{"id":361,"date":"2024-03-16T22:00:47","date_gmt":"2024-03-16T14:00:47","guid":{"rendered":"https:\/\/ultserver.com\/blog\/?p=361"},"modified":"2024-04-08T14:42:28","modified_gmt":"2024-04-08T06:42:28","slug":"%e5%88%b7%e9%a2%98%e6%97%b6%e5%ad%a6%e5%88%b0%e7%9a%84tips","status":"publish","type":"post","link":"https:\/\/ultserver.com\/blog\/programming-problems\/%e5%88%b7%e9%a2%98%e6%97%b6%e5%ad%a6%e5%88%b0%e7%9a%84tips\/","title":{"rendered":"\u5237\u9898\u65f6\u5b66\u5230\u7684TIPS"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\u8fb9\u754c\u6761\u4ef6<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$10^{9}$\u9700\u8981\u989d\u5916\u6ce8\u610f\uff0c\u901a\u5e38\u4f1a\u51fa\u73b0int\u6ea2\u51fa\u7684\u95ee\u9898<\/li>\n\n\n\n<li>256MB\u5185\u5b58\u5927\u7ea6\u53ef\u4ee5\u5b58\u50a8 8000 * 8000 \u768432\u4f4d\u6570\u636e<\/li>\n\n\n\n<li>\u5982\u679c\u5185\u5b58\u5141\u8bb8\uff0c\u6709\u65f6\u53ef\u4ee5\u4f7f\u7528\u6570\u7ec4\u66ff\u4ee3unordered_map\uff0c\u56e0\u4e3aunordered_map\u9700\u8981\u7f16\u5199\u989d\u5916\u7684\u54c8\u5e0c\u51fd\u6570\u6765\u8ba1\u7b97pair\u7b49\u590d\u6742\u7c7b\u578b\u952e\u7684\u54c8\u5e0c\u503c<\/li>\n\n\n\n<li>\u56de\u6eaf\u95ee\u9898\u901a\u5e38\u53ef\u4ee5\u4f7f\u7528\u7a7a\u95f4\u6362\u65f6\u95f4\uff0c\u8bb0\u5f55\u5404\u4e2a\u5206\u652f\u7684\u89e3\uff0c\u51cf\u5c11\u91cd\u590d\u8ba1\u7b97<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">\u4e8c\u53c9\u6811<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b8c\u5168\u4e8c\u53c9\u6811<\/h2>\n\n\n\n<p>\u6570\u7ec4\u8868\u793a\u7684\u5b8c\u5168\u4e8c\u53c9\u6811\u4e2d\uff0c\u7b2ci\u4e2a\u8282\u70b9\u4e0e\u5176\u5de6\u53f3\u5b50\u8282\u70b9\u7684\u5173\u7cfb\u4e3a\uff08i\u4ece0\u5f00\u59cb\uff09\uff1a<br>$$<br>\\begin{align}<br>&amp; i_{left}=2i + 1 \\\\<br>&amp; i_{right} = 2i + 2<br>\\end{align}<br>$$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u53c9\u641c\u7d22\u6811<\/h2>\n\n\n\n<p>\u4e8c\u53c9\u641c\u7d22\u6811\u6709\u4e00\u4e2a\u5f88\u597d\u7684\u6027\u8d28\uff0c\u5373\u5176\u4e2d\u5e8f\u904d\u5386\u7684\u7ed3\u679c\u4e25\u683c\u5347\u5e8f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u53c9\u6811\u904d\u5386<\/h2>\n\n\n\n<p>\u524d\u5e8f\u3001\u540e\u5e8f\u3001\u4e2d\u5e8f\u904d\u5386\u53ef\u4ee5\u7528\u6808\u6765\u8fdb\u884c\u5b9e\u73b0\uff0c\u4e14\u524d\u4e2d\u5e8f\u7684\u8fed\u4ee3\u4ee3\u7801\u7c7b\u4f3c\uff0c\u5982\u4e0b\uff1a<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:flex;align-items:center;padding:10px 0px 10px 16px;margin-bottom:-2px;width:100%;text-align:left;background-color:#2b2b2b;color:#c7c7c7\">C++<\/span><span role=\"button\" tabindex=\"0\" data-code=\"vector&lt;int&gt; traversal(TreeNode* root) {\n    stack&lt;TreeNode*&gt; stk;\n    vector&lt;int&gt; res;\n\n    while (root || !stk.empty()) {\n        while (root) {\n            stk.push(root);\n            \/\/ \u524d\u5e8f\uff1ares.push_back(root-&gt;val);\n            root = root-&gt;left;\n        }\n        root = stk.top();\n        stk.pop();\n        \/\/ \u4e2d\u5e8f\uff1ares.push_back(root-&gt;val);\n        root = root-&gt;right;\n    }\n\n    return res;\n}\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M4.5 12.75l6 6 9-13.5\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M16.5 8.25V6a2.25 2.25 0 00-2.25-2.25H6A2.25 2.25 0 003.75 6v8.25A2.25 2.25 0 006 16.5h2.25m8.25-8.25H18a2.25 2.25 0 012.25 2.25V18A2.25 2.25 0 0118 20.25h-7.5A2.25 2.25 0 018.25 18v-1.5m8.25-8.25h-6a2.25 2.25 0 00-2.25 