{"id":583,"date":"2026-03-24T22:30:38","date_gmt":"2026-03-24T14:30:38","guid":{"rendered":"https:\/\/www.vanforever.com.cn\/?p=583"},"modified":"2026-03-24T22:37:28","modified_gmt":"2026-03-24T14:37:28","slug":"%e5%b9%b3%e8%a1%a1%e4%ba%8c%e5%8f%89%e6%a0%91%e7%9a%84%e9%ab%98%e5%ba%a6%e4%b8%8e%e8%8a%82%e7%82%b9%e6%95%b0%e5%85%b3%e7%b3%bb%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.vanforever.com.cn\/?p=583","title":{"rendered":"\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u9ad8\u5ea6\u4e0e\u8282\u70b9\u6570\u5173\u7cfb\u8be6\u89e3"},"content":{"rendered":"<p>\u535a\u4e3b\u7684\u820d\u53cb\u9762\u8bd5\u9047\u5230\u8001\u5e08\u63d0\u95ee\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u7b80\u5355\u601d\u8003\u540e\u8be2\u95eeAI\uff0c\u53d1\u73b0\u548c\u6211\u7684\u7b54\u6848\u4e0d\u540c\uff0c\u770b\u540e\u89c9\u5f97\u5f88\u6709\u610f\u601d\uff0c\u4fbf\u6574\u7406\u6210\u6587\u7ae0\u4ee5\u4f9b\u5b66\u4e60\uff0c\u5e0c\u671b\u80fd\u5e2e\u52a9\u5230\u5927\u5bb6\u3002<br \/>\n<div  class='collapse-block shadow-sm collapse-block-transparent collapsed hide-border-left'><div class='collapse-block-title'><span class='collapse-block-title-inner'>\u67e5\u770b\u7279\u8272\u56fe\u7247<\/span><i class='collapse-icon fa fa-angle-down'><\/i><\/div><div class='collapse-block-body' style='display:none;'><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/pic.vanforever.com.cn\/Vanforever\/20260324\/wallhaven-5y5mo5_3840x2400.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" data-original=\"https:\/\/pic.vanforever.com.cn\/Vanforever\/20260324\/wallhaven-5y5mo5_3840x2400.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" width=\"3840\" height=\"2400\" \/><\/div><\/div><\/div><\/p>\n<h2 id=\"\u4e00\u4ec0\u4e48\u662f\u5e73\u8861\u4e8c\u53c9\u6811\">\u4e00\u3001\u4ec0\u4e48\u662f\u5e73\u8861\u4e8c\u53c9\u6811\uff1f<\/h2>\n<h3 id=\"11-\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u95ee\u9898\">1.1 \u4e8c\u53c9\u641c\u7d22\u6811\u7684\u95ee\u9898<\/h3>\n<p>\u666e\u901a\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff08BST\uff09\u5728\u6781\u7aef\u60c5\u51b5\u4e0b\u4f1a\u9000\u5316\u6210\u94fe\u8868\u3002\u4f8b\u5982\u6309\u9012\u589e\u987a\u5e8f\u63d2\u5165 1, 2, 3, 4, 5\uff1a<\/p>\n<pre><code>1\n \\\n  2\n   \\\n    3\n     \\\n      4\n       \\\n        5\n<\/code><\/pre>\n<p>\u6b64\u65f6\u6811\u7684\u9ad8\u5ea6\u4e3a 4\uff08\u8fb9\u6570\uff09\uff0c\u67e5\u627e\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4ece\u7406\u60f3\u7684 <script type=\"math\/tex\">O(\\log n)<\/script> \u9000\u5316\u5230 <script type=\"math\/tex\">O(n)<\/script>\u3002<\/p>\n<h3 id=\"12-\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u5b9a\u4e49\">1.2 \u5e73\u8861\u4e8c\u53c9\u6811\u7684\u5b9a\u4e49<\/h3>\n<p>\u5e73\u8861\u4e8c\u53c9\u6811\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5b83\u901a\u8fc7<strong>\u5e73\u8861\u7ea6\u675f<\/strong>\u4fdd\u8bc1\u6811\u7684\u9ad8\u5ea6\u59cb\u7ec8\u7ef4\u6301\u5728 <script type=\"math\/tex\">O(\\log n)<\/script> \u7ea7\u522b\u3002\u6700\u5e38\u89c1\u7684\u5e73\u8861\u4e8c\u53c9\u6811\u5305\u62ec\uff1a<\/p>\n<ul>\n<li><strong>AVL\u6811<\/strong>\uff1a\u4efb\u4f55\u8282\u70b9\u7684\u5de6\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u4e0d\u8d85\u8fc7 1<\/li>\n<li><strong>\u7ea2\u9ed1\u6811<\/strong>\uff1a\u901a\u8fc7\u989c\u8272\u6807\u8bb0\u4fdd\u8bc1\u9ed1\u9ad8\u5e73\u8861<\/li>\n<\/ul>\n<p>\u672c\u6587\u4ee5 <strong>AVL\u6811<\/strong> \u4e3a\u4f8b\u8fdb\u884c\u8ba8\u8bba\u3002<\/p>\n<h3 