{"id":457,"date":"2025-05-02T17:22:35","date_gmt":"2025-05-02T09:22:35","guid":{"rendered":"https:\/\/www.vcoco.top\/?p=457"},"modified":"2025-05-17T11:20:02","modified_gmt":"2025-05-17T03:20:02","slug":"%e5%86%8d%e6%88%98%e7%ae%97%e6%b3%95%e7%ab%9e%e8%b5%9b%ef%bc%88%e6%89%be%e5%b7%a5%e4%bd%9c%e7%af%87%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.vcoco.top\/index.php\/2025\/05\/02\/%e5%86%8d%e6%88%98%e7%ae%97%e6%b3%95%e7%ab%9e%e8%b5%9b%ef%bc%88%e6%89%be%e5%b7%a5%e4%bd%9c%e7%af%87%ef%bc%89\/","title":{"rendered":"\u518d\u6218\u57fa\u7840\u7b97\u6cd5\uff08\u627e\u5de5\u4f5c\u7bc7\uff09"},"content":{"rendered":"\n<ul class=\"wp-block-list\">\n<li>\u603b\u7ed3\u4e00\u4e9b\u81ea\u5df1\u5bb9\u6613\u9057\u5fd8\u4f46\u633a\u91cd\u8981\u7684\u7b97\u6cd5\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u624b\u6495\u7ecf\u5178\u7b97\u6cd5<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5feb\u901f\u6392\u5e8f<\/h3>\n\n\n\n<p>\u6838\u5fc3\u4ee3\u7801\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>void qsort(int ll, int rr)\r\n{\r\n    if(ll>=rr) return;\r\n    \r\n    int x=a&#91;ll+rr>>1], l=ll-1, r=rr+1;\r\n    \r\n    while(l&lt;r)\r\n    {\r\n        do l++; while(a&#91;l]&lt;x);\r\n        do r--; while(a&#91;r]>x);\r\n        if(l&lt;r) swap(a&#91;l], a&#91;r]);\r\n    }\r\n    \r\n    qsort(ll, r);\r\n    qsort(r+1, rr);\r\n}\r<\/code><\/pre>\n\n\n\n<p>\u7406\u89e3\u70b91\uff1a\u5982\u679c\uff0cl++\u7684\u65f6\u5019\u52a0\u5230 r \u7684\u4f4d\u7f6e\u3002\u7531\u4e0a\u4e00\u8f6e\u77e5\uff0cr \u7684\u4f4d\u7f6ea[r]\u4e00\u5b9a>=x\uff0c\u90a3\u4e48l++\u6700\u591a\u5230 l==r \u7684\u65f6\u5019\u505c\u6b62\u3002\u6b64\u65f6 a[r-1] &lt; x\uff0c\u6240\u4ee5 r\u5faa\u73af\u540e\u4e3ar-1\u3002\u6b64\u65f6l=r+1\u3002\u4e0d\u6ee1\u8db3if(l&lt;r)\u7684\u6761\u4ef6\u3002\u540c\u7406r&#8211;\u7684\u65f6\u5019\u51cf\u5230l\u7684\u4f4d\u7f6e\uff0c\u4e5f\u4e0d\u4f1a\u6ee1\u8db3\u4ea4\u6362\u6761\u4ef6\u3002<\/p>\n\n\n\n<p>\u7406\u89e3\u70b92\uff1a\u82e5x\u662f\u4e2d\u95f4\u4f4d\u7f6e\uff0c\u8fd9\u4e9b\u60c5\u51b5\u4e0d\u592a\u53ef\u80fd\u53d1\u751f\uff0c\u56e0\u4e3a\u80af\u5b9a\u4f1a\u5728 x\u7684\u4f4d\u7f6e\u505c\u4e0b\u6765\u3002<\/p>\n\n\n\n<p>\u5982\u4e0b\u4ee3\u7801\uff08while\u6bd4do while\u7b80\u6d01\uff09\u770b\u4f3c\u7b49\u4ef7\uff0c\u5b9e\u5219\u4f1a\u9677\u5165\u6b7b\u5faa\u73af\u3002\u5982\u5728\u67d0\u4e2a\u70b9 x=5, l \u5f53\u524d\u7684\u4f4d\u7f6e\u503c\u662f5, r \u5f53\u524d\u7684\u4f4d\u7f6e\u4e5f\u662f5\u3002\u4f46\u662f r>l\u3002\u6b64\u65f6\u4f1a\u4e0d\u65ad\u8fdb\u884c