2.25v6\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #4EC9B0\">vector<\/span><span style=\"color: #D4D4D4\">&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt; <\/span><span style=\"color: #DCDCAA\">traversal<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #4EC9B0\">TreeNode<\/span><span style=\"color: #569CD6\">*<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">root<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    stack&lt;TreeNode*&gt; stk;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    vector&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt; res;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> (root || !<\/span><span style=\"color: #9CDCFE\">stk<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">empty<\/span><span style=\"color: #D4D4D4\">()) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> (root) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #9CDCFE\">stk<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">push<\/span><span style=\"color: #D4D4D4\">(root);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #6A9955\">            \/\/ \u524d\u5e8f\uff1ares.push_back(root-&gt;val);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            root = <\/span><span style=\"color: #9CDCFE\">root<\/span><span style=\"color: #D4D4D4\">-&gt;<\/span><span style=\"color: #9CDCFE\">left<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        root = <\/span><span style=\"color: #9CDCFE\">stk<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">top<\/span><span style=\"color: #D4D4D4\">();<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #9CDCFE\">stk<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">pop<\/span><span style=\"color: #D4D4D4\">();<\/span><\/span>\n<span class=\"line\"><span style=\"color: #6A9955\">        \/\/ \u4e2d\u5e8f\uff1ares.push_back(root-&gt;val);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        root = <\/span><span style=\"color: #9CDCFE\">root<\/span><span style=\"color: #D4D4D4\">-&gt;<\/span><span style=\"color: #9CDCFE\">right<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> res;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">}<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p>\u800c\u540e\u5e8f\u7684\u4ee3\u7801\u8f83\u4e3a\u590d\u6742\uff0c\u4ee3\u7801\u5982\u4e0b\uff08\u4fee\u6539\u81ea<a href=\"https:\/\/blog.csdn.net\/zhpf225\/article\/details\/108863590\">\u672c\u6587<\/a>\u63d0\u4f9b\u7684\u4ee3\u7801\uff09\uff1a<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:flex;align-items:center;padding:10px 0px 10px 16px;margin-bottom:-2px;width:100%;text-align:left;background-color:#2b2b2b;color:#c7c7c7\">C++<\/span><span role=\"button\" tabindex=\"0\" data-code=\"vector&lt;int&gt; postorderTraversal(TreeNode* root) {  \n    stack&lt;TreeNode*&gt; stk;\n    vector&lt;int&gt; res;\n    TreeNode* cur = root;\n    TreeNode* pre = nullptr;\/\/\u7528\u6765\u8bb0\u5f55\u4e0a\u4e00\u4e2a\u5df2\u7ecf\u7ed3\u70b9\n    while(!s.empty() || cur){\n        while(cur){\n            s.push(cur);\n            cur = cur-&gt;left;\n        }       \n        cur = s.top();\n        \/\/\u4e0b\u9762\u7684\u5224\u65ad\u662f\u8bf4\u660e\uff0c\u53f3\u5b50\u6811\u5f53\u524d\u7684cur\u7684\u53f3\u5b50\u6811\u5df2\u7ecf\u904d\u5386\u5b8c\u4e86\uff0c\u53ef\u4ee5\u8fdb\u884c\u904d\u5386\u5f53\u524d\u7684\u7ed3\u70b9\u4e86\n        if(!cur-&gt;right || cur-&gt;right==pre){\n            res.push_back(cur-&gt;val);\n            