left) &gt;= 0){\n        root = rotateRight(root);\n    }\n    \/\/LR\u578b\u5224\u5b9a\n    else if(bf &gt; 1 &amp;&amp; getBalaceFactor(root-&gt;left) &lt; 0){\n        root-&gt;left = rotateLeft(root-&gt;left);\n        root = rotateRight(root);\n    }\n    \/\/RR\u578b\u5224\u5b9a\uff0c\u4ee5\u53ca\u7279\u6b8a\u60c5\u51b5\uff08\u53f3\uff09\n    else if(bf &lt; -1 &amp;&amp; getBalaceFactor(root-&gt;right) &lt;= 0){\n        root = rotateLeft(root);\n    }\n    \/\/RL\u578b\u5224\u5b9a\n    else if(bf &lt; -1 &amp;&amp; getBalaceFactor(root-&gt;right) &gt; 0){\n        root-&gt;right = rotateRight(root-&gt;right);\n        root = rotateLeft(root);\n    }\n    return root;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc\u503c\u5f97\u6ce8\u610f\u70b9\u662f\uff0c\u5220\u9664\u4ee3\u7801\u5904\u7406\u5ea6\u4e3a2\u7684\u70b9\u4f7f\u7528\u4e86\u8282\u70b9\u66ff\u6362\u7684\u601d\u60f3\uff0c\u548c\u4e4b\u524d\u7684\u4e00\u8fb9\u5b50\u6811\u5ac1\u63a5\u5230\u53e6\u5916\u4e00\u68f5\u5b50\u6811\u6700\u5c0f\u6216\u6700\u5927\u503c\u65b9\u5411\u7684\u65b9\u6848\u4e0d\u540c\u3002\u5ac1\u63a5\u65b9\u6848\u4f1a\u5927\u9762\u79ef\u6539\u53d8\u6811\u7684\u7ed3\u6784\uff0c\u800c\u66ff\u6362\u65b9\u6848\u5f88\u5c11\u6539\u53d8\u7ed3\u6784\uff0c\u5bf9\u4e8e\u4ee3\u7801\u7684\u5b9e\u73b0\u4f1a\u5bb9\u6613\u5f88\u591a\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee3\u7801\u4e2d\u66ff\u6362\u5220\u9664\u91c7\u53d6\u7684\u662f\u5c06\u53f3\u5b50\u6811\u6700\u5c0f\u8282\u70b9\u548c\u6839\u8282\u70b9\u66ff\u6362\uff0c\u7136\u540e\u526a\u5207\u6389\u5df2\u7ecf\u88ab\u66ff\u6362\u5230\u679d\u53f6\u4e0a\u7684\u539f\u6839\u8282\u70b9\u3002\u8fd9\u4e2a\u53d8\u52a8\u6700\u591a\u53ea\u53ef\u80fd\u53d1\u751f\u4e00\u5c42\u6811\u7684\u53d8\u52a8\uff0c\u6240\u4ee5\u8c03\u6574\u5e45\u5ea6\u5c0f\u5f88\u591a\uff0c\u800c\u4e4b\u524d\u7684\u5ac1\u63a5\u65b9\u6848\uff0c\u4f1a\u8ba9\u6574\u68f5\u6811\u5ac1\u63a5\u5230\u4e00\u4e2a\u8282\u70b9\u4e0a\uff0c\u5982\u679c\u6811\u5f88\u5e9e\u5927\uff0c\u90a3\u4e48\u4f1a\u5bfc\u81f4\u51fa\u73b0\u5f88\u7e41\u7410\u7684\u8c03\u6574\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7ea2\u9ed1\u6811<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u4e86\u89e3\u7ea2\u9ed1\u6811\u4e4b\u524d\uff0c\u5df2\u7ecf\u8c08\u8bba\u4e86AVL\u6811\uff0c\u4f46\u662fAVL\u6811\u770b\u4f3c\u4f3c\u4e4e\u5f88\u5b8c\u7f8e\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u4f9d\u65e7\u5b58\u5728\u4e00\u4e2a\u7f3a\u9677\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff08\u6bd4\u5982\u6240\u6709\u6570\u636e\u90fd\u662f\u987a\u5e8f\u63d2\u5165\uff09\uff0cAVL\u6811\u4f1a\u9ad8\u9891\u8c03\u6574\u4ee5\u7ef4\u62a4\u6811\u7684\u7ed3\u6784\uff0c\u4ece\u800c\u5bfc\u81f4\u5927\u91cf\u7684\u65f6\u95f4\u6d6a\u8d39\u5728\u6811\u7684\u7ef4\u62a4\u4e0a\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u4eba\u4eec\u5f00\u59cb\u5bfb\u627e\u53e6\u5916\u4e00\u79cd\u8c03\u6574\u7b56\u7565\uff0c\u4ee5\u5e73\u8861\u67e5\u8be2\u6548\u7387\u548c\u6811\u7684\u7ef4\u62a4\u6548\u7387\u4e4b\u95f4\u627e\u5230\u4e00\u4e2a\u5e73\u8861\u70b9\uff0c\u5728\u8fd9\u4e2a\u5927\u524d\u63d0\u4e0b\u7ea2\u9ed1\u6811\u5e94\u8fd0\u800c\u751f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ea2\u9ed1\u6811\u4e0d\u540c\u4e8eAVL\u6811\uff0c\u5b83\u6ca1\u6709\u8fd1\u4e4e\u4e25\u82db\u7684\u5e73\u8861\u7ed3\u6784\u6761\u4ef6\uff0c\u800c\u662f\u4f7f\u7528\u4e86\u66f4\u52a0\u5bbd\u677e\u7684\u6761\u4ef6\u2014\u2014\u6700\u6df1\u8282\u70b9\u7684\u9ad8\u5ea6\u6700\u9ad8\u4e0d\u80fd\u8d85\u8fc7\u6700\u6d45\u8282\u70b9\u9ad8\u5ea6\u76842\u500d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ea2\u9ed1\u6811\u7684\u7279\u6027\u6709\u56db\u4e2a\uff0c\u4e5f\u88ab\u7b80\u5316\u4e3a\u53e3\u8bc0\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5de6\u6839\u53f3\uff1a<\/strong>\u7531\u4e8e\u7ea2\u9ed1\u6811\u662f\u57fa\u4e8e\u4e8c\u53c9\u641c\u7d22\u6811\u53d1\u5c55\u800c\u6765\uff0c\u6240\u4ee5\u5b83\u6ee1\u8db3\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5de6\u8282\u70b9\u5c0f\u4e8e\u53f3\u8282\u70b9\u7684\u6027\u8d28<\/li>\n\n\n\n<li><strong>\u6839\u53f6\u9ed1\uff1a<\/strong>\u6839\u8282\u70b9\u548c\u53f6\u5b50\u8282\u70b9\u53ea\u80fd\u662f\u9ed1\u8272\uff0c\u8981\u6ce8\u610f\u7684\u662f\uff0c<mark style=\"background-color:#7bdcb5\" class=\"has-inline-color\">\u8fd9\u4e2a\u53f6\u5b50\u8282\u70b9\u6307\u7684\u662f\u7a7a\u8282\u70b9\uff0c\u800c\u4e0d\u662f\u5e38\u89c4\u610f\u4e49\u4e0a\u7684\u5ea6\u4e3a0\u7684\u8282\u70b9\u3002<\/mark><\/li>\n\n\n\n<li><strong>\u4e0d\u7ea2\u7ea2\uff1a<\/strong>\u76f8\u90bb\u7684\u8282\u70b9\u4e4b\u95f4\u4e0d\u80fd\u540c\u65f6\u51fa\u73b0\u4e24\u4e2a\u7ea2\u8272\u8282\u70b9\uff08\u4f46\u662f\u5141\u8bb8\u51fa\u73b0\u4e24\u4e2a\u9ed1\u8272\u8282\u70b9\uff09<\/li>\n\n\n\n<li><strong>\u9ed1\u8def\u540c\uff1a<\/strong>\u4ece\u6839\u8282\u70b9\u51fa\u53d1\u5230\u6bcf\u4e2a\u53f6\u5b50\u8282\u70b9\u4e4b\u95f4\u7ecf\u8fc7\u7684\u9ed1\u8272\u8282\u70b9\u7684\u6570\u91cf\u662f\u76f8\u540c\u7684\u3002<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/KN1RK5CVWGSF7J6PT8I.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"315\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/KN1RK5CVWGSF7J6PT8I.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1256\"  sizes=\"auto, (max-width: 587px) 100vw, 587px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u7ea2\u9ed1\u6811\u793a\u610f\u56fe<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u63d2\u5165<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ea2\u9ed1\u6811\u7684\u63d2\u5165\u601d\u8def\u4e5f\u662f\u4e0eAVL\u6811\u4e00\u81f4\uff0c\u4e3b\u8981\u5206\u4e3a\u4e09\u4e2a\u9636\u6bb5\u2014\u2014\u67e5\u627e\u3001\u63d2\u5165\u3001\u8c03\u6574\u3002\u540c\u65f6\u6700\u91cd\u8981\u6700\u6838\u5fc3\u7684\u4e5f\u662f\u8c03\u6574\u9636\u6bb5\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ea2\u9ed1\u6811\u7684\u8c03\u6574\u7b56\u7565\u4e5f\u662f\u56f4\u7ed5\u7ea2\u9ed1\u6811\u7684\u6027\u8d28\u8bde\u751f\u7684\uff0c\u4e3b\u8981\u6709\u51e0\u79cd\u8c03\u6574\u7b56\u7565\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1\u3001\u9ed8\u8ba4\u63d2\u5165\u7684\u8282\u70b9\u989c\u8272\u4e3a\u7ea2\u8272<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u6b63\u5e38\u60c5\u51b5\u4e0b\uff0c\u9ed8\u8ba4\u63d2\u5165\u8282\u70b9\u662f\u53ef\u4ee5\u4e3a\u7ea2\u8272\u8282\u70b9\u548c\u9ed1\u8272\u8282\u70b9\u7684\uff0c\u4f46\u662f\u7ea2\u8272\u8282\u70b9\u66f4\u4f18\u6240\u4ee5\u666e\u904d\u91c7\u7528\u9ed8\u8ba4\u7ea2\u8272\u8282\u70b9\u63d2\u5165\uff0c\u4ee5\u4e0b\u53ef\u4ee5\u8fdb\u884c\u5206\u6790\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\uff0c\u5982\u679c\u63d2\u5165\u7684\u662f\u9ed1\u8272\u8282\u70b9\uff0c\u90a3\u4e48\u4e00\u5b9a\u4f1a\u8fdd\u53cd\u7ea2\u9ed1\u6811\u7684<strong>\u9ed1\u8def\u540c<\/strong>\u6027\u8d28\uff0c\u63a5\u4e0b\u6765\u5c31\u4e00\u5b9a\u9700\u8981\u8fdb\u884c\u7ea2\u9ed1\u6811\u8c03\u6574\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53cd\u89c2\u63d2\u5165\u7ea2\u8272\u8282\u70b9\uff0c\u5219\u53ef\u80fd\u8fdd\u53cd<strong>\u6839\u53f6\u9ed1<\/strong>\u548c<strong>\u4e0d\u7ea2\u7ea2<\/strong>\u4e24\u4e2a\u6027\u8d28\uff0c\u4f46\u662f\u5f53\u5728\u5ea6\u4e3a0\u7684\u9ed1\u8272\u8282\u70b9\u4e0a\u63d2\u5165\u5230\u65f6\u5019\uff0c\u7ea2\u9ed1\u6811\u4e0d\u9700\u8981\u4efb\u4f55\u8c03\u6574\u3002\u800c\u4e14\u5373\u4fbf\u8fdd\u53cd\u4e86\u6027\u8d28\uff0c\u8c03\u6574\u8d77\u6765\u4e5f\u8981\u6bd4\u8fdd\u53cd<strong>\u9ed1\u8def\u540c<\/strong>\u8fd9\u6837\u6574\u68f5\u6811\u53d8\u52a8\u7684\u8c03\u6574