id=\"13-\u6811\u7684\u9ad8\u5ea6\u5b9a\u4e49\u91cd\u8981\">1.3 \u6811\u7684\u9ad8\u5ea6\u5b9a\u4e49\uff08\u91cd\u8981\uff01\uff09<\/h3>\n<p>\u5728\u8ba8\u8bba\u9ad8\u5ea6\u4e4b\u524d\uff0c\u5fc5\u987b\u660e\u786e\u5b9a\u4e49\u3002\u6811\u7684\u9ad8\u5ea6\u6709\u4e24\u79cd\u5e38\u89c1\u5b9a\u4e49\uff1a<\/p>\n<figure class=\"table-figure\">\n<table>\n<thead>\n<tr>\n<th>\u5b9a\u4e49<\/th>\n<th>\u7a7a\u6811\u9ad8\u5ea6<\/th>\n<th>\u5355\u8282\u70b9\u9ad8\u5ea6<\/th>\n<th>\u6ee1\u4e8c\u53c9\u6811\uff083\u4e2a\u8282\u70b9\uff09\u9ad8\u5ea6<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u8fb9\u6570\u5b9a\u4e49<\/strong><\/td>\n<td>-1<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td><strong>\u8282\u70b9\u6570\u5b9a\u4e49<\/strong>\uff08\u5c42\u6570\uff09<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u672c\u6587\u91c7\u7528 <strong>\u8fb9\u6570\u5b9a\u4e49<\/strong>\uff08\u7b97\u6cd5\u5bfc\u8bba\u7b49\u6559\u6750\u7684\u6807\u51c6\uff09\uff1a<\/p>\n<ul>\n<li>\u7a7a\u6811\u7684\u9ad8\u5ea6\u4e3a <strong>-1<\/strong><\/li>\n<li>\u53ea\u6709\u4e00\u4e2a\u6839\u8282\u70b9\u7684\u6811\u9ad8\u5ea6\u4e3a <strong>0<\/strong><\/li>\n<li>\u6811\u7684\u9ad8\u5ea6 = \u6839\u8282\u70b9\u5230\u6700\u8fdc\u53f6\u5b50\u8282\u70b9\u7684\u8fb9\u6570<\/li>\n<\/ul>\n<p>\u5982\u679c\u9762\u8bd5\u6216\u8003\u8bd5\u4e2d\u9047\u5230\uff0c\u5efa\u8bae\u5148\u548c\u5bf9\u65b9\u786e\u8ba4\u5b9a\u4e49\u3002\u4e24\u79cd\u5b9a\u4e49\u53ef\u4ee5\u76f8\u4e92\u8f6c\u6362\uff1a<strong>\u8282\u70b9\u6570\u9ad8\u5ea6 = \u8fb9\u6570\u9ad8\u5ea6 + 1<\/strong>\u3002<\/p>\n<hr \/>\n<h2 id=\"\u4e8c\u8282\u70b9\u6570\u4e0e\u9ad8\u5ea6\u7684\u5173\u7cfb\">\u4e8c\u3001\u8282\u70b9\u6570\u4e0e\u9ad8\u5ea6\u7684\u5173\u7cfb<\/h2>\n<h3 id=\"21-\u7ed9\u5b9a\u9ad8\u5ea6--\u210e-\u6c42\u8282\u70b9\u6570\u7684\u8303\u56f4\">2.1 \u7ed9\u5b9a\u9ad8\u5ea6 <script type=\"math\/tex\">h<\/script>\uff0c\u6c42\u8282\u70b9\u6570\u7684\u8303\u56f4<\/h3>\n<h4 id=\"\u6700\u5c0f\u8282\u70b9\u6570\u6700\u7626\u7684-avl-\u6811\">\u6700\u5c0f\u8282\u70b9\u6570\uff08\u6700\u201c\u7626\u201d\u7684 AVL \u6811\uff09<\/h4>\n<p>\u9ad8\u5ea6\u4e3a <script type=\"math\/tex\">h<\/script> \u7684 AVL \u6811\uff0c\u8981\u6ee1\u8db3\u5e73\u8861\u6761\u4ef6\uff0c\u8282\u70b9\u6570\u4e0d\u80fd\u592a\u5c11\u3002\u9012\u63a8\u5173\u7cfb\u5982\u4e0b\uff1a<\/p>\n<div id=\"mathjax-n704\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u521d\u59cb\u6761\u4ef6\uff1a<\/p>\n<div id=\"mathjax-n706\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<div id=\"mathjax-n707\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u9010\u9879\u8ba1\u7b97\u5f97\u5230\uff1a<\/p>\n<figure class=\"table-figure\">\n<table>\n<thead>\n<tr>\n<th><script type=\"math\/tex\">h<\/script><\/th>\n<th>-1<\/th>\n<th>0<\/th>\n<th>1<\/th>\n<th>2<\/th>\n<th>3<\/th>\n<th>4<\/th>\n<th>5<\/th>\n<th>6<\/th>\n<th>7<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><script type=\"math\/tex\">n_{\\min}(h)<\/script><\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>7<\/td>\n<td>12<\/td>\n<td>20<\/td>\n<td>33<\/td>\n<td>54<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<h4 id=\"\u6700\u5927\u8282\u70b9\u6570\u6ee1\u4e8c\u53c9\u6811\">\u6700\u5927\u8282\u70b9\u6570\uff08\u6ee1\u4e8c\u53c9\u6811\uff09<\/h4>\n<p>\u5f53\u6811\u662f\u5b8c\u7f8e\u5e73\u8861\u65f6\uff0c\u8282\u70b9\u6570\u6700\u591a\uff1a<\/p>\n<div id=\"mathjax-n734\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p><strong>\u9a8c\u8bc1<\/strong>\uff1a<\/p>\n<ul>\n<li><script