s.pop();\n            pre = cur;\n            cur = nullptr;\/\/\u8fd9\u4e00\u6b65\u5f88\u91cd\u8981\uff0c\u8fd9\u4e00\u6b65\u80fd\u591f\u4f7f\u5f97\u5728\u904d\u5386\u5b8c\u5f53\u524d\u7684cur\u4ee5\u53ca\u5176\u5de6\u53f3\u5b50\u6811\u4e4b\u540e\u80fd\u591f\u8fdb\u4e00\u6b65\u5f80\u6811\u7684\u4e0a\u65b9\u56de\u6eaf\n        }else{\n            cur = cur-&gt;right;\n        }\n    }\n    return res;\n}\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M4.5 12.75l6 6 9-13.5\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M16.5 8.25V6a2.25 2.25 0 00-2.25-2.25H6A2.25 2.25 0 003.75 6v8.25A2.25 2.25 0 006 16.5h2.25m8.25-8.25H18a2.25 2.25 0 012.25 2.25V18A2.25 2.25 0 0118 20.25h-7.5A2.25 2.25 0 018.25 18v-1.5m8.25-8.25h-6a2.25 2.25 0 00-2.25 2.25v6\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #4EC9B0\">vector<\/span><span style=\"color: #D4D4D4\">&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt; <\/span><span style=\"color: #DCDCAA\">postorderTraversal<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #4EC9B0\">TreeNode<\/span><span style=\"color: #569CD6\">*<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">root<\/span><span style=\"color: #D4D4D4\">) {  <\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    stack&lt;TreeNode*&gt; stk;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    vector&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt; res;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    TreeNode* cur = root;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    TreeNode* pre = <\/span><span style=\"color: #569CD6\">nullptr<\/span><span style=\"color: #D4D4D4\">;<\/span><span style=\"color: #6A9955\">\/\/\u7528\u6765\u8bb0\u5f55\u4e0a\u4e00\u4e2a\u5df2\u7ecf\u7ed3\u70b9<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\">(!<\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">empty<\/span><span style=\"color: #D4D4D4\">() || cur){<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\">(cur){<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">push<\/span><span style=\"color: #D4D4D4\">(cur);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            cur = <\/span><span style=\"color: #9CDCFE\">cur<\/span><span style=\"color: #D4D4D4\">-&gt;<\/span><span style=\"color: #9CDCFE\">left<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        }       <\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        cur = <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">top<\/span><span style=\"color: #D4D4D4\">();<\/span><\/span>\n<span class=\"line\"><span style=\"color: #6A9955\">        \/\/\u4e0b\u9762\u7684\u5224\u65ad\u662f\u8bf4\u660e\uff0c\u53f3\u5b50\u6811\u5f53\u524d\u7684cur\u7684\u53f3\u5b50\u6811\u5df2\u7ecf\u904d\u5386\u5b8c\u4e86\uff0c\u53ef\u4ee5\u8fdb\u884c\u904d\u5386\u5f53\u524d\u7684\u7ed3\u70b9\u4e86<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\">(!<\/span><span style=\"color: #9CDCFE\">cur<\/span><span style=\"color: #D4D4D4\">-&gt;<\/span><span style=\"color: #9CDCFE\">right<\/span><span style=\"color: #D4D4D4\"> || <\/span><span style=\"color: #9CDCFE\">cur<\/span><span style=\"color: #D4D4D4\">-&gt;<\/span><span style=\"color: #9CDCFE\">right<\/span><span style=\"color: #D4D4D4\">==pre){<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #9CDCFE\">res<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">push_back<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">cur<\/span><span style=\"color: #D4D4D4\">-&gt;<\/span><span style=\"color: #9CDCFE\">val<\/span><span style=\"color: #D4D4D4\">);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">pop<\/span><span style=\"color: #D4D4D4\">();<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            pre = cur;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            cur = <\/span><span style=\"color: #569CD6\">nullptr<\/span><span style=\"color: #D4D4D4\">;<\/span><span style=\"color: #6A9955\">\/\/\u8fd9\u4e00\u6b65\u5f88\u91cd\u8981\uff0c\u8fd9\u4e00\u6b65\u80fd\u591f\u4f7f\u5f97\u5728\u904d\u5386\u5b8c\u5f53\u524d\u7684cur\u4ee5\u53ca\u5176\u5de6\u53f3\u5b50\u6811\u4e4b\u540e\u80fd\u591f\u8fdb\u4e00\u6b65\u5f80\u6811\u7684\u4e0a\u65b9\u56de\u6eaf<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        }<\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\">{<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            cur = <\/span><span style=\"color: #9CDCFE\">cur<\/span><span style=\"color: #D4D4D4\">-&gt;<\/span><span style=\"color: #9CDCFE\">right<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> res;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">}<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h1 class=\"wp-block-heading\">\u6570\u7ec4<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b50\u5e8f\u5217<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5f02\u4f4d\u8bcd\u7684\u5224\u522b\u65b9\u6cd5<\/h3>\n\n\n\n<p>\u901a\u5e38\u5c06\u5b57\u7b26\u4e32\u8f6c\u5316\u4e3a\u7edf\u8ba1\u5404\u4e2a\u5b57\u6bcd\u51fa\u73b0\u6b21\u6570\u7684array\uff0c\u6bd4\u8f83\u65f6\u53ea\u9700\u8981\u6bd4\u8f83\u4e24\u4e2aarray\u662f\u5426\u76f8\u7b49\u3002\uff08$O(n)$\uff09<br>\u6216\u8005\u5229\u7528\u6392\u5e8f\u7684\u65b9\u5f0f\uff0c\u5c06\u5b57\u7b26\u4e32\u8fdb\u884c\u6392\u5e8f\u540e\u6bd4\u8f83\u3002\uff08$O(nlongn)$\uff09<\/p>\n\n\n\n<p>\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u8fd8\u53ef\u4ee5\u5bf9\u4e0a\u8ff0\u4e24\u8005\u6c42\u6563\u5217\u503c\u8fdb\u4e00\u6b65\u7684\u52a0\u901f\u76f8\u5173\u64cd\u4f5c\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u56de\u6587\u4e32\u7684\u5904\u7406\u6280\u5de7<\/h3>\n\n\n\n<p>\u7834\u574f\u5076\u6570\u56de\u6587\u4e32\u53ea\u9700\u8981\u641c\u7d22\u76f8\u90bb\u4e24\u4e2a\u76f8\u540c\u7684\u5b57\u7b26\uff0c\u5220\u53bb\u5176\u4e2d\u4e00\u4e2a\u5373\u53ef\u3002<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">\u94fe\u8868<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u5220\u9664\/\u63d2\u5165<\/h2>\n\n\n\n<p>\u7531\u4e8e\u5220\u9664\u548c\u63d2\u5165\u90fd\u6709\u53ef\u80fd\u6539\u53d8\u5934\u6307\u9488\uff0c\u56e0\u6b64\u901a\u5e38\u4f1a\u521b\u5efa\u4e00\u4e2a\u5047\u5934\uff0c\u5c06\u771f\u5934\u4f5c\u4e3a\u5176\u540e\u7ee7\uff0c\u4ece\u800c\u4fbf\u4e8e\u7edf\u4e00\u5904\u7406\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u73af<\/h2>\n\n\n\n<p>\u901a\u5e38\u5229\u7528\u5feb\u6162\u6307\u9488\u7684\u65b9\u5f0f\u5bf9\u73af\u8fdb\u884c\u76f8\u5173\u5904\u7406\u3002<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">\u6392\u5e8f<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u5e38\u89c1\u6392\u5e8f\u6c47\u603b\u8868<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>\u540d\u79f0<\/td><td>\u6700\u597d\u65f6\u95f4\u590d\u6742\u5ea6<\/td><td>\u6700\u574f\u65f6\u95f4\u590d\u6742\u5ea6<\/td><td>\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6<\/td><td>\u7a7a\u95f4\u590d\u6742\u5ea6<\/td><td>\u7a33\u5b9a\u6027<\/td><td>\u8bf4\u660e<\/td><\