\u65b9\u4fbf\u5f97\u591a\u3002\u6240\u4ee5\u76f8\u6bd4\u4e4b\u4e0b\u9ed8\u8ba4\u7ea2\u8272\u8282\u70b9\u66f4\u52a0\u5408\u9002\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2\u3001\u4e09\u7c7b\u60c5\u51b5\u8c03\u6574\u7ea2\u9ed1\u6811<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u60c5\u51b51\uff1a\u63d2\u5165\u8282\u70b9\u662f\u6839\u8282\u70b9<\/li>\n\n\n\n<li>\u60c5\u51b52\uff1a\u63d2\u5165\u8282\u70b9\u7684\u53d4\u53d4\u662f\u7ea2\u8272\u8282\u70b9<\/li>\n\n\n\n<li>\u60c5\u51b53\uff1a\u63d2\u5165\u8282\u70b9\u7684\u53d4\u53d4\u662f\u9ed1\u8272\u8282\u70b9<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0eAVL\u6811\u5173\u6ce8\u9ad8\u5ea6\u4e0d\u540c\uff0c\u7ea2\u9ed1\u6811\u5f15\u5165\u4e86\u4e00\u4e2a\u91cd\u8981\u7684\u89d2\u8272\u5c31\u662f\u53d4\u53d4\uff0c\u4e5f\u5c31\u662f\u7236\u4eb2\u8282\u70b9\u7684\u5144\u5f1f\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><code>\u60c5\u51b51<\/code>\u5f88\u597d\u89e3\u51b3\uff0c\u53ea\u9700\u8981\u5728\u63d2\u5165\u540e\u5c06\u8282\u70b9\u989c\u8272\u6539\u53d8\u4e3a\u9ed1\u8272\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><code>\u60c5\u51b52<\/code>\u5df2\u7ecf\u5f00\u59cb\u53d8\u5f97\u590d\u6742\u4e86\uff0c\u4f46\u662f\u4e3b\u8981\u8003\u8651\u7684\u662f\u989c\u8272\u7684\u53d8\u5316\u3002\u5f53\u53d1\u73b0\u63d2\u5165\u8282\u70b9\u7684\u989c\u8272\u4e0e\u7236\u4eb2\u8282\u70b9\u8fdd\u53cd\u4e86<strong>\u4e0d\u7ea2\u7ea2<\/strong>\u7279\u6027\uff0c\u90a3\u4e48\u5c31\u9700\u8981\u5c06\u7236\u4eb2\u548c\u53d4\u53d4\u8282\u70b9\u4ee5\u53ca\u7956\u7236\u8282\u70b9\u7684\u989c\u8272\u53cd\u8f6c\uff0c\u53cd\u8f6c\u4e4b\u540e\u518d\u5c06\u628a\u7956\u7236\u8282\u70b9\u770b\u4f5c\u63d2\u5165\u8282\u70b9\uff0c\u5982\u679c\u4e5f\u51fa\u73b0<strong>\u4e0d\u7ea2\u7ea2<\/strong>\u4e14\u53d4\u53d4\u4e3a\u7ea2\u8272\uff0c\u4e5f\u5c06\u5176\u7236\u4eb2\u53d4\u53d4\u548c\u7956\u7236\u4e5f\u53cd\u8f6c\u3002\u5f53\u7136\u5982\u679c\u5411\u4e0a\u904d\u5386\u7684\u8fc7\u7a0b\u51fa\u73b0\u4e86\u6839\u8282\u70b9\u90a3\u4e48\u5c31\u505c\u6b62\uff0c\u5e76\u4e14\u4fdd\u8bc1\u6839\u8282\u70b9\u4e3a\u9ed1\u8272\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/C5219H7HLPJ8EOGT1-668x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"668\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/C5219H7HLPJ8EOGT1-668x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1258\"  sizes=\"auto, (max-width: 668px) 100vw, 668px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u60c5\u51b52\u8c03\u6574\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6838\u5fc3\u70b91\uff1a<\/strong>\u4e3a\u4ec0\u4e48\u8981\u8c03\u6574\u989c\u8272\uff0c\u8fd9\u6837\u8c03\u6574\u989c\u8272\u96be\u9053\u4e0d\u4f1a\u5f71\u54cd\u5176\u4ed6\u5b50\u6811\u7684\u989c\u8272\u6392\u5e03\u5417\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u51fa\u73b0\u989c\u8272\u8c03\u6574\u7684\u539f\u56e0\u662f\u8fdd\u53cd\u4e86<strong>\u4e0d\u7ea2\u7ea2<\/strong>\u6027\u8d28\uff0c\u6700\u8ba9\u521d\u5b66\u8005\u4e0d\u89e3\u7684\u5c31\u662f\u8fd9\u79cd\u8c03\u6574\u4e3a\u4ec0\u4e48\u4e0d\u4f1a\u5f71\u54cd\u5230\u5176\u4ed6\u7684\u989c\u8272\u6392\u5e03\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\uff0c\u6dfb\u52a0\u7ea2\u8272\u8282\u70b9\u662f\u4e0d\u4f1a\u5f71\u54cd\u5230<strong>\u9ed1\u8def\u540c<\/strong>\u6027\u8d28\u7684\uff0c\u56e0\u4e3a\u5e76\u6ca1\u6709\u989d\u5916\u7684\u9ed1\u8272\u8282\u70b9\u5f15\u5165\u3002\u6240\u4ee5\u8fd9\u4e2a\u8c03\u6574\u7684\u4e3b\u8981\u601d\u60f3\u662f\u5c06\u7ea2\u8272\u8282\u70b9\u63d2\u5165\u540e\u91cd\u65b0\u8c03\u6574\u4e3a\u9ed1\u7ea2\u76f8\u95f4\u7684\u7ed3\u6784\u3002\u4ee5<code>\u60c5\u51b52<\/code>\u4e3a\u4f8b\uff0c<code>10\u300120\u300130<\/code>\u53d1\u751f\u4e86\u989c\u8272\u53cd\u8f6c\uff0c\u4f46\u662f\u4ed4\u7ec6\u60f3\u4e00\u60f3\u601d\u8def\uff0c<code>10<\/code>\u548c<code>30<\/code>\u90fd\u662f<code>20<\/code>\u7684\u5b69\u5b50\uff0c\u672c\u8d28\u4e0a\u53ef\u4ee5\u5c55\u5f00\u4e3a<code> 20(\u9ed1)-&gt;10(\u7ea2) <\/code>\u548c<code>20(\u9ed1)-&gt;30(\u7ea2)<\/code>\u3002\u9ed1\u7ea2\u4ea4\u6362\u989c\u8272\u540e\u662f<code>20(\u7ea2)-&gt;10(\u9ed1) <\/code>\u548c<code>20(\u7ea2)-&gt;30(\u9ed1)<\/code>\uff0c\u800c<code>20<\/code>\u662f\u540c\u4e00\u4e2a\u8282\u70b9\uff0c\u4e5f\u5c31\u662f\u8bf4\u53d8\u8272\u53ea\u4e0d\u8fc7\u662f\u4e24\u4e2a\u8282\u70b9\u989c\u8272\u4ea4\u6362\u987a\u5e8f\uff0c\u800c<code>10<\/code>\u5982\u679c\u5b58\u5728\u5b69\u5b50\uff0c\u90a3\u4e48\u53ea\u53ef\u80fd\u662f\u9ed1\u8272\uff0c\u90a3\u4e48<code>10<\/code>\u53d8\u6210\u9ed1\u8272\u540e\uff0c\u9ed1\u8272\u76f8\u90bb\u4e5f\u662f\u6ee1\u8db3\u6027\u8d28\u7684\u3002\u800c\u4e14\u5982\u679c\u8d70<code>10<\/code>\u7684\u5b50\u5b69\u5b50\u8fd9\u4e00\u6761\u8def\uff0c\u5982\u679c\u4e4b\u524d\u662f<code>\u9ed1-&gt;\u7ea2-&gt;\u9ed1<\/code>\uff0c\u90a3\u4e48\u73b0\u5728\u53d8\u6210<code>\u7ea2-&gt;\u9ed1-&gt;\u9ed1<\/code>\uff0c\u672c\u8d28\u4e0a\u4e0d\u4f1a\u5bf9\u6811\u7ed3\u6784\u6709\u5f71\u54cd\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u5bf9\u4e8e\u6839\u8282\u70b9\u7684\u4f4d\u7f6e\u4f1a\u88ab<strong>\u6839\u53f6\u9ed1<\/strong>\u6027\u8d28\u7ea0\u6b63\uff0c\u8fd9\u4e2a\u4e5f\u4e0d\u4f1a\u5f71\u54cd\u5230\u6574\u4f53\uff0c\u56e0\u4e3a\u6240\u6709\u7684\u8def\u5f84\u8d77\u59cb\u70b9\u90fd\u662f\u6839\u8282\u70b9\uff0c\u6839\u8282\u70b9\u662f\u4ec0\u4e48\u5373\u4fbf\u5e94\u8be5\u4e3a\u7ea2\u8272\u4f46\u662f\u88ab\u5f3a\u5236\u53cd\u8f6c\u6210\u9ed1\u8272\u4e5f\u65e0\u59a8\uff0c\u56e0\u4e3a\u6240\u6709\u8def\u7ebf\u589e\u52a0\u4e00\u4e2a\u9ed1\u8282\u70b9\u4e0d\u5f71\u54cd<strong>\u9ed1\u8def\u540c<\/strong>\u6027\u8d28<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><code>\u60c5\u51b53<\/code>\uff1a\u8fd9\u662f\u6700\u590d\u6742\u7684\u4e00\u79cd\u60c5\u51b5\uff0c\u5b83\u6d89\u53ca\u5230\u4e86\u65cb\u8f6c\u64cd\u4f5c\uff0c\u8fd9\u4e2a\u64cd\u4f5c\u548cAVL\u4e2d\u7684\u56db\u79cd\u65cb\u8f6c\u7c7b\u4f3c,\u4e5f\u662f<code>[LL\u578b RR\u578b LR\u578b RL\u578b]<\/code>\u56db\u79cd\u7c7b\u578b\u3002\u4e0d\u8fc7\u4e0e\u4e4b\u4e0d\u540c\u7684\u662f\uff0c\u589e\u52a0\u4e86\u53d8\u8272\u8fd9\u4e00\u64cd\u4f5c\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/N6YVLBJ1SPXWF6WSYZ9VI.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"730\" height=\"1020\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/N6YVLBJ1SPXWF6WSYZ9VI.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1259\"  sizes=\"auto, (max-width: 730px) 100vw, 730px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-LL\u578b\u65cb\u8f6c\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\u662fLL\u578b\uff0c\u8fd9\u91cc\u7684\u4f8b\u5b50\u4f7f\u7528\u4e86\u4e00\u4e2a\u6bd4\u8f83\u7279\u6b8a\u7684\u6848\u4f8b\uff0c\u56e0\u4e3a\u5f88\u591a\u5e38\u5e38\u5ffd\u7565\u4e86<code>NULL<\/code>\u8282\u70b9\u662f\u9ed1\u8272\u7684\uff0c\u8fd9\u91cc\u7684\u5c5e\u53d4\u53d4\u8282\u70b9\u672c\u8d28\u4e0a\u662f\u9ed1\u8272\u7684\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u8fd9\u4e2a\u6d41\u7a0b\u4e2d\u6700\u9700\u8981\u91cd\u70b9\u5173\u6ce8\u7684\u662f\u7956\u7236\u8282\u70b9\uff0c\u5176\u6b21\u4e3a\u65cb\u8f6c\u8282\u70b9\uff0c\u5728\u65cb\u8f6c\u5b8c\u6210\u540e\u5c06\u8fd9\u4e24\u4e2a\u8282\u70b9\u8fdb\u884c\u53d8\u8272\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/ZKYS4SKFLS741VY0-496x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/ZKYS4SKFLS741VY0-496x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1260\"  sizes=\"auto, (max-width: 496px) 100vw, 496px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-LR\u578b\u65cb\u8f6c\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">LR\u578b\u7684\u4f5c\u4e3a\u590d\u6742\u7c7b\u578b\u7684\u65cb\u8f6c\uff0c\u9700\u8981\u5148\u65cb\u8f6c\u5de6\u5b50\u6811\uff0c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u5b8c\u6210\u540e\u6210\u4e3aLL\u578b\u65f6\u624d\u5f00\u59cb\u8003\u8651\u53d8\u8272\u95ee\u9898\uff0c\u548cLL\u578b\u4e00\u6837\uff0c\u5148\u770b\u7956\u7236\u8282\u70b9\u518d\u770b\u65cb\u8f6c\u70b9\uff0c\u6700\u540e\u4e24\u8005\u8fdb\u884c\u53d8\u8272\u64cd\u4f5c\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/9MV7O@AZLF98BDBO2U3.