type=\"math\/tex\">h = 0<\/script>\uff08\u5355\u8282\u70b9\uff09\uff1a<script type=\"math\/tex\">2^{1} - 1 = 1<\/script> \u2705<\/li>\n<li><script type=\"math\/tex\">h = 1<\/script>\uff08\u6839+\u4e00\u5c42\uff09\uff1a<script type=\"math\/tex\">2^{2} - 1 = 3<\/script> \u2705<\/li>\n<\/ul>\n<blockquote><p><strong>\u6ce8\u610f<\/strong>\uff1a\u5982\u679c\u91c7\u7528\u8282\u70b9\u6570\u5b9a\u4e49\uff08\u5c42\u6570\uff09\uff0c\u516c\u5f0f\u53d8\u4e3a <script type=\"math\/tex\">n_{\\max}(H) = 2^{H} - 1<\/script>\uff0c\u5176\u4e2d <script type=\"math\/tex\">H = h + 1<\/script>\u3002<\/p><\/blockquote>\n<h4 id=\"\u8282\u70b9\u6570\u8303\u56f4\">\u8282\u70b9\u6570\u8303\u56f4<\/h4>\n<p>\u56e0\u6b64\uff0c\u7ed9\u5b9a\u9ad8\u5ea6 <script type=\"math\/tex\">h<\/script>\uff0c\u8282\u70b9\u6570 <script type=\"math\/tex\">n<\/script> \u6ee1\u8db3\uff1a<\/p>\n<div id=\"mathjax-n745\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<h3 id=\"22-\u7ed9\u5b9a\u8282\u70b9\u6570--\ud835\udc5b-\u6c42\u9ad8\u5ea6\u7684\u8303\u56f4\">2.2 \u7ed9\u5b9a\u8282\u70b9\u6570 <script type=\"math\/tex\">n<\/script>\uff0c\u6c42\u9ad8\u5ea6\u7684\u8303\u56f4<\/h3>\n<h4 id=\"\u6700\u5c0f\u9ad8\u5ea6\u6811\u5c3d\u91cf\u586b\u6ee1\">\u6700\u5c0f\u9ad8\u5ea6\uff08\u6811\u5c3d\u91cf\u586b\u6ee1\uff09<\/h4>\n<p>\u5f53\u6811\u5c3d\u53ef\u80fd\u63a5\u8fd1\u5b8c\u5168\u4e8c\u53c9\u6811\u65f6\uff0c\u9ad8\u5ea6\u6700\u5c0f\u3002\u6709\u4e24\u79cd\u7b49\u4ef7\u7684\u5199\u6cd5\uff1a<\/p>\n<div id=\"mathjax-n749\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u6216\u8005\uff1a<\/p>\n<div id=\"mathjax-n751\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p><strong>\u9a8c\u8bc1<\/strong>\uff1a<script type=\"math\/tex\">n=3<\/script> \u65f6\uff0c<script type=\"math\/tex\">\\lfloor \\log_2 3 \\rfloor = \\lfloor 1.58 \\rfloor = 1<\/script>\uff0c\u6b63\u786e\u3002<\/p>\n<blockquote><p><strong>\u5e38\u89c1\u7591\u60d1<\/strong>\uff1a\u5411\u4e0a\u53d6\u6574\u51cf1 \u548c \u5411\u4e0b\u53d6\u6574+1 \u4e00\u6837\u5417\uff1f<br \/>\n<strong>\u7b54\u6848<\/strong>\uff1a\u4e0d\u4e00\u6837\u3002<script type=\"math\/tex\">\\lceil x \\rceil - 1<\/script> \u548c <script type=\"math\/tex\">\\lfloor x \\rfloor + 1<\/script> \u901a\u5e38\u4e0d\u76f8\u7b49\u3002\u4f46\u5728\u6700\u5c0f\u9ad8\u5ea6\u516c\u5f0f\u4e2d\uff0c<script type=\"math\/tex\">\\lceil \\log_2(n+1) \\rceil - 1 = \\lfloor \\log_2 n \\rfloor<\/script>\uff0c\u8fd9\u662f\u4e00\u4e2a\u7279\u4f8b\uff0c\u4e0d\u662f\u901a\u7528\u89c4\u5f8b\u3002<\/p><\/blockquote>\n<h4 id=\"\u6700\u5927\u9ad8\u5ea6\u6811\u5c3d\u91cf\u7626\">\u6700\u5927\u9ad8\u5ea6\uff08\u6811\u5c3d\u91cf\u7626\uff09<\/h4>\n<p>\u5f53\u6811\u5c3d\u91cf\u201c\u7626\u9ad8\u201d\u4f46\u4ecd\u6ee1\u8db3 AVL \u6761\u4ef6\u65f6\uff0c\u9ad8\u5ea6\u6700\u5927\u3002\u6700\u5927\u9ad8\u5ea6\u662f\u6ee1\u8db3 <script type=\"math\/tex\">n_{\\min}(h) \\le n<\/script> \u7684\u6700\u5927 <script type=\"math\/tex\">h<\/script>\uff1a<\/p>\n<div id=\"mathjax-n757\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<h4 id=\"\u5c0f--\ud835\udc5b--\u7684\u5b8c\u6574\u5bf9\u7167\u8868\u8fb9\u6570\u5b9a\u4e49\">\u5c0f <script type=\"math\/tex\">n<\/script> \u7684\u5b8c\u6574\u5bf9\u7167\u8868\uff08\u8fb9\u6570\u5b9a\u4e49\uff09<\/h4>\n<figure class=\"table-figure\">\n<table>\n<thead>\n<tr>\n<th><script type=\"math\/tex\">n<\/script><\/th>\n<th><script type=\"math\/tex\">h_{\\min}<\/script><\/th>\n<th><script