while(l&lt;r) \u8fd9\u4e2a\u5faa\u73af\u3002\uff08\u76f8\u540c\u76845\u4ea4\u6362\u4e86\u4f4d\u7f6e\u8fd8\u662f\u4e0d\u53d8\uff09<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>void qsort(int ll, int rr)\n{\n    if(ll>=rr) return;\n    \n    int x=a&#91;ll+rr>>1], l=ll, r=rr;\n    \n    while(l&lt;r)\n    {\n        while(l&lt;r &amp;&amp; a&#91;l]&lt;x) l++;\n        while(l&lt;r &amp;&amp; a&#91;r]>x) r--;\n        if(l&lt;r) swap(a&#91;l], a&#91;r]);\n    }\n    \n    qsort(ll, r);\n    qsort(r+1, rr);\n}<\/code><\/pre>\n\n\n\n<p>\u4e0a\u9762\u7684\u4ee3\u7801\u6539\u6210 while(l&lt;r &amp;&amp; a[r]>=x) r&#8211;; \u4e5f\u4e0d\u884c\uff0c>=x \u4f1a\u8ba9\u4e00\u4fa7\u7565\u8fc7=x\u7684\u70b9\uff0c\u9020\u6210\u5931\u8d25\u3002<\/p>\n\n\n\n<p>\u6848\u4f8b<\/p>\n\n\n\n<p><code>x=133<\/code><\/p>\n\n\n\n<p>\u7b2c\u4e00\u8f6e\uff1a<code>128 90 83 67 98 8 67 6 116 164 11 60 238 133 153 241 248 232 175 233 196 260 181 160 133 160 216 291 a[l]=116 a[r]=241<\/code><\/p>\n\n\n\n<p>\u7b2c\u4e8c\u8f6e\uff1a<code>128 90 83 67 98 8 67 6 116 60 11 164 238 133 153 241 248 232 175 233 196 260 181 160 133 160 216 291 a[l]=60 a[r]=164<\/code><\/p>\n\n\n\n<p>\u4e0a\u9762\u7b2c\u4e00\u4e2a\u6848\u4f8b\u4e2d\uff0c\u8fd0\u884c\u5b8c\u4e4b\u540e\uff0ca[l]=116\u7684\u4f4d\u7f6e\uff0ca[r]=241\u7684\u4f4d\u7f6e\uff0cr \u5f80\u524d\u8d70\uff0c\u56e0\u4e3a \u662f >= x\uff0c\u5219\u4f1a\u8df3\u8fc7133\u7684\u4f4d\u7f6e\uff0c\u6700\u7ec8\u8d70\u5230 60 \u7684\u4f4d\u7f6e\uff0cl\u8d70\u5230164\u7684\u4f4d\u7f6e\uff0c\u7136\u540e\u4ea4\u6362\u5f97\u5230\u7b2c\u4e8c\u8f6e\u7684\u7ed3\u679c\uff0c\u663e\u7136\uff1a\u4e0d\u6ee1\u8db3\u8981\u6c42\uff08238>133\uff09\u3002<\/p>\n\n\n\n<p><strong>\u603b\u4f53\u5206\u6790<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group is-vertical is-layout-flex wp-container-core-group-is-layout-8cf370e7 wp-block-group-is-layout-flex\">\n<p>1.\u5212\u5206\u60c5\u51b5\uff1a\u4ee5r\u4e3a\u5212\u5206\u65f6\uff0cx\u4e0d\u80fd\u9009q[rr]\u3002\u82e5\u4ee5l\u4e3a\u5212\u5206,\u5219x\u4e0d\u80fd\u9009q[ll]<\/p>\n\n\n\n<p>\u5047\u8bbe x = q[rr]<\/p>\n\n\n\n<p>\u5173\u952e\u53e5\u5b50quick_sort(q, ll, r), quick_sort(q, r + 1, rr);<\/p>\n\n\n\n<p>\u7531\u4e8e r \u7684\u6700\u5c0f\u503c\u662f ll, \u6240\u4ee5 q[r+1..rr] \u4e0d\u4f1a\u9020\u6210\u65e0\u9650\u5212\u5206<\/p>\n\n\n\n<p>\u4f46q[ll..r](\u5373quick_sort(q, ll, r))\u5374\u53ef\u80fd\u9020\u6210\u65e0\u9650\u5212\u5206\uff0c\u56e0\u4e3a r \u53ef\u80fd\u53d6\u5230 rr\u3002<br>\u4e3e\u4f8b\uff1a\u82e5x\u9009\u4e3aq[rr]\uff0c\u6570\u7ec4\u4e2dq[ll..rr-1] &lt; x, \u90a3\u4e48\u8fd9\u4e00\u8f6e\u5faa\u73af\u7ed3\u675f\u65f6 l = rr,  