/tr><tr><td>\u5192\u6ce1<\/td><td>$O(n)$<\/td><td>$O(n^2)$<\/td><td>$O(n^2)$<\/td><td>$O(1)$<\/td><td>T<\/td><td>\u6709\u5e8f\u60c5\u51b5\u4e0b\u6700\u597d\uff0c\u5012\u5e8f\u60c5\u51b5\u4e0b\u6700\u574f\u3002<\/td><\/tr><tr><td>\u63d2\u5165<\/td><td>$O(n)$<\/td><td>$O(n^2)$<\/td><td>$O(n^2)$<\/td><td>$O(1)$<\/td><td>T<\/td><td>\u6709\u5e8f\u60c5\u51b5\u4e0b\u6700\u597d\uff0c\u5012\u5e8f\u60c5\u51b5\u4e0b\u6700\u574f\u3002<br>\u9002\u7528\u4e8e\u6570\u636e\u91cf\u5c11\u3001\u57fa\u672c\u6709\u5e8f\u7684\u60c5\u51b5\u3002<\/td><\/tr><tr><td>\u9009\u62e9<\/td><td>$O(n^2)$<\/td><td>$O(n^2)$<\/td><td>$O(n^2)$<\/td><td>$O(1)$<\/td><td>F<\/td><td>\u867d\u7136\u65f6\u95f4\u590d\u6742\u5ea6\u9ad8\uff0c\u4f46\u662f\u4ea4\u6362\u6b21\u6570\u5c11\u3002\u56e0\u6b64\u6bd4\u5192\u6ce1\u6548\u7387\u8981\u9ad8\u3002<br>\u627e\u6700\u503c\u8fdb\u884c\u4ea4\u6362\u5bfc\u81f4\u4e0d\u7a33\u5b9a\u3002<\/td><\/tr><tr><td>\u5e0c\u5c14<\/td><td>$O(n^{1.3~2})$<\/td><td>$O(n^{1.3~2})$<\/td><td>$O(n^{1.3~2})$<\/td><td>$O(1)$<\/td><td>F<\/td><td>\u7f29\u5c0f\u589e\u91cf\u63d2\u5165\u6392\u5e8f\u3002<br>\u589e\u91cf\u53ef\u4ee5\u81ea\u884c\u9009\u62e9\uff0c\u4f1a\u5bf9\u65f6\u95f4\u590d\u6742\u5ea6\u4ea7\u751f\u5f71\u54cd\u3002<br>\u8de8\u5143\u7d20\u4ea4\u6362\u5bfc\u81f4\u4e0d\u7a33\u5b9a\u3002<\/td><\/tr><tr><td>\u5806<\/td><td>$O(nlogn)$<\/td><td>$O(nlogn)$<\/td><td>$O(nlogn)$<\/td><td>$O(1)$<\/td><td>F<\/td><td>\u5efa\u5806$O(n)$\uff0c\u6392\u5e8f$O(nlong)$\u3002<br>\u76f8\u5bf9\u4e8e\u5feb\u6392\u7684\u4ea4\u6362\u6b21\u6570\u591a\u3001\u8bbf\u5b58\u4e0d\u8fde\u7eed<\/td><\/tr><tr><td>\u5f52\u5e76<\/td><td>$O(nlogn)$<\/td><td>$O(nlogn)$<\/td><td>$O(nlogn)$<\/td><td>$O(n)$<\/td><td>T<\/td><td>\u6bcf\u6b21\u90fd\u5148\u653e\u5de6\u4fa7\u7684\u6570\uff0c\u5373\u53ef\u4fdd\u8bc1\u7a33\u5b9a\u3002<\/td><\/tr><tr><td>\u5feb\u901f<\/td><td>$O(nlogn)$<\/td><td>$O(n^2)$<\/td><td>$O(nlogn)$<\/td><td>$O(logn ~ n)$<\/td><td>F<\/td><td>\u6b63\u5e8f\u3001\u5012\u5e8f\u60c5\u51b5\u6700\u574f\uff08\u65f6\u95f4\u7a7a\u95f4\u90fd\u662f\uff09\u3002<br>\u53ef\u4ee5\u5229\u7528\u6808\u5b9e\u73b0\u3002<br>\u4e2d\u5fc3\u70b9\u7684\u9009\u53d6\u975e\u5e38\u91cd\u8981\uff0c\u53ef\u4ee5\u5229\u7528\u4e09\u6570\u53d6\u4e2d\u3001\u968f\u673a\u9009\u53d6\u7684\u65b9\u6cd5\u8fdb\u884c\u4f18\u5316\u3002<br>\u4e5f\u53ef\u4ee5\u5728\u5143\u7d20\u5c11\u4e8e\u4e00\u5b9a\u6570\u503c\u65f6\u505a\u63d2\u5165\u6392\u5e8f\u3002<br>\u8fd8\u53ef\u4ee5\u5229\u7528\u4e09\u5411\u5207\u5206\u7684\u65b9\u6cd5\uff0c\u8df3\u8fc7\u76f8\u540c\u5143\u7d20\u3002<\/td><\/tr><tr><td>\u6876<\/td><td>$O(n)$<\/td><td>$O(n^2)$<\/td><td>$O(n)$<\/td><td>$O(n)$<\/td><td>T<\/td><td>\u6876\u5185\u4f7f\u7528\u94fe\u8868\u63d2\u5165\u6392\u5e8f<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><a href=\"https:\/\/www.chengxuchu.com\/2-algorithm_base\/04-%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95\/%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E5%BF%85%E7%9F%A5%E5%BF%85%E4%BC%9A.html\">\u53c2\u8003\u6587\u7ae0<\/a><\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u5feb\u901f\u6392\u5e8f<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5feb\u901f\u6392\u5e8f\u7684\u4e0d\u540c\u5b9e\u73b0\u65b9\u6cd5<\/h3>\n\n\n\n<p>\u672c\u79d1\u4e0a\u8bfe\u4e14\u4e2a\u4eba\u4e00\u76f4\u89c9\u5f97\u6bd4\u8f83\u597d\u7406\u89e3\u7684\u662f\u7a7a\u7a74\u6cd5\uff0c\u5373\u4e0b\u8ff0\u8fd9\u79cd\u5b9e\u73b0\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:flex;align-items:center;padding:10px 