type=\"math\/tex\">h_{\\max}<\/script><\/th>\n<th>\u8bf4\u660e<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>-1<\/td>\n<td>-1<\/td>\n<td>\u7a7a\u6811<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>\u5355\u8282\u70b9<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>\u4e24\u4e2a\u8282\u70b9\u53ea\u80fd\u5f62\u6210\u4e00\u5c42<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>\u9ad8\u5ea62\u9700\u8981\u81f3\u5c114\u4e2a\u8282\u70b9\uff0c\u6240\u4ee53\u4e2a\u8282\u70b9\u6700\u9ad8\u53ea\u80fd\u5230\u9ad8\u5ea61<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>\u521a\u597d\u8fbe\u5230\u9ad8\u5ea62\u7684\u6700\u5c0f\u8282\u70b9\u6570<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>\u9ad8\u5ea63\u9700\u8981\u81f3\u5c117\u4e2a\u8282\u70b9<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>\u9ad8\u5ea63\u9700\u8981\u81f3\u5c117\u4e2a\u8282\u70b9<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>\u521a\u597d\u8fbe\u5230\u9ad8\u5ea63\u7684\u6700\u5c0f\u8282\u70b9\u6570<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<td>\u9ad8\u5ea64\u9700\u8981\u81f3\u5c1112\u4e2a\u8282\u70b9<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<td>\u9ad8\u5ea64\u9700\u8981\u81f3\u5c1112\u4e2a\u8282\u70b9<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<td>\u9ad8\u5ea64\u9700\u8981\u81f3\u5c1112\u4e2a\u8282\u70b9<\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<td>\u9ad8\u5ea64\u9700\u8981\u81f3\u5c1112\u4e2a\u8282\u70b9<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>\u521a\u597d\u8fbe\u5230\u9ad8\u5ea64\u7684\u6700\u5c0f\u8282\u70b9\u6570<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<blockquote><p><strong>\u5982\u679c\u4f60\u91c7\u7528\u8282\u70b9\u6570\u5b9a\u4e49\uff08\u5c42\u6570\uff09<\/strong>\uff0c\u53ea\u9700\u5c06\u6240\u6709\u9ad8\u5ea6\u503c\u52a01\u5373\u53ef\u3002<\/p><\/blockquote>\n<hr \/>\n<h2 id=\"\u4e09\u8fd1\u4f3c\u516c\u5f0f\u4e0e-144-\u7684\u6765\u6e90\">\u4e09\u3001\u8fd1\u4f3c\u516c\u5f0f\u4e0e 1.44 \u7684\u6765\u6e90<\/h2>\n<h3 id=\"31-\u6e10\u8fd1\u8fd1\u4f3c\">3.1 \u6e10\u8fd1\u8fd1\u4f3c<\/h3>\n<p>\u5bf9\u4e8e\u8f83\u5927\u7684 <script type=\"math\/tex\">n<\/script>\uff0cAVL \u6811\u7684\u9ad8\u5ea6\u8303\u56f4\u53ef\u4ee5\u8fd1\u4f3c\u4e3a\uff1a<\/p>\n<ul>\n<li>\u6700\u5c0f\u9ad8\u5ea6\uff1a<script type=\"math\/tex\">h_{\\min} \\approx \\log_2 n<\/script><\/li>\n<li>\u6700\u5927\u9ad8\u5ea6\uff1a<script type=\"math\/tex\">h_{\\max} \\approx 1.44 \\log_2 n<\/script><\/li>\n<\/ul>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0cAVL \u6811\u7684\u9ad8\u5ea6\u6700\u591a\u6bd4\u5b8c\u5168\u4e8c\u53c9\u6811\u9ad8\u51fa\u7ea6 <strong>44%<\/strong>\u3002<\/p>\n<h3 id=\"32-\u4e3a\u4ec0\u4e48\u662f-144\">3.2 \u4e3a\u4ec0\u4e48\u662f 1.44\uff1f<\/h3>\n<p>\u8fd9\u4e2a\u7cfb\u6570\u6765\u81ea AVL \u6811\u6700\u5c0f\u8282\u70b9\u6570\u7684\u9012\u63a8\u4e0e\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u5173\u7cfb\u3002<\/p>\n<h4 id=\"\u7b2c\u4e00\u6b65\u9012\u63a8\u8fd1\u4f3c\">\u7b2c\u4e00\u6b65\uff1a\u9012\u63a8\u8fd1\u4f3c<\/h4>\n<p>\u5ffd\u7565\u9012\u63a8\u4e2d\u7684 <script type=\"math\/tex\">+1<\/script>\uff1a<\/p>\n<div id=\"mathjax-n846\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u8fd9\u4e0e\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u5f62\u5f0f\u76f8\u540c\u3002<\/p>\n<h4 id=\"\u7b2c\u4e8c\u6b65\u6590\u6ce2\u90a3\u5951\u6570\u5217\u4e0e\u9ec4\u91d1\u5206\u5272\u6bd4\">\u7b2c\u4e8c\u6b65\uff1a\u6590\u6ce2\u90a3\u5951\u6570\u5217\u4e0e\u9ec4\u91d1\u5206\u5272\u6bd4<\/h4>\n<p>\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u5b9a\u4e49\u662f\uff1a<\/p>\n<div