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1018\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/9MV7O@AZLF98BDBO2U3.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1261\"  sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-RR\u578b\u65cb\u8f6c\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">RR\u578b\u548cLL\u578b\u4e00\u6a21\u4e00\u6837\uff0c\u53ea\u662f\u65b9\u5411\u76f8\u53cd\uff0c\u540c\u65f6\u53d8\u8272\u7684\u903b\u8f91\u4f9d\u65e7\u662f\u5148\u786e\u8ba4\u7956\u7236\u8282\u70b9\u518d\u786e\u8ba4\u65cb\u8f6c\u8282\u70b9<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/LT6QYW0P2D32IV1V7Q-491x1024.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"491\" height=\"1024\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/LT6QYW0P2D32IV1V7Q-491x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1262\"  sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-RL\u578b\u65cb\u8f6c\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u65cb\u8f6c\u64cd\u4f5c\u548cLR\u578b\u7c7b\u4f3c\uff0c\u540c\u65f6\u53d8\u8272\u4e5f\u548cLR\u578b\u4e00\u6837\uff0c\u5f53RL\u578b\u8f6c\u6362\u4e3aRR\u578b\u5f00\u59cb\u624d\u8003\u8651\u53d8\u8272\u8282\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6838\u5fc3\u70b92<\/strong>\uff1a\u4e3a\u4ec0\u4e48\u8981\u8fdb\u884c\u65cb\u8f6c\uff0c\u800c\u4e0d\u80fd\u50cf\u60c5\u51b52\u4e00\u6837\u8fdb\u884c\u53d8\u8272\u8c03\u6574\u5462\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#f78da7\" class=\"has-inline-color\">\u7528\u53f6\u5b50\u8282\u70b9\u7684\u4f4d\u7f6e\u505a\u4f8b\u5b50\u5206\u6790<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\u7b2c\u4e00\u70b9\uff0c\u5148\u5206\u6790\u53d1\u751f\u65cb\u8f6c\u7684\u60c5\u51b5\u3002\u63d2\u5165\u7684\u662f\u7ea2\u8272\u8282\u70b9\uff0c\u90a3\u4e48\u7236\u4eb2\u8282\u70b9\u4e00\u5b9a\u662f\u7ea2\u8272\u8282\u70b9\uff0c\u800c\u4e0d\u8fdd\u53cd<strong>\u4e0d\u7ea2\u7ea2<\/strong>\u6027\u8d28\uff0c\u7956\u7236\u8282\u70b9\u4e00\u5b9a\u662f\u9ed1\u8272\u8282\u70b9\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u53d1\u751f\u65cb\u8f6c\u60c5\u51b5\u7684\u65f6\u5019\uff0c\u53d4\u53d4\u8282\u70b9\u548c\u7956\u7236\u8282\u70b9\u4e00\u5b9a\u662f\u9ed1\u8272\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u8fd9\u4e2a\u60c5\u51b5\u4e0b\u5982\u679c\u6309\u7167\u60c5\u51b52\u6765\u53d8\u8272\uff0c\u5c31\u4f1a\u5bfc\u81f4\u53d4\u53d4\u8282\u70b9\u548c\u7956\u7236\u8282\u70b9\u53cd\u8f6c\u6210\u7ea2\u8272\u4ece\u800c\u7834\u574f<strong>\u4e0d\u7ea2\u7ea2<\/strong>\u6027\u8d28\uff0c\u6b64\u5916\u53d4\u53d4\u8282\u70b9\u7684\u8def\u5f84\u540c\u65f6\u4f1a\u5bfc\u81f4\u5931\u53bb\u4e00\u4e2a\u9ed1\u8272\u8282\u70b9\uff0c\u53c8\u8fdd\u53cd\u4e86<strong>\u9ed1\u8def\u540c<\/strong>\u6027\u8d28\u3002\u4e3a\u4e86\u8c03\u6574\u4e00\u4e2a\u7ed3\u6784\u53c8\u591a\u51fa\u4e24\u4e2a\u7834\u574f\u7ed3\u6784\u7684\u60c5\u51b5\uff0c\u663e\u7136\u662f\u4e0d\u7406\u667a\u7684\uff0c\u6240\u4ee5\u9700\u8981\u4f7f\u7528\u53e6\u5916\u4e00\u4e2a\u8c03\u6574\u601d\u8def\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6574\u4f53\u7684\u601d\u8def\u601d\u8003:<\/p>\n\n\n\n<p 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class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u65b0GIF\u52a8\u56fe-1.gif'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"505\" height=\"588\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u65b0GIF\u52a8\u56fe-1.gif\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1272\"\/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u53d8\u8272\u8c03\u6574\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u65cb\u8f6c\u8c03\u6574\u7684\u6838\u5fc3\u601d\u60f3\u5219\u66f4\u52a0\u7c97\u66b4\uff0c\u7531\u4e8e\u65e0\u6cd5\u5c06\u989c\u8272\u4f20\u9012\u5230\u6839\u8282\u70b9\u62b9\u6740\uff0c\u90a3\u4e48\u5c31\u76f4\u63a5\u628a\u591a\u51fa\u7684\u7ea2\u8272\u8282\u70b9\u63d2\u5165\u5230\u53d4\u53d4\u8def\u5f84\u7684\u4e00\u8fb9\uff0c\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u63d2\u5165\u5230\u53e6\u5916\u4e00\u8fb9\uff0c\u4e3b\u8981\u539f\u56e0\u662f\u53d1\u751f\u65cb\u8f6c\u8c03\u6574\u7684\u524d\u63d0\u4e2d\uff0c\u53d4\u53d4\u5b50\u6811\u548c\u7956\u7236\u5b50\u6811\u4e00\u5b9a\u662f\u4e24\u4e2a\u76f8\u90bb\u7684\u9ed1\u8272\u8282\u70b9\u3002\u8be6\u60c5\u8bc1\u660e\u5728<strong>\u6838\u5fc3\u70b93<\/strong>\u4e2d\u6709\u63d0\u5230\u3002\u5f53\u7136\u4e5f\u4e0d\u662f\u7b80\u5355\u7684\u4e22\u8fc7\u53bb\uff0c\u540c\u65f6\u8fd8\u4f1a\u4f7f\u7528\u65cb\u8f6c\u7ef4\u62a4\u6811\u7684\u7ed3\u6784\uff0c\u4ee5\u9632\u6811\u51fa\u73b0\u5931\u8861\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6838\u5fc3\u70b93\uff1a<\/strong>\u4e3a\u4ec0\u4e48<code>\u60c5\u51b53<\/code>\u4e0d\u9700\u8981\u50cf<code>\u60c5\u51b52<\/code>\u65cb\u8f6c\u5b8c\u6210\u4e00\u6b21\u540e\u63a5\u7740\u56de\u6eaf\u8c03\u6574\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\uff0c\u8fd9\u91cc\u6709\u4e00\u4e2a\u6613\u9519\u7684\u70b9\uff1a<mark style=\"background-color:#ff6900\" class=\"has-inline-color\"><code>\u60c5\u51b53<\/code>\u4e0d\u9700\u8981\u56de\u6eaf\u8c03\u6574\uff0c\u4f46\u662f<code>\u60c5\u51b52<\/code>\u56de\u6eaf\u8c03\u6574\u662f\u6709\u53ef\u80fd\u89e6\u53d1<code>\u60c5\u51b53<\/code>\u7684<\/mark>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u4ed4\u7ec6\u5206\u6790\u4e00\u4e0b\u51fa\u73b0\u60c5\u51b53\u5728\u65f6\u5019\uff0c\u5177\u6709\u666e\u904d\u6027\u7684\u5c40\u90e8\u7684\u7ea2\u9ed1\u6811\u5b50\u6811\u662f\u4ec0\u4e48\u6837\u5b50\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5df2\u77e5\u4e00\u4e2a\u53d4\u53d4\u8282\u70b9\u4e00\u5b9a\u662f\u9ed1\u8272\uff0c\u7236\u4eb2\u8282\u70b9\u4e00\u5b9a\u662f\u7ea2\u8272\u63d2\u5165\u8282\u70b9\u4f4d\u7f6e\u4e00\u5b9a\u662f\u7ea2\u8272\u3002\uff08\u6ce8\u610f\uff0c\u7531\u4e8e\u662f\u666e\u9002\u6027\uff0c\u6240\u4ee5\u4ee5\u6700\u7279\u6027\u7684\u60c5\u51b5\u2014\u2014\u4e5f\u5c31\u662f\u7ecf\u8fc7\u4e00\u6b21\u60c5\u51b52\u8c03\u6574\u4e4b\u540e\u7684\u6837\u5b50\u4e3a\u4f8b\uff09\u3002\u7531\u4e8e\u5728\u63d2\u5165\u524d\u7ea2\u9ed1\u6811\u4e00\u5b9a\u662f\u9075\u5b88\u89c4\u5219\u7684\uff0c\u6240\u4ee5\u6b64\u65f6\u7684\u7956\u7236\u8282\u70b9\u4e0d\u53ef\u80fd\u662f\u7ea2\u8272\uff08\u4e0d\u7136\u4f1a\u4e0e\u7236\u4eb2\u8282\u70b9\u51b2\u7a81\uff09\uff0c\u53ef\u4ee5\u5f97\u51fa\u7956\u7236\u8282\u70b9\u4e00\u5b9a\u662f\u9ed1\u8272\uff0c\u4e8e\u662f\u53ef\u4ee5\u5f97\u51fa\u4e00\u4e2a\u5177\u6709\u666e\u9002\u6027\u7684\u6a21\u578b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/e9307591223c28e88fc530ecb78ff839.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"558\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/e9307591223c28e88fc530ecb78ff839.