0px 10px 16px;margin-bottom:-2px;width:100%;text-align:left;background-color:#2b2b2b;color:#c7c7c7\">C++<\/span><span role=\"button\" tabindex=\"0\" data-code=\"int quickSelect(vector&lt;int&gt;&amp; nums, int i, int j, int k) {\n    int left = i, right = j;\n\n    int pivot = nums[right];\n    while (left &lt; right) {\n        while (left &lt; right &amp;&amp; nums[left] &gt;= pivot) left++;\n        if (left &lt; right) nums[right] = nums[left];\n        while (left &lt; right &amp;&amp; nums[right] &lt;= pivot) right--;\n        if (left &lt; right) nums[left] = nums[right];\n    }\n    nums[left] = pivot;\n\n    if (left == k) {\n        return nums[left];\n    }\n    else if (left &lt; k) {\n        return quickSelect(nums, left + 1, j, k);\n    }\n    else {\n        return quickSelect(nums, i, left - 1, k);\n    }\n}\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M4.5 12.75l6 6 9-13.5\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M16.5 8.25V6a2.25 2.25 0 00-2.25-2.25H6A2.25 2.25 0 003.75 6v8.25A2.25 2.25 0 006 16.5h2.25m8.25-8.25H18a2.25 2.25 0 012.25 2.25V18A2.25 2.25 0 0118 20.25h-7.5A2.25 2.25 0 018.25 18v-1.5m8.25-8.25h-6a2.25 2.25 0 00-2.25 2.25v6\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">quickSelect<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #4EC9B0\">vector<\/span><span style=\"color: #D4D4D4\">&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt;<\/span><span style=\"color: #569CD6\">&amp;<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">i<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">j<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">k<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> left = i, right = j;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> pivot = <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[right];<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> (left &lt; right) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> (left &lt; right &amp;&amp; <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[left] &gt;= pivot) left++;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (left &lt; right) <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[right] = <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[left];<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> (left &lt; right &amp;&amp; <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[right] &lt;= pivot) right--;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (left &lt; right) <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[left] = <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[right];<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[left] = pivot;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (left == k) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[left];<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (left &lt; k) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">quickSelect<\/span><span style=\"color: #D4D4D4\">(nums, left + <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">, j, k);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\"> {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">quickSelect<\/span><span style=\"color: #D4D4D4\">(nums, i, left - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">, k);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">}<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p>\u8fd9\u79cd\u65b9\u6cd5\u5b58\u5728\u4e00\u4e2a\u95ee\u9898\uff0c\u5373\u5982\u679c\u6570\u7ec4\u4e2d\u5b58\u5728\u5927\u91cf\u7684\u76f8\u540c\u5143\u7d20\uff0c\u4f8b\u5982\u8003\u8651\u4e00\u4e2a\u5168\u4e3a0\u7684\u6570\u5217\uff0c\u90a3\u4e48\u5728\u53f3\u79fb\u5de6\u6307\u9488\u65f6\uff0c\u5c31\u4f1a\u76f4\u63a5\u5c06\u5de6\u6307\u9488\u79fb\u52a8\u5230\u6700\u53f3\u8fb9\uff0c\u4f7f\u5f97\u5feb\u6392\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u9000\u5316\u5230$O(n^2)$\u3002<\/p>\n\n\n\n<p>\u76f8\u53cd\u7684\uff0c\u5982\u679c\u4f7f\u7528\u4ea4\u6362\u6cd5\uff0c\u5c31\u53ef\u4ee5\u89e3\u51b3\u4e0a\u8ff0\u60c5\u51b5\uff1a<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:flex;align-items:center;padding:10px 0px 10px 16px;margin-bottom:-2px;width:100%;text-align:left;background-color:#2b2b2b;color:#c7c7c7\">C++<\/span><span role=\"button\" tabindex=\"0\" data-code=\"int quickSelect(vector&lt;int&gt;&amp; nums, int i, int j, int k) {\n    if (i == j) return nums[k];\n\n    int pivot = nums[i];\n    int left = i - 1, right = j + 1;\n    while (left &lt; right) {\n        do left++; while(nums[left] &gt; pivot);\n        do right--; while (nums[right] &lt; pivot);\n        if (left &lt; right) swap(nums[left], nums[right]);\n    }\n\n    if (right &gt;= k) {\n        return quickSelect(nums, i, right, k);\n    }\n    else {\n        return quickSelect(nums, right + 1, j, k);\n    }\n}\n\nint findKthLargest(vector&lt;int&gt;&amp; nums, int k) {\n    return quickSelect(nums, 0, nums.size() - 1, k - 1);\n}\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M4.5 12.75l6 6 9-13.5\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M16.5 8.25V6a2.25 2.25 0 00-2.25-2.25H6A2.25 2.25 0 003.75 6v8.25A2.25 2.25 0 006 16.5h2.25m8.25-8.25H18a2.25 2.25 0 012.25 2.25V18A2.25 2.25 0 0118 20.25h-7.5A2.25 2.25 0 018.25 18v-1.5m8.25-8.25h-6a2.25 2.25 0 00-2.25 2.25v6\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">quickSelect<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #4EC9B0\">vector<\/span><span style=\"color: #D4D4D4\">&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt;<\/span><span style=\"color: #569CD6\">&amp;<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">i<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">j<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">k<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (i == j) <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[k];<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> pivot = <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[i];<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> left = i - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">, right = j + <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> (left &lt; right) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">do<\/span><span style=\"color: #D4D4D4\"> left++; <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[left] &gt; pivot);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">do<\/span><span style=\"color: #D4D4D4\"> right--; <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[right] &lt; pivot);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (left &lt; right) <\/span><span style=\"color: #DCDCAA\">swap<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[left], <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">[right]);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (right &gt;= k) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">quickSelect<\/span><span