id=\"mathjax-n850\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u901a\u89e3\u662f\u6bd4\u5185\u516c\u5f0f\uff1a<\/p>\n<div id=\"mathjax-n852\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u5176\u4e2d <script type=\"math\/tex\">\\phi = \\frac{1+\\sqrt{5}}{2} \\approx 1.618<\/script>\uff0c\u662f\u9ec4\u91d1\u5206\u5272\u6bd4\u3002<\/p>\n<p>\u5f53 <script type=\"math\/tex\">n<\/script> \u8f83\u5927\u65f6\uff0c\u7b2c\u4e8c\u9879\u8d8b\u8fd1\u4e8e 0\uff0c\u6240\u4ee5\uff1a<\/p>\n<div id=\"mathjax-n855\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u5bf9\u4e8e AVL \u6811\uff1a<\/p>\n<div id=\"mathjax-n857\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<h4 id=\"\u7b2c\u4e09\u6b65\u53cd\u89e3\u9ad8\u5ea6\">\u7b2c\u4e09\u6b65\uff1a\u53cd\u89e3\u9ad8\u5ea6<\/h4>\n<p>\u7531\u8fd1\u4f3c\u516c\u5f0f\uff1a<\/p>\n<div id=\"mathjax-n860\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u4e24\u8fb9\u53d6\u81ea\u7136\u5bf9\u6570\uff1a<\/p>\n<div id=\"mathjax-n862\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u5ffd\u7565\u5e38\u6570\u9879\uff08\u5f53 <script type=\"math\/tex\">n<\/script> \u5f88\u5927\u65f6\uff0c<script type=\"math\/tex\">\\ln n<\/script> \u8fdc\u5927\u4e8e\u5e38\u6570\uff09\uff0c\u5f97\u5230\uff1a<\/p>\n<div id=\"mathjax-n864\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p><strong>\u8865\u5145\u8bf4\u660e<\/strong>\uff1a\u4e3a\u4ec0\u4e48\u4e0a\u9762\u662f <script type=\"math\/tex\">h+2<\/script>\uff0c\u8fd9\u91cc\u53d8\u6210\u4e86 <script type=\"math\/tex\">h<\/script>\uff1f<\/p>\n<p>\u56e0\u4e3a\u4e25\u683c\u63a8\u5bfc\u5f97\u5230\u7684\u662f <script type=\"math\/tex\">h \\approx \\frac{\\ln n}{\\ln \\phi} - 2<\/script>\u3002\u5e38\u6570 <script type=\"math\/tex\">-2<\/script> \u5728\u6e10\u8fd1\u5206\u6790\u4e2d\u4e0d\u5f71\u54cd\u7cfb\u6570\uff0c\u56e0\u6b64\u901a\u5e38\u7b80\u5199\u4e3a <script type=\"math\/tex\">h \\approx \\frac{\\ln n}{\\ln \\phi}<\/script>\u3002\u6211\u4eec\u6700\u7ec8\u5173\u5fc3\u7684\u662f <script type=\"math\/tex\">h<\/script> \u4e0e <script type=\"math\/tex\">\\log_2 n<\/script> \u7684\u6bd4\u4f8b\u5173\u7cfb\uff0c\u5e38\u6570\u9879\u53ef\u4ee5\u5ffd\u7565\u3002<\/p>\n<h4 id=\"\u7b2c\u56db\u6b65\u6362\u6210\u4ee5-2-\u4e3a\u5e95\u7684\u5bf9\u6570\">\u7b2c\u56db\u6b65\uff1a\u6362\u6210\u4ee5 2 \u4e3a\u5e95\u7684\u5bf9\u6570<\/h4>\n<p><strong>\u6211\u4eec\u7684\u76ee\u6807\u662f\u627e\u5230 <script type=\"math\/tex\">h<\/script> \u4e0e <script type=\"math\/tex\">\\log_2 n<\/script> \u7684\u6bd4\u4f8b\u5173\u7cfb<\/strong>\u3002\u56e0\u6b64\u8bbe\uff1a<\/p>\n<div id=\"mathjax-n869\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u5176\u4e2d <script type=\"math\/tex\">c<\/script> \u5c31\u662f\u6211\u4eec\u8981\u8ba1\u7b97\u7684\u7cfb\u6570\u3002<\/p>\n<p>\u5c06 <script type=\"math\/tex\">h \\approx \\frac{\\ln n}{\\ln \\phi}<\/script> \u4ee3\u5165\uff1a<\/p>\n<div id=\"mathjax-n872\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u7531\u4e8e <script type=\"math\/tex\">\\log_2 n = \\frac{\\ln n}{\\ln 2}<\/script>\uff0c\u4ee3\u5165\u5f97\uff1a<\/p>\n<div id=\"mathjax-n874\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u4e24\u8fb9\u540c\u65f6\u9664\u4ee5 <script type=\"math\/tex\">\\ln n<\/script>\uff08<script type=\"math\/tex\">n > 1<\/script> \u65f6 <script type=\"math\/tex\">\\ln n \\neq 