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1267\"  sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/div><figcaption class=\"wp-element-caption\"><br>\u56fe-\u60c5\u51b53RR\u578b\u57fa\u7840\u6a21\u578b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">LL\u578b\u662fRR\u578b\u7684\u955c\u50cf\uff0c\u539f\u7406\u4e00\u81f4\u3002\u800cRR\u578b\u7684\u57fa\u7840\u6a21\u578b\u65cb\u8f6c\uff0c\u672c\u8d28\u4e0a\u662f\u6839\u8282\u70b9\u53d8\u6210\u5de6\u5b69\u5b50\u53f3\u5b69\u5b50\u53d8\u6210\u6839\u8282\u70b9\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/fb5e0461b8b25e9a97cd40451a1863bc.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"747\" height=\"492\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/fb5e0461b8b25e9a97cd40451a1863bc.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1268\"  sizes=\"auto, (max-width: 747px) 100vw, 747px\" \/><\/div><figcaption class=\"wp-element-caption\"><br>\u56fe-\u60c5\u51b53RR\u578b\u57fa\u7840\u6a21\u578b-2<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u6837\u7684\u64cd\u4f5c\u4f1a\u5bfc\u81f4\u8fdd\u53cd\u9ed1\u8def\u540c\u6027\u8d28\uff0c\u4f46\u662f\u63a5\u4e0b\u6765\u7684\u4e00\u6b65\u81f3\u5173\u91cd\u8981\uff0c\u90a3\u5c31\u662f\u5c06\u65b0\u5de6\u5b69\u5b50\u548c\u6839\u8282\u70b9\u989c\u8272\u4e92\u6362\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/74b174a9e6266720d88aa789516dc7e8.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"724\" height=\"461\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/74b174a9e6266720d88aa789516dc7e8.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1269\"  sizes=\"auto, (max-width: 724px) 100vw, 724px\" \/><\/div><figcaption class=\"wp-element-caption\"><br>\u56fe-\u60c5\u51b53RR\u578b\u57fa\u7840\u6a21\u578b-3<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u6709\u6700\u540e\u7684\u7ed3\u679c\u53ef\u4ee5\u770b\u5230\u65cb\u8f6c\u4e4b\u540e\u7684\u6839\u8282\u70b9\u4e00\u5b9a\u662f\u9ed1\u8272\uff0c\u540c\u7406RL\u578b\u6a21\u578b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/a81bed8f0a08f84180c9bf9128acd8a1.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"657\" height=\"488\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/a81bed8f0a08f84180c9bf9128acd8a1.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1270\"  sizes=\"auto, (max-width: 657px) 100vw, 657px\" \/><\/div><figcaption class=\"wp-element-caption\"><br>\u56fe-\u60c5\u51b53RL\u578b\u57fa\u7840\u6a21\u578b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">LR\u578b\u6a21\u578b\u548cRL\u578b\u6a21\u578b\u662f\u955c\u50cf\u3002\u53ea\u5206\u6790RL\u6a21\u578b\uff0c\u4f1a\u53d1\u73b0\u9996\u6b21\u65cb\u8f6c\u7684\u76ee\u6807\u662f\u5c06\u6a21\u578b\u6539\u53d8\u4e3aRR\u578b\uff0c\u800c\u8fd9\u4e2a\u65cb\u8f6c\u662f\u53d1\u751f\u5728\u4e24\u4e2a\u7ea2\u8272\u8282\u70b9\u4e4b\u95f4\u7684\uff0c\u6240\u4ee5\u5bf9\u4e8e\u7956\u7236\u8282\u70b9\u6765\u8bf4\uff0c\u4e0d\u7ba1\u5982\u4f55\u65cb\u8f6c\uff0c\u59cb\u7ec8\u53f3\u5b69\u5b50\u90fd\u662f\u4e00\u4e2a\u7ea2\u8272\u8282\u70b9\u3002\u800c\u6b64\u524d\u6240\u8bf4\u7684\u7956\u5148\u8282\u70b9\u548c\u65cb\u8f6c\u4e2d\u5fc3\u8282\u70b9\u4ea4\u6362\u989c\u8272\uff0c\u4e5f\u53ef\u4ee5\u8bf4\u662f\u5404\u81ea\u5206\u522b\u53d8\u8272\uff0c\u56e0\u4e3a\u4e0d\u53ef\u80fd\u51fa\u73b0\u540c\u8272\u60c5\u51b5\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u65b0GIF\u52a8\u56fe.gif'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"698\" height=\"566\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/09\/\u65b0GIF\u52a8\u56fe.gif\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1271\"\/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u60c5\u51b53RL\u578b\u57fa\u7840\u6a21\u578b-2<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e4b\u540e\u5c31\u4f1a\u8f6c\u53d8\u4e3aRR\u578b\uff0c\u6240\u4ee5\u6700\u7ec8\u7684\u5206\u6790\u53ef\u4ee5\u77e5\u9053\uff0c\u53ea\u8981\u662f\u89e6\u53d1\u4e86<code>\u60c5\u51b53<\/code>\u53d8\u6362\uff0c\u53d8\u6362\u7ed3\u675f\u540e\u7684\u6839\u8282\u70b9\u4e00\u5b9a\u662f\u9ed1\u8272\uff0c\u800c\u53c8\u53ef\u4ee5\u77e5\u9053\u9ed1\u8272\u8282\u70b9\u662f\u53ef\u4ee5\u76f8\u90bb\u7684\uff0c\u6240\u4ee5\u60c5\u51b53\u53d8\u6362\u662f\u4e0d\u53ef\u80fd\u89e6\u53d1\u56de\u6eaf\u7684\uff0c<mark style=\"background-color:#f78da7\" class=\"has-inline-color\">\u4e00\u6b21\u7ea2\u9ed1\u6811\u8c03\u6574\u4e2d\u6700\u591a\u53ea\u4f1a\u53d1\u751f\u4e00\u6b21<code>\u60c5\u51b53<\/code>\u8c03\u6574\u3002<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">\u4ee3\u7801\u793a\u4f8b<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u524d\u7f6e\u4ee3\u7801<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>typedef enum{\n    RED,\n    BLACK\n}TreeColor;\n\/\/\u6811\u7684\u5b9a\u4e49\ntypedef struct Node\n{\n    int data;\/\/\u6811\u7684\u6570\u636e\n    TreeColor treeColor;\/\/\u8282\u70b9\u989c\u8272\n    struct Node* left;\/\/\u5de6\u5b69\u5b50\n    struct Node* right;\/\/\u53f3\u5b69\u5b50\n    struct Node* parent;\/\/\u7236\u4eb2\u8282\u70b9\n}Node;\n\/\/\u521b\u5efa\u8282\u70b9\nNode* createNode(int data){\n    Node* temp = (Node*)malloc(sizeof(Node));\n    temp-&gt;data = data;\n    temp-&gt;treeColor = RED;\/\/\u9ed8\u8ba4\u4e3a\u7ea2\u8272\u8282\u70b9\n    temp-&gt;left = NULL;\n    temp-&gt;right = NULL;\n    temp-&gt;parent = NULL;\n    return temp;\n}\n\/\/\u989c\u8272\u53cd\u8f6c\nvoid colorReversal(Node* node){\n    if(node == NULL) return;\n    node-&gt;treeColor = ( node-&gt;treeColor == RED ? BLACK : RED );\n}\n\/\/\u8fd4\u56de\u6811\u7684\u6839\u8282\u70b9\nNode* getRoot(Node* node){\n    if(node == NULL) return NULL;\n    while(node-&gt;parent != NULL){\n        node = node-&gt;parent;\n    }\n    return node;\n}\n\/\/\u83b7\u53d6\u53d4\u53d4\u8282\u70b9\nNode* getUncleNode(Node* node){\n    \/\/\u68c0\u67e5\u8282\u70b9\u5f53\u524d\u8282\u70b9\uff0c\u7236\u4eb2\u8282\u70b9\uff0c\u7237\u7237\u8282\u70b9\u662f\u5426\u5b58\u5728\uff0c\u5982\u679c\u6709\u4e00\u4e2a\u4e0d\u5b58\u5728\u5219\u8fd4\u56de\n    if (node == NULL || node-&gt;parent == NULL || node-&gt;parent-&gt;parent == NULL) return NULL;\n    Node* father = node-&gt;parent;\/\/\u83b7\u53d6\u7236\u4eb2\u8282\u70b9\n    Node* ancestor = node-&gt;parent-&gt;parent;\/\/\u83b7\u53d6\u7956\u5148\u8282\u70b9\n    return ancestor-&gt;left != father ? father : ancestor-&gt;right;\/\/\u8fd4\u56de\u53d4\u53d4\u8282\u70b9\n}\n\/\/\u8fd4\u56de\u8282\u70b9\u7684\u53d4\u53d4\u7684\u989c\u8272\nTreeColor uncleColor(Node* node){\n    Node* temp = getUncleNode(node);\/\/\u83b7\u53d6\u53d4\u53d4\u8282\u70b9\n    if(temp == NULL)\n        return BLACK;\n    else\n        return temp-&gt;treeColor;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u65cb\u8f6c\u8c03\u6574<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u5de6\u65cb\nNode* rotateLeft(Node* root){\n    \/\/\u6839\u8282\u70b9\u4e3aNULL\u5219\u76f4\u63a5\u9000\u51fa\n    if(root == NULL) return NULL;\n    \/\/\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u6839\u8282\u70b9\n    Node* newRoot = root-&gt;right;\/\/\u65b0\u6839\u8282\u70b9\u4e0d\u53ef\u80fd\u51fa\u73b0NULL\u60c5\u51b5\n    \/\/\u66f4\u65b0\u65b0\u6839\u8282\u70b9\u7236\u4eb2\n    newRoot-&gt;parent = root-&gt;parent;\n    \/\/\u8c03\u6574\u65e7\u53f3\u5b69\u5b50\u5de6\u8282\u70b9\u7684\u7236\u4eb2\n    root-&gt;right = newRoot-&gt;left;\n    if(newRoot-&gt;left != NULL){\n        newRoot-&gt;left-&gt;parent = root;\n    }\n    \/\/\u8c03\u6574\u65e7\u6839\u8282\u70b9\u7236\u4eb2\n    newRoot-&gt;left = root;\n    root-&gt;parent = newRoot;\n    return newRoot;\n}\n\/\/\u53f3\u65cb\nNode* rotateRight(Node* root){\n    \/\/\u6839\u8282\u70b9\u4e3aNULL\u5219\u76f4\u63a5\u9000\u51fa\n    if(root == NULL) return NULL;\n    Node* newRoot = root-&gt;left;\/\/\u65b0\u6839\u8282\u70b9\u4e0d\u53ef\u80fd\u51fa\u73b0NULL\u60c5\u51b5\n    \/\/\u66f4\u65b0\u65b0\u6839\u8282\u70b9\u7236\u4eb2\n    newRoot-&gt;parent = root-&gt;parent;\n    \/\/\u8c03\u6574\u65e7\u5de6\u5b69\u5b50\u53f3\u8282\u70b9\u7684\u7236\u4eb2\n    root-&gt;left = newRoot-&gt;right;\n    if(newRoot-&gt;right != NULL){\n        newRoot-&gt;right-&gt;parent = root;\n    }\n    \/\/\u8c03\u6574\u65e7\u6839\u8282\u70b9\u7236\u4eb2\n    newRoot-&gt;right = root;\n    root-&gt;parent = newRoot;\n    return newRoot;\n}\n\/\/\u5bf9\u4e00\u68f5\u5b50\u6811\u8fdb\u884c\u65cb\u8f6c\uff0c\u5e76\u8fd4\u56de\u65cb\u8f6c\u540e\u7684\u65b0\u6839\u8282\u70b9\nNode* balance(Node* node){\n    \/\/\u83b7\u53d6\u7236\u4eb2\u8282\u70b9\n    Node* father = node-&gt;parent;\n    \/\/\u83b7\u53d6\u7956\u5148\u8282\u70b9\n    Node* ancestor = node-&gt;parent-&gt;parent;\n    \/\/\u65cb\u8f6c\u4e2d\u5fc3\n    Node* rotate_center = NULL;\n    \/\/LL\u578b\n    if(father == ancestor-&gt;left &amp;&amp; node == father-&gt;left){\n        \/\/\u65cb\u8f6c\u5e76\u66f4\u65b0\u65cb\u8f6c\u4e2d\u5fc3\n        rotate_center = rotateRight(ancestor);     \n    }\n    \/\/RR\u578b\n    else if(father == ancestor-&gt;right &amp;&amp; node == father-&gt;right){\n        \/\/\u65cb\u8f6c\u5e76\u66f4\u65b0\u65cb\u8f6c\u4e2d\u5fc3\n        rotate_center = rotateLeft(ancestor);\n    }\n    \/\/LR\u578b\n    else if(father == ancestor-&gt;left &amp;&amp; node == father-&gt;right){\n        \/\/\u5148\u65cb\u8f6c\u5b50\u6811\n        ancestor-&gt;left = rotateLeft(ancestor-&gt;left);\n        rotate_center = rotateRight(ancestor);\n    }\n    \/\/RL\u578b\n    else if(father == ancestor-&gt;right &amp;&amp; node == father-&gt;left){\n        \/\/\u5148\u65cb\u8f6c\u5b50\u6811\n        ancestor-&gt;right = rotateRight(ancestor-&gt;right);\n        rotate_center = rotateLeft(ancestor);\n    }\n    \/\/\u7956\u5148\u548c\u65cb\u8f6c\u4e2d\u5fc3\u53d8\u8272\n    colorReversal(ancestor);\n    colorReversal(rotate_center);\n    return rotate_center;\n}\n\n\/\/\u65cb\u8f6c\u8c03\u6574,\u8f93\u5165\u63d2\u5165\u8282\u70b9\u5730\u5740\uff0c\u8fd4\u56de\u6839\u8282\u70b9\nNode* rotateAdjustment(Node* node){\n    \/\/\u5982\u679c\u8282\u70b9\u4e3a\u7a7a\u3001\u6216\u7236\u4eb2\u8282\u70b9\u4e3a\u7a7a\u3001\u6216\u7956\u5148\u8282\u70b9\u4e3a\u7a7a\uff0c\u5219\u4e0d\u6ee1\u8db3\u8c03\u6574\u524d\u63d0\n    if(node == NULL || node-&gt;parent == NULL || node-&gt;parent-&gt;parent == NULL){\n        return getRoot(node);\/\/\u76f4\u63a5\u8fd4\u56de\u6811\u7684\u6839\u8282\u70b9\n    }\n    \/\/\u83b7\u53d6\u7956\u5148\u8282\u70b9\u7684\u7236\u4eb2\u8282\u70b9\uff0c\u7528\u4e8e\u63a5\u6536\u65cb\u8f6c\u4e4b\u540e\u7684\u5b50\u6811\u7684\u5730\u5740\n    Node* root = node-&gt;parent-&gt;parent-&gt;parent;\n    \/\/\u5982\u679c\u7956\u5148\u8282\u70b9\u7684\u7236\u4eb2\u8282\u70b9\u5b58\u5728\uff0c\u90a3\u4e48\u610f\u5473\u7740\u8c03\u6574\u7684\u6811\u5c40\u90e8\u6811\n    if(root != NULL){\n        if(root-&gt;left == node-&gt;parent-&gt;parent){\n            root-&gt;left = balance(node);\n        }else{\n            root-&gt;right = balance(node);\n        }\n        \/\/\u8c03\u6574\u5b8c\u6210\uff0c\u5bfb\u627e\u8fd9\u68f5\u6811\u7684\u6839\u8282\u70b9\u5e76\u8fd4\u56de\n        return getRoot(node);\n    }\n    \/\/\u5982\u679c\u7956\u5148\u8282\u70b9\u7684\u7236\u4eb2\u8282\u70b9\u4e0d\u5b58\u5728\uff0c\u5219\u610f\u5473\u7740\u8c03\u6574\u7684\u662f\u6574\u68f5\u6811\n    else{\n        \/\/\u8c03\u6574\u7684\u7ed3\u679c\u5c31\u662f\u8fd9\u68f5\u6811\u7684\u65b0\u6839\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\n        return balance(node);\n    }\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u53d8\u8272\u8c03\u6574<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u53d8\u8272\u8c03\u6574\uff0c\u8f93\u5165\u63d2\u5165\u8282\u70b9\u5730\u5740\uff0c\u8fd4\u56de\u6839\u8282\u70b9\nNode* colorAdjustment(Node* node){\n    if(node == NULL) return NULL;\n    \/\/\u6ca1\u6709\u904d\u5386\u5230\u6839\u8282\u70b9\uff0c\u4e14\u4f9d\u65e7\u6ee1\u8db3\u8c03\u6574\u524d\u63d0\n    while(node-&gt;parent != NULL &amp;&amp; node-&gt;parent-&gt;parent != NULL  &amp;&amp; node-&gt;parent-&gt;treeColor == RED){\n        \/*\u68c0\u67e5\u8c03\u6574\u7c7b\u578b*\/\n        \/\/\u5982\u679c\u4e3a\u53d8\u8272\u8c03\u6574\n        if(uncleColor(node) == RED){\n            \/\/\u7236\u4eb2\u8282\u70b9\u53d8\u8272\n            colorReversal(node-&gt;parent);\n            \/\/\u7237\u7237\u8282\u70b9\u53d8\u8272\n            colorReversal(node-&gt;parent-&gt;parent);\n            \/\/\u53d4\u53d4\u8282\u70b9\u53d8\u8272\n            colorReversal(getUncleNode(node));\n            \/\/\u66f4\u65b0node\n            node = node-&gt;parent-&gt;parent;\n        }\n        \/\/\u5982\u679c\u4e3a\u65cb\u8f6c\u8c03\u6574\n        else{\n            return rotateAdjustment(node); \n        }\n    }\n    \/\/\u5982\u679c\u904d\u5386\u5230\u4e86\u6839\u8282\u70b9\uff0c\u5219\u5f3a\u884c\u53d8\u9ed1\n    if(node-&gt;parent == NULL){\n        node-&gt;treeColor = BLACK;\n        return node;\n    }\n    \/\/\u8fd4\u56de\u6839\u8282\u70b9\n    return getRoot(node);\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u7efc\u5408\u63d2\u5165\u51fd\u6570<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u5728\u7ea2\u9ed1\u6811\u672b\u7aef\u7684\u5bf9\u5e94\u4f4d\u7f6e\u6dfb\u52a0\u4e00\u4e2a\u8282\u70b9\uff0c\u5e76\u4e14\u8fd4\u56de\u8fd9\u4e2a\u65b0\u8282\u70b9\u7684\u5730\u5740\nNode* RBTree_addNodeAtLocation(Node* root,int data){\n    if(root == NULL) return NULL;\n    \/\/\u67e5\u627e\u4f4d\u7f6e\n    Node* cur = root;\n    Node* parent = NULL;\n    \/\/\u904d\u5386\u7ea2\u9ed1\u6811\n    while (cur != NULL) {\n        parent = cur;\n        \/\/\u5982\u679c\u6570\u636e\u5c0f\u4e8e\u5f53\u524d\u8282\u70b9\u5219\u5f80\u5de6\u904d\u5386\n        if (data &lt; cur-&gt;data) {\n            cur = cur-&gt;left;\n        } \n        \/\/\u5982\u679c\u6570\u636e\u5927\u4e8e\u5f53\u524d\u8282\u70b9\u5219\u5f80\u53f3\u904d\u5386\n        else if (data &gt; cur-&gt;data) {\n            cur = cur-&gt;right;\n        } \n        \/\/\u5982\u679c\u6570\u636e\u7b49\u4e8e\u5f53\u524d\u8282\u70b9\u5219\u9000\u51fa\n        else {\n            return NULL; \/\/ \u8282\u70b9\u5df2\u5b58\u5728\n        }\n    }\n    \/\/\u521b\u5efa\u4e00\u4e2a\u65b0\u8282\u70b9\n    Node* temp = createNode(data);\n    if (temp == NULL) return NULL;\/\/\u521b\u5efa\u5931\u8d25\u5219\u9000\u51fa\n    \/\/\u5224\u65ad\u5e94\u8be5\u5de6\u63d2\u8fd8\u662f\u53f3\u63d2\n    temp-&gt;parent = parent;\n    if (data &lt; parent-&gt;data) {\n        parent-&gt;left = temp;\/\/\u5de6\u63d2\n    } else {\n        parent-&gt;right = temp;\/\/\u53f3\u63d2\n    }\n    \/\/\u8fd4\u56de\u8282\u70b9\u5730\u5740\n    return temp;\n}\n\/\/\u7efc\u5408\u63d2\u5165\u51fd\u6570\u5165\u53e3\nNode* insert(Node* root,int data){\n    \/*\u6811\u6ca1\u6709\u8282\u70b9*\/\n    if(root == NULL){\n        root = createNode(data);\/\/\u6dfb\u52a0\u4e00\u4e2a\u65b0\u8282\u70b9\n        root-&gt;treeColor = BLACK;\/\/\u5c06\u8282\u70b9\u53d8\u4e3a\u9ed1\u8272\n        return root;\n    }\n\n    \/*\u6811\u6709\u8282\u70b9*\/\n    \/\/\u5148\u5728\u6811\u7684\u5bf9\u5e94\u7684\u4f4d\u7f6e\u6dfb\u52a0\u8282\u70b9\uff0c\u83b7\u53d6\u8fd9\u4e2a\u8282\u70b9\u7684\u5730\u5740\n    Node* cur = RBTree_addNodeAtLocation(root,data);\n    \/\/\u63d2\u5165\u5931\u8d25\u6216\u8005\u5df2\u7ecf\u5b58\u5728\u8282\u70b9\u5219\u8fd4\u56de\n    