{"id":33211,"date":"2025-04-27T02:52:39","date_gmt":"2025-04-26T18:52:39","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/33211.html"},"modified":"2025-04-27T02:52:39","modified_gmt":"2025-04-26T18:52:39","slug":"%e6%af%8f%e6%97%a5c-c%e9%a2%98-%e5%a4%87%e6%88%98%e8%93%9d%e6%a1%a5%e6%9d%afp1049-noip-2001-%e6%99%ae%e5%8f%8a%e7%bb%84-%e8%a3%85%e7%ae%b1%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/33211.html","title":{"rendered":"\u6bcf\u65e5c\/c++\u9898 \u5907\u6218\u84dd\u6865\u676f(P1049 [NOIP 2001 \u666e\u53ca\u7ec4] \u88c5\u7bb1\u95ee\u9898)"},"content":{"rendered":"<h2>\u6d1b\u8c37P1049 \u88c5\u7bb1\u95ee\u9898\u9898\u89e3&#xff1a;\u52a8\u6001\u89c4\u5212\u5728\u80cc\u5305\u95ee\u9898\u4e2d\u7684\u7ecf\u5178\u5e94\u7528<\/h2>\n<h3>\u9898\u76ee\u63cf\u8ff0<\/h3>\n<p>P1049 \u88c5\u7bb1\u95ee\u9898\u662f\u4e00\u9053\u5178\u578b\u76840-1\u80cc\u5305\u95ee\u9898\u53d8\u79cd\u3002\u9898\u76ee\u8981\u6c42\u5728\u7ed9\u5b9a\u7bb1\u5b50\u5bb9\u91cfV\u548cn\u4e2a\u7269\u54c1\u4f53\u79ef\u7684\u60c5\u51b5\u4e0b&#xff0c;\u9009\u62e9\u82e5\u5e72\u7269\u54c1\u88c5\u5165\u7bb1\u5b50&#xff0c;\u4f7f\u5f97\u7bb1\u5b50\u7684\u5269\u4f59\u7a7a\u95f4\u6700\u5c0f\u3002\u6700\u7ec8\u8f93\u51fa\u8fd9\u4e2a\u6700\u5c0f\u5269\u4f59\u7a7a\u95f4\u7684\u503c\u3002<\/p>\n<h3>\u89e3\u9898\u601d\u8def<\/h3>\n<p>\u672c\u9898\u672c\u8d28\u662f\u6c42\u4e0d\u8d85\u8fc7\u7bb1\u5b50\u5bb9\u91cf\u7684\u6700\u5927\u88c5\u8f7d\u4f53\u79ef&#xff0c;\u5c5e\u4e8e\u7ecf\u5178\u76840-1\u80cc\u5305\u95ee\u9898\u3002\u52a8\u6001\u89c4\u5212\u662f\u89e3\u51b3\u6b64\u7c7b\u95ee\u9898\u7684\u6700\u4f18\u89e3\u6cd5&#xff0c;\u5176\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u9010\u6b65\u6784\u5efa\u6700\u4f18\u89e3\u3002<\/p>\n<h4>\u52a8\u6001\u89c4\u5212\u4e09\u8981\u7d20<\/h4>\n<li>\u72b6\u6001\u5b9a\u4e49&#xff1a;dp[j]\u8868\u793a\u5bb9\u91cf\u4e3aj\u7684\u80cc\u5305\u5728\u5f53\u524d\u51b3\u7b56\u4e0b\u80fd\u88c5\u7684\u6700\u5927\u4f53\u79ef<\/li>\n<li>\u72b6\u6001\u8f6c\u79fb&#xff1a;dp[j] &#061; max(dp[j], dp[j &#8211; w[i]] &#043; w[i])\n<ul>\n<li>\u4e0d\u9009\u7b2ci\u4e2a\u7269\u54c1&#xff1a;dp[j]\u4fdd\u6301\u539f\u503c<\/li>\n<li>\u9009\u7b2ci\u4e2a\u7269\u54c1&#xff1a;dp[j &#8211; w[i]] &#043; w[i]&#xff08;\u9700\u4fdd\u8bc1j \u2265 w[i]&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>\u521d\u59cb\u5316&#xff1a;dp[0] &#061; 