0<\/script>\uff09\uff1a<\/p>\n<div id=\"mathjax-n876\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u56e0\u6b64\uff1a<\/p>\n<div id=\"mathjax-n878\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u4ee3\u5165\u6570\u503c\uff1a<\/p>\n<ul>\n<li><script type=\"math\/tex\">\\ln 2 \\approx 0.693147<\/script><\/li>\n<li><script type=\"math\/tex\">\\ln \\phi = \\ln 1.618034 \\approx 0.481212<\/script><\/li>\n<\/ul>\n<div id=\"mathjax-n885\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<h4 id=\"\u7b2c\u4e94\u6b65\u7ed3\u8bba\">\u7b2c\u4e94\u6b65\uff1a\u7ed3\u8bba<\/h4>\n<div id=\"mathjax-n887\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<hr \/>\n<h3 id=\"33-\u8865\u5145\u6590\u6ce2\u90a3\u5951\u6570\u5217\u4e0e\u9ec4\u91d1\u5206\u5272\u6bd4\u7684\u5173\u7cfb\">3.3 \u8865\u5145\uff1a\u6590\u6ce2\u90a3\u5951\u6570\u5217\u4e0e\u9ec4\u91d1\u5206\u5272\u6bd4\u7684\u5173\u7cfb<\/h3>\n<p>\u4e3a\u4ec0\u4e48\u6590\u6ce2\u90a3\u5951\u6570\u5217\u4f1a\u6d89\u53ca <script type=\"math\/tex\">\\phi<\/script>\uff1f<\/p>\n<p>\u4ece\u9012\u63a8 <script type=\"math\/tex\">F(n) = F(n-1) + F(n-2)<\/script> \u51fa\u53d1\uff0c\u5047\u8bbe\u6bd4\u503c\u8d8b\u4e8e\u5e38\u6570 <script type=\"math\/tex\">r<\/script>\uff0c\u5373 <script type=\"math\/tex\">F(n) \\approx r \\cdot F(n-1)<\/script>\uff0c\u4ee3\u5165\u5f97\uff1a<\/p>\n<div id=\"mathjax-n892\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u4e24\u8fb9\u9664\u4ee5 <script type=\"math\/tex\">F(n-2)<\/script>\uff1a<\/p>\n<div id=\"mathjax-n894\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u5f53 <script type=\"math\/tex\">n<\/script> \u5f88\u5927\u65f6\uff0c<script type=\"math\/tex\">\\frac{F(n-1)}{F(n-2)} \\to r<\/script>\uff0c\u6240\u4ee5\uff1a<\/p>\n<div id=\"mathjax-n896\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u8fd9\u6b63\u662f\u9ec4\u91d1\u5206\u5272\u6bd4\u6ee1\u8db3\u7684\u65b9\u7a0b\uff0c\u56e0\u6b64 <script type=\"math\/tex\">r = \\phi<\/script>\u3002\u6240\u4ee5\u4efb\u4f55\u5f62\u5982 <script type=\"math\/tex\">F(n) = F(n-1) + F(n-2)<\/script> \u7684\u9012\u63a8\uff0c\u5176\u89e3\u90fd\u4f1a\u6d89\u53ca <script type=\"math\/tex\">\\phi<\/script>\u3002<\/p>\n<hr \/>\n<h2 id=\"\u56db\u4e3a\u4ec0\u4e48-avl-\u6811\u7684\u5f62\u72b6\u4e0d\u552f\u4e00\">\u56db\u3001\u4e3a\u4ec0\u4e48 AVL \u6811\u7684\u5f62\u72b6\u4e0d\u552f\u4e00\uff1f<\/h2>\n<h3 id=\"41-\u5e73\u8861\u6761\u4ef6\u7684\u677e\u5f1b\u6027\">4.1 \u5e73\u8861\u6761\u4ef6\u7684\u677e\u5f1b\u6027<\/h3>\n<p>AVL \u6811\u53ea\u8981\u6c42\u5de6\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee \u2264 1\uff0c\u5e76\u6ca1\u6709\u8981\u6c42\u5f62\u72b6\u552f\u4e00\u3002\u56e0\u6b64\uff0c\u7ed9\u5b9a\u76f8\u540c\u7684\u8282\u70b9\u96c6\u5408\uff0c\u53ef\u4ee5\u6784\u9020\u51fa\u591a\u79cd\u4e0d\u540c\u7684 AVL \u6811\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u8282\u70b9\u96c6 {1, 2, 3} \u53ef\u4ee5\u6784\u9020\uff1a<\/p>\n<ul>\n<li><strong>\u5f62\u72b6 A<\/strong>\uff1a2 \u4e3a\u6839\uff0c1 \u548c 3 \u5206\u5de6\u53f3 \u2192 \u5b8c\u7f8e\u5e73\u8861<\/li>\n<li><strong>\u5f62\u72b6 B<\/strong>\uff1a1 \u4e3a\u6839\uff0c2 \u4e3a\u53f3\u5b69\u5b50\uff0c3 \u4e3a 2 \u7684\u53f3\u5b69\u5b50 \u2192 \u5e73\u8861\u56e0\u5b50\u4e3a (0, 1, 0)\uff0c\u4ecd\u6ee1\u8db3 AVL \u6761\u4ef6<\/li>\n<\/ul>\n<h3 id=\"42-\u4ec0\u4e48\u65f6\u5019\u5f62\u72b6\u552f\u4e00\">4.2 \u4ec0\u4e48\u65f6\u5019\u5f62\u72b6\u552f\u4e00\uff1f<\/h3>\n<p>\u53ea\u6709\u5f53\u7ea6\u675f\u6761\u4ef6\u975e\u5e38\u5f3a\u65f6\u624d\u4f1a\u552f\u4e00\uff0c\u4f8b\u5982\uff1a<\/p>\n<ul>\n<li><strong>\u5b8c\u5168\u4e8c\u53c9\u6811<\/strong>\uff1a\u7ed9\u5b9a <script type=\"math\/tex\">n<\/script>\uff0c\u5f62\u72b6\u552f\u4e00<\/li>\n<li><strong>\u4e8c\u53c9\u641c\u7d22\u6811 + \u56fa\u5b9a\u63d2\u5165\u987a\u5e8f<\/strong>\uff1a\u5f62\u72b6\u552f\u4e00\uff08\u4f46\u987a\u5e8f\u53d8\u5219\u5f62\u72b6\u53d8\uff09<\/li>\n<\/ul>\n<p>\u5e73\u8861\u4e8c\u53c9\u6811\u4e0d\u5c5e\u4e8e\u8fd9\u79cd\u60c5\u51b5\u3002<\/p>\n<hr \/>\n<h2 id=\"\u4e94\u5e38\u89c1\u7591\u60d1\u89e3\u7b54\">\u4e94\u3001\u5e38\u89c1\u7591\u60d1\u89e3\u7b54<\/h2>\n<h3 id=\"51-\u5411\u4e0a\u53d6\u6574\u51cf1-\u548c-\u5411\u4e0b\u53d6\u65741-\u4e00\u6837\u5417\">5.1 \u5411\u4e0a\u53d6\u6574\u51cf1 \u548c \u5411\u4e0b\u53d6\u6574+1 \u4e00\u6837\u5417\uff1f<\/h3>\n<p><strong>\u4e0d\u4e00\u6837<\/strong>\u3002<script type=\"math\/tex\">\\lceil x \\rceil - 1<\/script> \u548c <script type=\"math\/tex\">\\lfloor x \\rfloor + 1<\/script> \u901a\u5e38\u4e0d\u76f8\u7b49\u3002\u4f8b\u5982 <script type=\"math\/tex\">x = 1.2<\/script> \u65f6\uff0c\u524d\u8005\u4e3a 1\uff0c\u540e\u8005\u4e3a 2\u3002<\/p>\n<p>\u4f46\u5728\u6700\u5c0f\u9ad8\u5ea6\u516c\u5f0f\u4e2d\uff0c<script type=\"math\/tex\">\\lceil \\log_2(n+1) \\rceil - 1 = \\lfloor \\log_2 n \\rfloor<\/script>\uff0c\u8fd9\u662f\u4e00\u4e2a\u7279\u4f8b\uff0c\u4e0d\u662f\u901a\u7528\u89c4\u5f8b\u3002<\/p>\n<h3 id=\"52-\u8282\u70b9\u6570--\ud835\udc5b--1--\u65f6\u516c\u5f0f--\ud835\udc5b-max--\u210e---2-\u210e--1-\u2212-1--\u600e\u4e48\u5904\u7406\">5.2 \u8282\u70b9\u6570 <script type=\"math\/tex\">n=1<\/script> \u65f6\uff0c\u516c\u5f0f <script type=\"math\/tex\">n_{\\max}(h) = 2^{h+1} - 1<\/script> \u600e\u4e48\u5904\u7406\uff1f<\/h3>\n<p>\u8fd9\u4e2a\u516c\u5f0f\u662f <strong>\u7ed9\u5b9a\u9ad8\u5ea6\u6c42\u6700\u5927\u8282\u70b9\u6570<\/strong>\uff0c\u4e0d\u662f\u7ed9\u5b9a\u8282\u70b9\u6570\u6c42\u9ad8\u5ea6\u3002\u5f53 <script type=\"math\/tex\">h = 0<\/script> \u65f6\uff1a<\/p>\n<div id=\"mathjax-n923\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" contenteditable=\"false\" spellcheck=\"false\" data-math-tag-before=\"0\" data-math-tag-after=\"0\" data-math-labels=\"[]\">\n<div class=\"md-math-container\"><\/div>\n<\/div>\n<p>\u6b63\u786e\uff0c\u5355\u8282\u70b9\u6811\u6700\u591a\u6709 1 \u4e2a\u8282\u70b9\u3002<\/p>\n<h3 id=\"53-\u5982\u679c\u6211\u91c7\u7528\u8282\u70b9\u6570\u5b9a\u4e49\u5c42\u6570\u516c\u5f0f\u600e\u4e48\u53d8\">5.3 \u5982\u679c\u6211\u91c7\u7528\u8282\u70b9\u6570\u5b9a\u4e49\uff08\u5c42\u6570\uff09\uff0c\u516c\u5f0f\u600e\u4e48\u53d8\uff1f<\/h3>\n<figure class=\"table-figure\">\n<table>\n<thead>\n<tr>\n<th>\u516c\u5f0f<\/th>\n<th>\u8fb9\u6570\u5b9a\u4e49\uff08\u672c\u6587\u91c7\u7528\uff09<\/th>\n<th>\u8282\u70b9\u6570\u5b9a\u4e49\uff08\u5c42\u6570\uff09<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u6700\u5927\u8282\u70b9\u6570<\/td>\n<td><script type=\"math\/tex\">n_{\\max}(h) = 2^{h+1} - 1<\/script><\/td>\n<td><script type=\"math\/tex\">n_{\\max}(H) = 2^{H} - 1<\/script><\/td>\n<\/tr>\n<tr>\n<td>\u6700\u5c0f\u9ad8\u5ea6<\/td>\n<td><script type=\"math\/tex\">h_{\\min}(n) = \\lfloor \\log_2 n \\rfloor<\/script><\/td>\n<td><script type=\"math\/tex\">H_{\\min}(n) = \\lfloor \\log_2 n \\rfloor + 1<\/script><\/td>\n<\/tr>\n<tr>\n<td>\u5173\u7cfb<\/td>\n<td>&#8211;<\/td>\n<td><script type=\"math\/tex\">H = h + 1<\/script><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<h3 