if(cur == NULL) return root;\n\n    \/*\u8c03\u6574\u6811\u7ed3\u6784*\/\n    \/\/\u68c0\u67e5\u6811\u662f\u5426\u6ee1\u8db3\u8c03\u6574\u524d\u63d0\n    if(cur-&gt;parent-&gt;parent == NULL || cur-&gt;parent-&gt;treeColor != RED){\n        \/\/\u6811\u7684\u8be5\u8def\u5f84\u53ea\u6709\u4e24\u5c42\uff0c\u6216\u8005\u7236\u4eb2\u8282\u70b9\u4e0d\u662f\u7ea2\u8272\uff0c\u5219\u4e0d\u6ee1\u8db3\u8c03\u6574\u7684\u524d\u63d0\n        return root;\n    }\n\n    \/*\u68c0\u67e5\u8c03\u6574\u7c7b\u578b*\/\n    \/\/\u53d4\u53d4\u8282\u70b9\u4e3a\u7ea2\u8272\uff0c\u5219\u8fdb\u884c\u53d8\u8272\u8c03\u6574\n    if(uncleColor(cur) == RED){\n        root = colorAdjustment(cur);\n    }\n    \/\/\u53d4\u53d4\u8282\u70b9\u4e3a\u9ed1\u8272\uff0c\u5219\u8fdb\u884c\u65cb\u8f6c\u8c03\u6574\n    else{\n        root = rotateAdjustment(cur);\n    }\n    return root;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u8fd9\u4e2a\u4ee3\u7801\u4e2d\uff0c\u6211\u5b8c\u5168\u907f\u514d\u4e86\u4f7f\u7528\u9012\u5f52\u7684\u65b9\u5f0f\u5b9e\u73b0\uff0c\u539f\u56e0\u6709\u51e0\u70b9\uff1a<\/p>\n\n\n\n<ul 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class=\"wp-block-paragraph\">LL\u578b\u6709\u4e24\u79cd\u60c5\u51b5\uff0c\u4f46\u662f\u90fd\u5fc5\u987b\u6709\u4e00\u4e2a\u5de6\u5b69\u5b50\u8282\u70b9\u3002\u9996\u5148\u8981\u660e\u767d\u6574\u4e2a\u64cd\u4f5c\u7684\u76ee\u7684\u662f\u8ba9\u53f3\u5b50\u6811\u591a\u51fa\u4e00\u4e2a\u53ef\u4ee5\u7528\u6765\u53d8\u8272\u7684\u8282\u70b9\uff0c\u90a3\u4e48\u73b0\u5728\u6240\u505a\u7684\u76ee\u7684\u5c31\u662f\u5c06\u5144\u5f1f\u8282\u70b9\u7684\u5de6\u5b69\u5b50\u8f6c\u79fb\u5230\u53f3\u5b50\u6811\u4e0a\u3002\u4e8e\u662f\u53ef\u4ee5\u8981\u5c06\u7ea2\u8272\u4e0a\u79fb\u3002\u4ee5<code>\u56fe-LL\u578b<\/code>\u4e2d\u7684\u53f3\u56fe\u4e3a\u4f8b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/67037e2962dc7.gif'><img class=\"lazyload lazyload-style-2\" 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src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1302\"  sizes=\"auto, (max-width: 927px) 100vw, 927px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-RR\u578b<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#7bdcb5\" class=\"has-inline-color\"><strong>\u60c5\u51b51.1.1\uff1aLR\u578b\u4e0eRL\u578b<\/strong><\/mark><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/1Y6EIV51XDWB_SP3WY.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\" 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src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"492\" height=\"476\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/6704faf4801f8.gif\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1307\"\/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u9519\u8bef\u65cb\u8f6c\u7ed3\u679c<\/figcaption><\/figure>\n\n\n\n<p 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class=\"wp-block-paragraph\">\u5c06\u76ee\u5149\u770b\u5230\u5144\u5f1f\u8282\u70b9\uff0c\u5144\u5f1f\u8282\u70b9\u4e0e\u5b69\u5b50\u5de6\u65cb\uff0c\u5219\u53ef\u4ee5\u5c06\u5b69\u5b50\u8282\u70b9\u8f6c\u53d8\u4e3a\u5de6\u5b69\u5b50\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/WES5YO9A023D42KAAN.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"475\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/WES5YO9A023D42KAAN.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1308\"  sizes=\"auto, (max-width: 496px) 100vw, 496px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u4e00\u6b21\u65cb\u8f6c<\/figcaption><\/figure>\n\n\n\n<p 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href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/670513acb8efb.gif'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"494\" height=\"477\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/670513acb8efb.gif\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1311\"\/><\/div><figcaption class=\"wp-element-caption\">\u56fe-LR\u5b8c\u6574\u53d8\u6362\u3002<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u53ef\u4ee5\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark 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data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/67051c892f622.gif\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1313\"\/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u4e24\u7c7b\u60c5\u51b5<\/figcaption><\/figure>\n\n\n\n<p 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class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/670528225f4d0.gif'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"272\" height=\"234\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/670528225f4d0.gif\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1316\"\/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u5b8c\u6574\u8c03\u6574\u8fc7\u7a0b<\/figcaption><\/figure>\n\n\n\n<p 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class=\"wp-block-paragraph\">\u65cb\u8f6c\u5b8c\u6210\u540e\uff0c\u5206\u6790<code>\u56fe-\u65cb\u8f6c\u4e2d\u95f4\u6b65\u9aa41<\/code> \u53f3\u56fe\u7684\u53f3\u5b50\u6811\uff0c\u4ee5\u7ea2\u8282\u70b9\u4e3a\u4e2d\u5fc3\uff0c\u4f1a\u53d1\u73b0\u5c11\u4e86\u4e00\u4e2a\u9ed1\u8272\u8282\u70b9\u3002\u4ed4\u7ec6\u4f46\u662f\u53ef\u4ee5\u770b\u4f5c\u4e00\u4e2a\u65b0\u7684\u72b6\u6001\u8fdb\u884c\u5206\u6790\uff0c\u53f3\u5b50\u6811\u6070\u597d\u662f\u4e00\u4e2a\u521a\u5220\u9664\u4e86\u4e00\u4e2a\u8282\u70b9\u7684\u72b6\u6001\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/JKAXH7PEBSH7VM2C.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"379\" height=\"291\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/JKAXH7PEBSH7VM2C.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1292\"  sizes=\"auto, (max-width: 379px) 100vw, 379px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u90a3\u4e48\u5c31\u53ef\u4ee5\u6839\u636e\u8fd9\u4e2a\u72b6\u6001\u6765\u8fdb\u884c\u4e00\u4e2a\u65b0\u7684\u8f6c\u6362\uff0c\u8fdb\u5165\u53e6\u5916\u4e00\u4e2a\u5927\u7c7b\u60c5\u51b5\u2014\u2014\u89c2\u5bdf\u8fd9\u4e2a\u4e0d\u5b58\u5728\u7684\u8282\u70b9\u7684\u5144\u5f1f\u8282\u70b9\u3002\u5982\u679c\u5144\u5f1f\u8282\u70b9\u662f\u9ed1\u8272\u5219\u8fdb\u884c\u9ed1\u8272\u8c03\u6574\uff1a<a href=\"#\u5144\u5f1f\u8282\u70b9\u4e3a\u9ed1\u8272\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">#\u5144\u5f1f\u8282\u70b9\u4e3a\u9ed1\u8272\uff08\u8df3\u8f6c\uff09<\/mark><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd8\u53ef\u80fd\u5b58\u5728\u5176\u4ed6\u7279\u6b8a\u60c5\u51b5\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/14HJANF@VJHCZP1DJXNE.png'><img class=\"lazyload lazyload-style-2\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"416\" height=\"403\" data-original=\"http:\/\/blog.chxzking.cn\/wp-content\/uploads\/2024\/10\/14HJANF@VJHCZP1DJXNE.