style=\"color: #D4D4D4\">(nums, i, right, k);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\"> {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">quickSelect<\/span><span style=\"color: #D4D4D4\">(nums, right + <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">, j, k);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">}<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">findKthLargest<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #4EC9B0\">vector<\/span><span style=\"color: #D4D4D4\">&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt;<\/span><span style=\"color: #569CD6\">&amp;<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">k<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">quickSelect<\/span><span style=\"color: #D4D4D4\">(nums, <\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">nums<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">size<\/span><span style=\"color: #D4D4D4\">() - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">, k - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">}<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p>\u53ef\u4ee5\u770b\u5230\uff0c\u5982\u679c\u4f7f\u7528\u8fd9\u79cd\u5b9e\u73b0\u65b9\u5f0f\uff0c\u5168\u96f6\u7684\u6570\u5217\u6700\u7ec8\u7684\u4e2d\u5fc3\u70b9\u4f4d\u7f6e\u5c06\u4f1a\u4f4d\u4e8e\u6570\u7ec4\u4e2d\u592e\uff0c\u4f7f\u5f97\u65f6\u95f4\u590d\u6742\u5ea6\u4fdd\u6301\u5728$O(nlogn)$\u3002<br>\u4e0d\u8fc7\u9700\u8981\u6ce8\u610f\uff0c\u8fd9\u79cd\u65b9\u6cd5\u65e0\u6cd5\u5f97\u5230\u6bcf\u6b21\u5212\u5206\u65f6\u4e2d\u5fc3\u70b9\u7684\u6700\u7ec8\u4f4d\u7f6e\uff0c\u8be5\u65b9\u6cd5\u53ea\u80fd\u4fdd\u8bc1\u533a\u95f4$[i, right]$\u548c\u533a\u95f4$[right + 1, j]$\u4e2d\u7684\u5143\u7d20\u5206\u522b\u5c0f\u4e8e\u7b49\u4e8e\/\u5927\u4e8e\u7b49\u4e8e\u4e2d\u5fc3\u70b9\u3002\u53ea\u6709\u5728<code>i==j<\/code>\u65f6\uff0c\u4e2d\u5fc3\u70b9\u4f4d\u7f6e\u624d\u80fd\u786e\u5b9a\u3002<\/p>\n\n\n\n<p>\u53c2\u8003\uff1a<\/p>\n\n\n\n<p>[1] <a href=\"https:\/\/en.wikipedia.org\/wiki\/Quicksort#Hoare_partition_scheme\">\u5feb\u901f\u6392\u5e8f Wiki<\/a><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">\u56fe\u8bba<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">\u56fe\u904d\u5386\u65f6\u5df2\u8bbf\u95ee\u7684\u8bb0\u5f55\u4f4d\u7f6e<\/h3>\n\n\n\n<p>\u5728\u8fdb\u884c\u56fe\u904d\u5386\u65f6\uff0c\u5e94\u5f53\u6ce8\u610f\uff0c\u66f4\u65b0\u5df2\u8bbf\u95ee\u6570\u7ec4\u5e94\u8be5\u53d1\u751f\u5728\u5165\u6808\/\u961f\u65f6\uff0c\u800c\u4e0d\u662f\u51fa\u6808\/\u961f\uff0c\u540e\u8005\u867d\u7136\u4e0d\u4f1a\u5bfc\u81f4\u6b7b\u5faa\u73af\uff0c\u4f46\u662f\u4f1a\u5bfc\u81f4\u4e00\u4e2a\u8282\u70b9\u88ab\u591a\u6b21\u8bbf\u95ee\u3002<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">\u6570\u5b66<\/h1>\n\n\n\n<p>\u6700\u5927\u516c\u7ea6\u6570\u548c\u6700\u5c0f\u516c\u500d\u6570\u6ee1\u8db3\uff1a$ab=lcm(a.b)gcm(a,b)$<\/p>\n\n\n\n<p>\u7ea6\u745f\u592b\u73af\u7684\u9012\u63a8\u516c\u5f0f\uff1a$x^\\prime = (x + k) % n$\uff0c\u5176\u4e2d$k = m % n$\u3002\u8be5\u9012\u5f52\u5f0f\u628a\u5b50\u95ee\u9898\u7684\u83b7\u80dc\u8005\u7f16\u53f7\u6620\u5c04\u5230\u4e0a\u5c42\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u8bb0\u5f55\u4e86\u4e00\u4e9b\u5728\u5237\u9898\u8fc7\u7a0b\u4e2d\u9047\u5230\u7684\u4e00\u4e9bTIPS<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","wikipediapreview_detectlinks":true,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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