id=\"54-\u6700\u5c0f\u9ad8\u5ea6\u80fd\u5199\u6210---log-2-\u2061-\ud835\udc5b---1--\u5417\">5.4 \u6700\u5c0f\u9ad8\u5ea6\u80fd\u5199\u6210 <script type=\"math\/tex\">\\lfloor \\log_2 n \\rfloor + 1<\/script> \u5417\uff1f<\/h3>\n<p><strong>\u53ef\u4ee5\uff0c\u4f46\u524d\u63d0\u662f\u91c7\u7528\u8282\u70b9\u6570\u5b9a\u4e49\uff08\u5c42\u6570\uff09<\/strong>\u3002\u5982\u679c\u4f60\u91c7\u7528\u8fb9\u6570\u5b9a\u4e49\uff0c\u6700\u5c0f\u9ad8\u5ea6\u5c31\u662f <script type=\"math\/tex\">\\lfloor \\log_2 n \\rfloor<\/script>\uff0c\u4e0d\u9700\u8981\u52a0 1\u3002<\/p>\n<p>\u5efa\u8bae\u5728\u6587\u7ae0\u5f00\u5934\u660e\u786e\u4f60\u4f7f\u7528\u7684\u5b9a\u4e49\uff0c\u907f\u514d\u6df7\u6dc6\u3002<\/p>\n<hr \/>\n<h2 id=\"\u516d\u603b\u7ed3\">\u516d\u3001\u603b\u7ed3<\/h2>\n<figure class=\"table-figure\">\n<table>\n<thead>\n<tr>\n<th>\u95ee\u9898<\/th>\n<th>\u7ed3\u8bba<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>AVL \u6811\u7684\u9ad8\u5ea6\u8303\u56f4<\/td>\n<td><script type=\"math\/tex\">\\log_2 n \\le h \\le 1.44 \\log_2 n<\/script>\uff08\u8fb9\u6570\u5b9a\u4e49\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u4e3a\u4ec0\u4e48\u662f 1.44<\/td>\n<td>\u6765\u81ea\u6590\u6ce2\u90a3\u5951\u9012\u63a8\u4e0e\u9ec4\u91d1\u5206\u5272\u6bd4 <script type=\"math\/tex\">\\phi<\/script>\uff1a<script type=\"math\/tex\">\\frac{\\ln 2}{\\ln \\phi} \\approx 1.44<\/script><\/td>\n<\/tr>\n<tr>\n<td>\u5f62\u72b6\u662f\u5426\u552f\u4e00<\/td>\n<td>\u5426\uff0c\u5e73\u8861\u6761\u4ef6\u5141\u8bb8\u591a\u79cd\u5408\u6cd5\u7ed3\u6784<\/td>\n<\/tr>\n<tr>\n<td>\u4e24\u79cd\u9ad8\u5ea6\u5b9a\u4e49\u5982\u4f55\u8f6c\u6362<\/td>\n<td>\u8282\u70b9\u6570\u9ad8\u5ea6 = \u8fb9\u6570\u9ad8\u5ea6 + 1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<hr \/>\n<h2 id=\"\u4e03\u53c2\u8003\u8d44\u6599\">\u4e03\u3001\u53c2\u8003\u8d44\u6599<\/h2>\n<ul>\n<li>AVL \u6811\u9012\u63a8\u516c\u5f0f\uff1a<script type=\"math\/tex\">n_{\\min}(h) = n_{\\min}(h-1) + n_{\\min}(h-2) + 1<\/script><\/li>\n<li>\u9ec4\u91d1\u5206\u5272\u6bd4\uff1a<script type=\"math\/tex\">\\phi = \\frac{1+\\sqrt{5}}{2}<\/script><\/li>\n<li>\u6590\u6ce2\u90a3\u5951\u6bd4\u5185\u516c\u5f0f\uff1a<script type=\"math\/tex\">F(n) = \\frac{\\phi^n - (-\\phi)^{-n}}{\\sqrt{5}}<\/script><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u535a\u4e3b\u7684\u820d\u53cb\u9762\u8bd5\u9047\u5230\u8001\u5e08\u63d0\u95ee\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u7b80\u5355\u601d\u8003\u540e\u8be2\u95eeAI\uff0c\u53d1\u73b0\u548c\u6211\u7684\u7b54\u6848\u4e0d\u540c\uff0c\u770b\u540e\u89c9\u5f97\u5f88\u6709\u610f\u601d\uff0c\u4fbf\u6574\u7406\u6210\u6587\u7ae0\u4ee5 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,16],"tags":[14,12],"class_list":["post-583","post","type-post","status-publish","format-standard","hentry","category-18","category-16","tag-14","tag-12"],"_links":{"self":[{"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=\/wp\/v2\/posts\/583","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=583"}],"version-history":[{"count":4,"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=\/wp\/v2\/posts\/583\/revisions"}],"predecessor-version":[{"id":588,"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=\/wp\/v2\/posts\/583\/revisions\/588"}],"wp:attachment":[{"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=583"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=583"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vanforever.com.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}