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1317\"  sizes=\"auto, (max-width: 416px) 100vw, 416px\" \/><\/div><figcaption class=\"wp-element-caption\">\u56fe-\u53f3\u5b50\u6811\u5c40\u90e8\u5206\u67902<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u540c\u6837\u4e5f\u662f\u6309\u7167\u5144\u5f1f\u8282\u70b9\u89c2\u5bdf\uff0c\u5e76\u5206\u7c7b\u8fdb\u884c\u8c03\u6574\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8e\u662f\u5c31\u6709\u4e86\u4ee5\u4e0b\u7ed3\u8bba\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#9b51e0\" class=\"has-inline-color\">\u5f53\u5144\u5f1f\u8282\u70b9\u662f\u7ea2\u8272\u65f6\uff0c\u5c06\u7ea2\u8272\u4f20\u9012\u5230\u6839\u8282\u70b9\uff0c\u7136\u540e\u6839\u636e\u60c5\u51b5\u8fdb\u884c\u5de6\u65cb\u6216\u8005\u53f3\u65cb\u3002\u7136\u540e\u5c06\u89c6\u89d2\u9501\u5b9a\u5728\u4e4b\u524d\u7684\u88ab\u5220\u9664\u5b50\u6811\uff0c\u901a\u8fc7\u88ab\u6dfb\u52a0\u8fc7\u6765\u7684\u8282\u70b9\u7684\u989c\u8272\uff0c\u7ee7\u7eed\u8fdb\u884c\u65b0\u4e00\u8f6e\u7684\u8c03\u6574\u64cd\u4f5c\u3002<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:#fcb900\" class=\"has-inline-color\">\u5b8c\u6574\u7684\u7ea2\u9ed1\u6811\u4ee3\u7801\u793a\u4f8b\uff1a<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u57fa\u7840\u524d\u7f6e\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u5de6\u65cb\nNode* rotateLeft(Node* root){\n    \/\/\u6839\u8282\u70b9\u4e3aNULL\u5219\u76f4\u63a5\u9000\u51fa\n    if(root == NULL) return NULL;\n    \/\/\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u6839\u8282\u70b9\n    Node* newRoot = root-&gt;right;\/\/\u65b0\u6839\u8282\u70b9\u4e0d\u53ef\u80fd\u51fa\u73b0NULL\u60c5\u51b5\n    \/\/\u66f4\u65b0\u65b0\u6839\u8282\u70b9\u7236\u4eb2\n    newRoot-&gt;parent = root-&gt;parent;\n    \/\/\u8c03\u6574\u65e7\u53f3\u5b69\u5b50\u5de6\u8282\u70b9\u7684\u7236\u4eb2\n    root-&gt;right = newRoot-&gt;left;\n    if(newRoot-&gt;left != NULL){\n        newRoot-&gt;left-&gt;parent = root;\n    }\n    \/\/\u8c03\u6574\u65e7\u6839\u8282\u70b9\u7236\u4eb2\n    newRoot-&gt;left = root;\n    root-&gt;parent = newRoot;\n    return newRoot;\n}\n\/\/\u53f3\u65cb\nNode* rotateRight(Node* root){\n    \/\/\u6839\u8282\u70b9\u4e3aNULL\u5219\u76f4\u63a5\u9000\u51fa\n    if(root == NULL) return NULL;\n    Node* newRoot = root-&gt;left;\/\/\u65b0\u6839\u8282\u70b9\u4e0d\u53ef\u80fd\u51fa\u73b0NULL\u60c5\u51b5\n    \/\/\u66f4\u65b0\u65b0\u6839\u8282\u70b9\u7236\u4eb2\n    newRoot-&gt;parent = root-&gt;parent;\n    \/\/\u8c03\u6574\u65e7\u5de6\u5b69\u5b50\u53f3\u8282\u70b9\u7684\u7236\u4eb2\n    root-&gt;left = newRoot-&gt;right;\n    if(newRoot-&gt;right != NULL){\n        newRoot-&gt;right-&gt;parent = root;\n    }\n    \/\/\u8c03\u6574\u65e7\u6839\u8282\u70b9\u7236\u4eb2\n    newRoot-&gt;right = root;\n    root-&gt;parent = newRoot;\n    return newRoot;\n}\n\/\/\u8fd4\u56de\u6811\u7684\u6839\u8282\u70b9\nNode* getRoot(Node* node){\n    if(node == NULL) return NULL;\n    while(node-&gt;parent != NULL){\n        node = node-&gt;parent;\n    }\n    return node;\n}\n\/\/\u83b7\u53d6\u5144\u5f1f\u8282\u70b9\nNode* brotherNode(Node* node){\n    \/\/\u6821\u9a8c\u7236\u4eb2\u8282\u70b9\u7684\u6b63\u786e\u6027\n    if(node-&gt;parent == NULL) return NULL;\n    \/\/\u67e5\u8be2\u5144\u5f1f\u8282\u70b9\n    if(node != node-&gt;parent-&gt;left){\n        return node-&gt;parent-&gt;left;\n    }\n    else{\n        return node-&gt;parent-&gt;right;\n    }\n}\n\/\/\u83b7\u53d6\u8282\u70b9\u989c\u8272\nTreeColor NodeColor(Node* node){\n    return (node == NULL) ? BLACK : node-&gt;treeColor;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8282\u70b9\u67e5\u627e<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/*\u7b2c\u4e00\u90e8\u5206\uff1a\u8282\u70b9\u67e5\u627e*\/\n\/\/\u540e\u7ee7\u4ea4\u6362\u51fd\u6570\nNode* HandleNodeWithTwoChildren(Node* node){\n    \/\/\u6821\u9a8c\n    if(node == NULL) return NULL;\n    \/\/\u67e5\u627e\n    Node* temp = node;\n    node = node-&gt;right;\n    while(node-&gt;left != NULL){\n        node = node-&gt;left;\n    }\n    temp-&gt;data = node-&gt;data;\n    return node;\n}\n\/\/\u5bfb\u627e\u5220\u9664\u8282\u70b9\nNode* FindTargetNode(Node* root, int data){\n    \/\/\u5224\u65ad\u7ea2\u9ed1\u6811\u662f\u5426\u5b58\u5728\n    if(root == NULL) return NULL;\n    \/\/\u58f0\u660e\u4e00\u4e2a\u7528\u4e8e\u904d\u5386\u7684\u53d8\u91cf\n    Node* cur = root;\n    \/\/\u904d\u5386\n    while(cur != NULL){\n        \/\/\u5982\u679c\u76ee\u6807\u8282\u70b9\u5c0f\u4e8e\u5f53\u524d\u8282\u70b9\u7684\u503c,\u90a3\u4e48\u5f80\u5de6\u904d\u5386\n        if(data &lt; cur-&gt;data){\n            cur = cur-&gt;left;\n        }\n        \/\/\u5982\u679c\u76ee\u6807\u8282\u70b9\u5927\u4e8e\u5f53\u524d\u8282\u70b9\u7684\u503c,\u90a3\u4e48\u5f80\u53f3\u904d\u5386\n        else if(data &gt; cur-&gt;data){\n            cur = cur-&gt;right;\n        }\n        \/\/\u627e\u5230\u76ee\u6807\u8282\u70b9\n        else {\n            \/\/\u5982\u679c\u5ea6\u4e3a2\u5219\u8981\u8fdb\u884c\u989d\u5916\u5904\u7406\n            if(cur-&gt;left != NULL &amp;&amp; cur-&gt;right != NULL){\n                cur = HandleNodeWithTwoChildren(cur);\n            }\n            \/\/\u8fd4\u56de\u627e\u5230\u7684\u8282\u70b9\n            return cur;\n        }\n    }\n    \/\/\u6ca1\u6709\u627e\u5230\u76ee\u6807\u8282\u70b9\n    return NULL;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5220\u9664\u4e0e\u8c03\u6574<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/*\u7b2c\u4e8c\u90e8\u5206\uff1a\u5220\u9664\u53ca\u5176\u8c03\u6574*\/\n\/\/\u5220\u9664\u5ea6\u4e3a1\u7684\u70b9\nNode* DeleteNodeWithOneChild(Node* target){\n    \/\/\u83b7\u53d6\u5b69\u5b50\u8282\u70b9\n    Node* child = (target-&gt;left != NULL) ? (target-&gt;left) : (target-&gt;right);\n    \/\/\u5b69\u5b50\u8282\u70b9\u53d8\u9ed1\n    child-&gt;treeColor = BLACK;\n    \/\/\u5982\u679c\u5220\u9664\u7684\u662f\u6839\u8282\u70b9\n    if(target-&gt;parent == NULL){\n        child-&gt;parent = NULL;\n        free(target);\n        return child;\n    }\n    \/\/\u5982\u679c\u5220\u9664\u7684\u8282\u70b9\u662f\u666e\u901a\u8282\u70b9\n    child-&gt;parent = target-&gt;parent;\n    \/\/\u5982\u679ctarget\u662f\u7236\u4eb2\u8282\u70b9\u7684\u5de6\u5b69\u5b50\n    if(target == target-&gt;parent-&gt;left){\n        target-&gt;parent-&gt;left = child;\n    }\n    \/\/\u5982\u679ctarget\u662f\u7236\u4eb2\u8282\u70b9\u7684\u53f3\u5b69\u5b50\n    else{\n        target-&gt;parent-&gt;right = child;\n    }\n    free(target);\n    return child;\n}\n\n\/\/\u5ea6\u4e3a0\u7684\u5927\u7c7b\uff1a\u5982\u679c\u5220\u9664\u8282\u70b9\u662f\u7ea2\u8272\nNode* DeleteRedLeafNode(Node* target){\n    Node* father = target-&gt;parent;\n    (father-&gt;left == target) ? (father-&gt;left = NULL) : (father-&gt;right = NULL);\n    free(target);\n    return father;\n}\n\n\/\/\u5982\u679c\u5144\u5f1f\u8282\u70b9\u662f\u9ed1\u8272\u5e76\u4e14\u5b58\u5728\u7ea2\u8272\u8282\u70b9\uff08\u8fd4\u56de\u8c03\u6574\u540e\u7684\u5c40\u90e8\u5b50\u6811\u6839\u8282\u70b9\uff09\nNode* DeleteWhenHasRedNephews(Node* brother){\n    \/\/\u83b7\u53d6\u7956\u5148\u8282\u70b9\n    Node* ancester = brother-&gt;parent-&gt;parent;\n    \/\/\u83b7\u53d6\u7236\u4eb2\u8282\u70b9\n    Node* father = brother-&gt;parent;\n    Node* father_copy = father;\n\n    \/\/LL\u578b\n    if(brother == father-&gt;left &amp;&amp; NodeColor(brother-&gt;left) == RED){\n        \/\/\u989c\u8272\u4fee\u6539\n        brother-&gt;left-&gt;treeColor = brother-&gt;treeColor;\n        brother-&gt;treeColor = father-&gt;treeColor;\n        father-&gt;treeColor = BLACK;\n        \/\/\u65cb\u8f6c\n        father = rotateRight(father);\n    }\n    \/\/RR\u578b\n    else if(brother == father-&gt;right &amp;&amp; NodeColor(brother-&gt;right) == RED){\n        \/\/\u989c\u8272\u4fee\u6539\n        brother-&gt;right-&gt;treeColor = brother-&gt;treeColor;\n        brother-&gt;treeColor = father-&gt;treeColor;\n        father-&gt;treeColor = BLACK;\n        \/\/\u65cb\u8f6c\n        father = rotateLeft(father);\n    }\n    \/\/LR\u578b\n    else if(brother == father-&gt;left &amp;&amp; NodeColor(brother-&gt;left) == BLACK){\n        \/\/\u9996\u6b21\u8c03\u6574\uff0c\u8f6c\u5316\u4e3aLL\u578b\n        brother = rotateLeft(brother);\n        father-&gt;left = brother;\n        \/\/\u4e8c\u6b21\u65cb\u8f6c\n        father = rotateRight(father);\n    }\n    \/\/RL\u578b\n    else if(brother == father-&gt;right &amp;&amp; NodeColor(brother-&gt;right) == BLACK){\n        \/\/\u9996\u6b21\u8c03\u6574\uff0c\u8f6c\u5316\u4e3aRR\u578b\n        brother = rotateRight(brother);\n        father-&gt;right = brother;\n        \/\/\u4e8c\u6b21\u65cb\u8f6c\n        father = rotateLeft(father);\n    }\n    \/\/\u5c06\u65b0father\u8282\u70b9\u4e0e\u7956\u5148\u8282\u70b9\u8fde\u63a5\u8d77\u6765\u3002\n    \/\/\u5982\u679c\u7956\u5148\u4e0d\u5b58\u5728\uff0c\u5219\u76f4\u63a5\u8fd4\u56de\n    if(ancester == NULL){\n        return father;\n    }\n    \/\/\u5982\u679c\u7236\u4eb2\u8282\u70b9\u662f\u7956\u5148\u7684\u5de6\u5b69\u5b50\n    if(ancester-&gt;left == father_copy){\n        ancester-&gt;left = father;\n    }\n    \/\/\u5982\u679c\u7236\u4eb2\u8282\u70b9\u662f\u7956\u5148\u7684\u53f3\u5b69\u5b50\n    else{\n        ancester-&gt;right = father;\n    }\n    return father;\n}\n\n\/\/\u5982\u679c\u5220\u9664\u7684\u662f\u9ed1\u8272\u8282\u70b9\uff0c\u4e14\u5144\u5f1f\u4e3a\u7ea2\u8272\uff08\u8fd4\u56de\u8c03\u6574\u540e\u7684\u5c40\u90e8\u5b50\u6811\u6839\u8282\u70b9\uff09\nNode* DeleteBlackLeafNodeWithRedSibling(Node* brother){\n    \/\/\u58f0\u660e\u53d8\u91cf\n    Node* father = brother-&gt;parent;\n    Node* ancestor = father-&gt;parent;\n    Node* resultNode = father;\n    \/\/\u989c\u8272\u4ea4\u6362\n    TreeColor temp = brother-&gt;treeColor;\n    brother-&gt;treeColor = father-&gt;treeColor;\n    father-&gt;treeColor = temp;\n\n    \/\/\u65cb\u8f6c\u8c03\u6574\n    if(brother == father-&gt;left){\/\/\u53f3\u65cb\n        father = rotateRight(father);\n    }\n    else if(brother == father-&gt;right){\/\/\u5de6\u65cb\n        father = rotateLeft(father);\n    }\n    \/\/\u7236\u4eb2\u8282\u70b9\u662f\u6574\u68f5\u6811\u7684\u6839\u8282\u70b9\n    if(ancestor == NULL){\n        return resultNode;\n    }\n    \/\/\u66f4\u65b0\u7956\u5148\u8282\u70b9\u4e0e\u7236\u4eb2\u8282\u70b9\u7684\u5173\u7cfb\n    (ancestor-&gt;left == resultNode) ? (ancestor-&gt;left = father) : (ancestor-&gt;right = father);\n    return resultNode;\n}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5220\u9664\u8c03\u7528\u63a5\u53e3<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u5220\u9664\u51fd\u6570\nNode* TreeDelete(Node* root, int data){\n    \/\/\u83b7\u53d6\u76ee\u6807\u8282\u70b9\n    Node* cur = FindTargetNode(root,data);\n    if(cur == NULL) return root;\/\/\u8282\u70b9\u67e5\u627e\u51fa\u9519\n    \/\/\u6839\u636e\u5ea6\u7684\u60c5\u51b5\u5206\u7c7b\u5904\u7406\n    \/\/\u5982\u679c\u5ea6\u4e3a0\n    if(cur-&gt;left == NULL &amp;&amp; cur-&gt;right == NULL){\n        \/\/\u5982\u679c\u5220\u9664\u7684\u662f\u6839\u8282\u70b9\n        if(cur-&gt;parent == NULL){\n            free(cur);\n            return NULL;\n        }\n        \/\/\u89c2\u5bdf\u5220\u9664\u7684\u8282\u70b9\u662f\u5426\u4e3a\u7ea2\u8272\uff0c\u5982\u679c\u5220\u9664\u8282\u70b9\u662f\u7ea2\u8272\n        if(cur-&gt;treeColor == RED){\n            cur = DeleteRedLeafNode(cur);\n            return getRoot(cur);\n        }\n        \/\/\u5982\u679c\u5220\u9664\u8282\u70b9\u662f\u9ed1\u8272\n        \/\/\u83b7\u53d6\u5144\u5f1f\u8282\u70b9\n        Node* brother = brotherNode(cur);\n        \/\/\u5220\u9664\u64cd\u4f5c\n        (cur == cur-&gt;parent-&gt;left) ? (cur-&gt;parent-&gt;left = NULL) : (cur-&gt;parent-&gt;right = NULL);\n        free(cur);\n        cur = NULL;\n        \/\/\u8c03\u6574\n        while(1){\n            \/\/\u89c2\u5bdf\u5144\u5f1f\u8282\u70b9\u662f\u5426\u4e3a\u9ed1\u8272\uff0c\u5982\u679c\u4e3a\u9ed1\u8272\n            if(NodeColor(brother) == BLACK){\n                \/\/\u5224\u65ad\u5144\u5f1f\u8282\u70b9\u662f\u5426\u5b58\u5728\u7ea2\u8272\u5b69\u5b50\uff0c\u5982\u679c\u4e0d\u5b58\u5728\u7ea2\u8272\n                if(NodeColor(brother-&gt;left) == BLACK &amp;&amp; NodeColor(brother-&gt;right) == BLACK){\n                    brother-&gt;treeColor = RED;\/\/\u5144\u5f1f\u8282\u70b9\u53d8\u6210\u7ea2\u8272\n                    \/\/\u68c0\u67e5\u7236\u4eb2\u8282\u70b9\u662f\u5426\u4e3a\u7ea2\u8272\n                    if(NodeColor(brother-&gt;parent) == RED){\n                        brother-&gt;parent-&gt;treeColor = BLACK;\/\/\u7236\u4eb2\u8282\u70b9\u53d8\u9ed1\n                        return getRoot(brother);\n                    }\n                    \/\/\u5982\u679c\u7236\u4eb2\u8282\u70b9\u4e3a\u9ed1\u8272\uff0c\u5e76\u4e14\u662f\u6574\u4e2a\u7ea2\u9ed1\u6811\u7684\u6839\u8282\u70b9\u65f6\n                    else if(NodeColor(brother-&gt;parent) == BLACK &amp;&amp; brother-&gt;parent-&gt;parent == NULL){\n                        return brother-&gt;parent;\/\/\u7531\u4e8e\u7236\u4eb2\u8282\u70b9\u662f\u6839\u8282\u70b9\uff0c\u76f4\u63a5\u8fd4\u56de\n                    }\n                    \/\/\u5982\u679c\u7236\u4eb2\u8282\u70b9\u4e3a\u9ed1\u8272\uff0c\u5e76\u4e14\u7236\u4eb2\u8282\u70b9\u4e4b\u4e0a\u5b58\u5728\u66f4\u9ad8\u7ef4\u5ea6\u7684\u6811\n                    else{\n                        \/\/\u66f4\u65b0\u5144\u5f1f\u8282\u70b9\uff0c\u6ce8\u610f\u70b9\u63d0\u5347\u5230\u66f4\u9ad8\u5c42\u6b21\u7684\u7ef4\u5ea6\u4e0a\n                        Node* father = brother-&gt;parent;\n                        Node* ancestor = father-&gt;parent;\n                        brother = father != ancestor-&gt;left ? ancestor-&gt;left : ancestor-&gt;right;\n                    }\n                }\n                \/\/\u5982\u679c\u4e3a\u5b58\u5728\u7ea2\u8272\n                else{\n                    \/\/printf(\"\u6211\u8fdb\u5165\u4e860\u5ea6\u65e0\u53cc\u9ed1\u7684\u4f4d\u7f6e\\n\");\n                    cur = DeleteWhenHasRedNephews(brother);\n                    return getRoot(cur);\n                }\n            }\n            \/\/\u5982\u679c\u662f\u7ea2\u8272\n            else{\n                Node*temp = DeleteBlackLeafNodeWithRedSibling(brother);\n                brother = temp-&gt;left ? temp-&gt;left : temp-&gt;right;\n            }\n        }\n    }\n    \/\/\u5982\u679c\u5ea6\u4e3a1\n    else{\n        cur = DeleteNodeWithOneChild(cur);\n        return getRoot(cur);\n    } \n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u524d\u8a00 \u94fe\u8868\u8131\u79bb\u4e86\u6570\u7ec4\u7684\u7a7a\u95f4\u9650\u5236\uff0c\u7406\u8bba\u4e0a\u53ef\u4ee5\u65e0\u9650\u5ef6\u4f38\uff0c\u5177\u6709\u9ad8\u6548\u7684\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\uff0c\u4f46\u662f\u4e0e\u4e4b\u4ed8\u51fa\u7684\u4ee3\u4ef7\u662f\u2014\u2014\u94fe\u8868\u7684\u67e5 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,5],"tags":[17,18,33,22,23],"class_list":["post-1183","post","type-post","status-publish","format-standard","hentry","category-learning","category-data_structure","tag-c-2","tag-c","tag-linux","tag-pointer","tag-data_structure"],"_links":{"self":[{"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/posts\/1183","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1183"}],"version-history":[{"count":65,"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/posts\/1183\/revisions"}],"predecessor-version":[{"id":1401,"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/posts\/1183\/revisions\/1401"}],"wp:attachment":[{"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1183"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.chxzking.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}