0&#xff0c;\u5176\u4f59\u521d\u59cb\u5316\u4e3a0<\/li>\n<li>\u904d\u5386\u987a\u5e8f&#xff1a;\n<ul>\n<li>\u5916\u5c42\u5faa\u73af\u904d\u5386\u6bcf\u4e2a\u7269\u54c1<\/li>\n<li>\u5185\u5c42\u5faa\u73af\u9006\u5e8f\u904d\u5386\u80cc\u5305\u5bb9\u91cf&#xff08;\u4fdd\u8bc1\u6bcf\u4e2a\u7269\u54c1\u53ea\u88ab\u9009\u62e9\u4e00\u6b21&#xff09;<\/li>\n<\/ul>\n<\/li>\n<h3>\u4ee3\u7801\u8be6\u89e3<\/h3>\n<p><span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span><span class=\"token string\">&lt;bits\/stdc&#043;&#043;.h&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> v<span class=\"token punctuation\">,<\/span> n<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> w<span class=\"token punctuation\">[<\/span><span class=\"token number\">35<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span>  <span class=\"token comment\">\/\/ \u5b58\u50a8\u7269\u54c1\u4f53\u79ef&#xff08;1-based\u7d22\u5f15&#xff09;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> dp<span class=\"token punctuation\">[<\/span><span class=\"token number\">20005<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span>  <span class=\"token comment\">\/\/ \u52a8\u6001\u89c4\u5212\u6570\u7ec4<\/span><\/p>\n<p>    cin <span class=\"token operator\">&gt;&gt;<\/span> v <span class=\"token operator\">&gt;&gt;<\/span> n<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>i<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        cin <span class=\"token operator\">&gt;&gt;<\/span> w<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>i<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>          <span class=\"token comment\">\/\/ \u904d\u5386\u6bcf\u4e2a\u7269\u54c1<\/span><br \/>\n        <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> v<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&gt;&#061;<\/span> w<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#8212;<\/span>j<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>   <span class=\"token comment\">\/\/ \u9006\u5e8f\u904d\u5386\u80cc\u5305\u5bb9\u91cf<\/span><br \/>\n            dp<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>dp<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> dp<span class=\"token punctuation\">[<\/span>j <span class=\"token operator\">&#8211;<\/span> w<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> w<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    cout <span class=\"token operator\">&lt;&lt;<\/span> v <span class=\"token operator\">&#8211;<\/span> dp<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span>  <span class=\"token comment\">\/\/ \u5269\u4f59\u7a7a\u95f4&#061;\u603b\u5bb9\u91cf-\u6700\u5927\u88c5\u8f7d\u4f53\u79ef<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h4>\u5173\u952e\u4ee3\u7801\u89e3\u6790<\/h4>\n<li>\u6570\u7ec4\u521d\u59cb\u5316&#xff1a;dp\u6570\u7ec4\u521d\u59cb\u5168\u4e3a0&#xff0c;\u8868\u793a\u521d\u59cb\u65f6\u80cc\u5305\u5bb9\u91cf\u4e3a0<\/li>\n<li>\u53cc\u91cd\u5faa\u73af\u7ed3\u6784&#xff1a;\n<ul>\n<li>\u5916\u5c42\u5faa\u73af\u63a7\u5236\u7269\u54c1\u9009\u62e9\u987a\u5e8f<\/li>\n<li>\u5185\u5c42\u5faa\u73af\u901a\u8fc7\u9006\u5e8f\u66f4\u65b0\u4fdd\u8bc1\u6bcf\u4e2a\u7269\u54c1\u53ea\u88ab\u9009\u62e9\u4e00\u6b21<\/li>\n<\/ul>\n<\/li>\n<li>\u72b6\u6001\u8f6c\u79fb&#xff1a;\u901a\u8fc7\u6bd4\u8f83\u9009\u62e9\u5f53\u524d\u7269\u54c1\u4e0e\u4e0d\u9009\u62e9\u5f53\u524d\u7269\u54c1\u4e24\u79cd\u60c5\u51b5&#xff0c;\u66f4\u65b0\u6700\u4f18\u89e3<\/li>\n<li>\u7ed3\u679c\u8ba1\u7b97&#xff1a;v &#8211; dp[v]\u76f4\u63a5\u5f97\u5230\u6700\u5c0f\u5269\u4f59\u7a7a\u95f4&#xff0c;\u907f\u514d\u4e8c\u6b21\u904d\u5386<\/li>\n<h3>\u590d\u6742\u5ea6\u5206\u6790<\/h3>\n<ul>\n<li>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(nV)&#xff0c;\u5176\u4e2dn\u4e3a\u7269\u54c1\u6570\u91cf&#xff0c;V\u4e3a\u80cc\u5305\u5bb9\u91cf<\/li>\n<li>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;O(V)&#xff0c;\u4f7f\u7528\u4e00\u7ef4\u6570\u7ec4\u4f18\u5316\u7a7a\u95f4<\/li>\n<li>\u5b9e\u9645\u8868\u73b0&#xff1a;\u5f53n&#061;30&#xff0c;V&#061;20000\u65f6&#xff0c;\u603b\u8fd0\u7b97\u91cf\u7ea6\u4e3a60\u4e07\u6b21&#xff0c;\u53ef\u57281\u79d2\u5185\u5b8c\u6210<\/li>\n<\/ul>\n<h3>\u6ce8\u610f\u4e8b\u9879<\/h3>\n<li>\u7269\u54c1\u4f53\u79ef\u5904\u7406&#xff1a;\u5f53\u7269\u54c1\u4f53\u79ef\u5927\u4e8e\u5f53\u524d\u80cc\u5305\u5bb9\u91cf\u65f6\u81ea\u52a8\u8df3\u8fc7&#xff08;j &gt;&#061; w[i]\u5224\u65ad&#xff09;<\/li>\n<li>\u9006\u5e8f\u66f4\u65b0&#xff1a;\u5fc5\u987b\u9006\u5e8f\u904d\u5386\u80cc\u5305\u5bb9\u91cf&#xff0c;\u5426\u5219\u4f1a\u5bfc\u81f4\u91cd\u590d\u9009\u62e9\u540c\u4e00\u7269\u54c1<\/li>\n<li>\u7ed3\u679c\u9a8c\u8bc1&#xff1a;\u6700\u7ec8\u8f93\u51fav &#8211; dp[v]\u800c\u975e\u76f4\u63a5\u8f93\u51fadp[v]&#xff0c;\u66f4\u7b26\u5408\u9898\u76ee\u8981\u6c42<\/li>\n<li>\u8fb9\u754c\u6761\u4ef6&#xff1a;\u5f53\u6ca1\u6709\u7269\u54c1\u65f6&#xff08;n&#061;0&#xff09;&#xff0c;\u5269\u4f59\u7a7a\u95f4\u5373\u4e3aV\u672c\u8eab<\/li>\n<h3>\u6837\u4f8b\u5206\u6790<\/h3>\n<p>\u8f93\u5165&#xff1a;<\/p>\n<p>24<br \/>\n6<br \/>\n8<br \/>\n3<br \/>\n12<br \/>\n7<br \/>\n9<br \/>\n7<\/p>\n<p>\u6267\u884c\u6d41\u7a0b&#xff1a;<\/p>\n<li>\u521d\u59cb\u5316dp[0] &#061; 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