{"id":291,"date":"2022-07-30T02:24:28","date_gmt":"2022-07-29T18:24:28","guid":{"rendered":"https:\/\/blog.cirno.fun\/?p=291"},"modified":"2024-09-12T09:36:48","modified_gmt":"2024-09-12T01:36:48","slug":"%e5%bf%ab%e9%80%9f%e9%80%89%e6%8b%a9%e7%ae%97%e6%b3%95-%e7%ac%ack%e4%b8%aa%e6%95%b0","status":"publish","type":"post","link":"https:\/\/blog.sssn.tech\/?p=291","title":{"rendered":"\u5feb\u901f\u9009\u62e9\u7b97\u6cd5\u2014\u2014\u7b2ck\u4e2a\u6570"},"content":{"rendered":"<p>\u5feb\u901f\u9009\u62e9\u7b97\u6cd5\u53ef\u4ee5\u5feb\u901f\u9009\u51fa\u65e0\u5e8f\u6570\u5217\u7b2ck\u5927(\u5c0f)\u7684\u6570\uff0c\u6bd4\u8d77\u5feb\u901f\u6392\u5e8f\uff0c\u5b83\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u66f4\u4f18\u79c0\uff0c\u8fbe\u5230\u4e86<code>O(N)<\/code>\u7ea7\u522b<\/p>\n<p>\u4ed6\u7684\u601d\u60f3\u548c\u5feb\u901f\u6392\u5e8f\u6781\u4e3a\u76f8\u4f3c\uff0c\u90fd\u662f\u57fa\u4e8e\u5206\u6cbb\u7684\u4e09\u6b65\u8d70 \u5bf9\u4e8e\u5728\u533a\u95f4<code>[L,R]<\/code>\u9009\u51fa\u7b2ck\u5c0f\u6570\u7684\u95ee\u9898,\u5904\u7406\u65b9\u5f0f\u5982\u4e0b\uff1a<\/p>\n<ol>\n<li>\u5728[L,R]\u4e0a\u4efb\u53d6\u4e00\u4e2a\u57fa\u51c6\u6570x<\/li>\n<li>\u7528\u548c\u5feb\u901f\u6392\u5e8f\u4e00\u6837\u7684\u65b9\u6cd5\u5c06x\u5f52\u4f4d<\/li>\n<li>\u6211\u4eec\u5c06x\u5f52\u4f4d\u540e\uff0c\u6bd4x\u5c0f\u7684\u6570\u7684\u4e2a\u6570\u8bb0\u4e3aSL\uff0c\u6b64\u65f6\u5206\u7c7b\u8ba8\u8bba:\n<ol>\n<li>\u5982\u679ck&lt;=SL,\u5219\u8bf4\u660e\u76ee\u6807\u6570\u5728x\u5de6\u4fa7\u533a\u95f4\u91cc\uff0c\u6211\u4eec\u9012\u5f52\u5bfb\u627e\uff0c\u5373\u5728\u5de6\u4fa7\u533a\u95f4\u5bfb\u627e\u7b2ck\u5c0f\u6570\uff0c\u6b64\u65f6\u4e0d\u518d\u9700\u8981\u5904\u7406\u53f3\u4fa7\u533a\u95f4<\/li>\n<li>\u5982\u679ck&gt;SL,\u5219\u8bf4\u660e\u76ee\u6807\u6570\u5728x\u53f3\u4fa7,\u6b64\u65f6\u6211\u4eec\u5411\u53f3\u4fa7\u9012\u5f52\uff0c\u800c\u95ee\u9898\u53d8\u6210\u4e86\u5728\u53f3\u4fa7\u533a\u95f4\u5bfb\u627e\u7b2c<strong>k-SL<\/strong>\u5c0f\u7684\u6570<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>\u5bf9\u4e8e\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u8ba8\u8bba: \u7b2c\u4e00\u6b21\u64cd\u4f5c\u662f\u626b\u9762\u6574\u4e2a\u6570\u5217\uff0c\u65f6\u95f4\u662fN\uff0c\u7b2c\u4e8c\u6b21\u662f\u5bf9\u4e00\u4e2a\u5b50\u533a\u95f4\u64cd\u4f5c\uff0c\u65f6\u95f4\u662fN\/2,\u7136\u540e\u662fN\/4,\u4ee5\u6b64\u7c7b\u63a8\uff0c\u65f6\u95f4\u662f<\/p>\n<pre><code class=\"language-katex\">\\sum_{i=0}^{d}N(\\frac{1}{2})^{i}\\le 2N<\/code><\/pre>\n<p>\u6b64\u65f6\u7684\u590d\u6742\u53d6<code>O(N)<\/code>\u5c31\u597d<\/p>\n<p>\u6e90\u7801<\/p>\n<pre><code class=\"language-cpp\">void q_select(int a[],int l,int r,int k){\n    \/\/\u5728\u6570\u7ec4a\u7684\u533a\u95f4l,r\u4e2d\uff0c\u5bfb\u627e\u7b2ck\u5c0f\u6570\n    if(l&gt;=r)\n        return ;\n    int x=a[(l+r)\/2],i=l-1,j=r+1;\n    while(i&lt;j){\n        do i++; 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