r= rr\uff0c\u663e\u7136\u4f1a\u9020\u6210\u65e0\u9650\u5212\u5206\u3002<\/p>\n\n\n\n<p>2.while(a[l]&lt;x)\u7684\u5faa\u73af\u4e0d\u80fd\u7528&lt;=\uff0ca[r] > x \u4e5f\u4e0d\u80fd\u7528>=\u3002\u4e3e\u4f8b\uff1a\u5982\u679c a \u6570\u7ec4\u5168\u662f\u76f8\u540c\u7684\u6570\uff0c\u5219\u4f1a\u8d8a\u754c\u9020\u6210\u5404\u79cd\u9519\u8bef\u3002<\/p>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Trie\u6811<\/h2>\n\n\n\n<p>\u8fd9\u4e2a\u6811\u6bd4\u8f83\u5947\u7279\u3002\u5373\u4fbf\u662f\u590d\u4e60\uff0c\u4e5f\u4e0d\u592a\u6e05\u695ap\u662f\u600e\u4e48\u8d70\u7684\u4e86\u3002p\u4e0d\u662f\u5e8f\u5217\u957f\u5ea6\uff0c\u800c\u662f\u5b50\u8282\u70b9\u3002<\/p>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/837\/\" target=\"_blank\" rel=\"noreferrer noopener\">Trie\u5b57\u7b26\u4e32\u7edf\u8ba1<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.vcoco.top\/wp-content\/uploads\/2025\/05\/Trie\u6811-1024x640.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"640\" data-original=\"https:\/\/www.vcoco.top\/wp-content\/uploads\/2025\/05\/Trie\u6811-1024x640.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-458\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u6700\u5927\u8fde\u7eed\u5b50\u5e8f\u548c<\/h2>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a rel=\"noreferrer noopener\" href=\"https:\/\/www.acwing.com\/problem\/content\/description\/1481\/\" target=\"_blank\">\u6700\u5927\u5b50\u5e8f\u548c<\/a><\/p>\n\n\n\n<p>\u9898\u89e3\uff1a<a href=\"https:\/\/www.acwing.com\/solution\/content\/46448\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u8d2a\u5fc3\/\u52a8\u6001\u89c4\u5212<\/a> <\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u7bc7<\/h2>\n\n\n\n<p>\u65b9\u6cd51\uff1adp\uff0c\u590d\u6742\u5ea6 $O(n^2)$ \u4e14\u53ea\u80fd\u5f97\u5230\u957f\u5ea6\u3002<a href=\"https:\/\/www.acwing.com\/activity\/content\/problem\/content\/1003\/\">\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217 I<\/a><\/p>\n\n\n\n<p>\u65b9\u6cd52\uff1a\u7ef4\u62a4\u540e\u7f00\u6700\u5c0f\u7684\u4e0a\u5347\u5e8f\u5217\u3002\u6bcf\u6b21\u4e8c\u5206\u63d2\u5165\u3002\uff08\u53ef\u8f93\u51fa\u6700\u957f\u5e8f\u5217\uff09<a rel=\"noreferrer noopener\" href=\"https:\/\/www.acwing.com\/activity\/content\/problem\/content\/1004\/\" target=\"_blank\">\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217 II<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217<\/h2>\n\n\n\n<p>dp\u8fc7\u7a0b\u4f1a\u6709\u96c6\u5408\u91cd\u53e0\uff0c\u4f46\u662f\u4e0d\u5f71\u54cd\u7ed3\u679c\uff0c\u56e0\u4e3a\u72b6\u6001\u51fd\u6570\u662f\u53d6MAX\u3002<\/p>\n\n\n\n<p>$f[i][j]=max(f[i-1][j], f[i][j-1])$ \u8fd9\u91cc\u6709\u91cd\u53e0\uff0c\u4e24\u8005\u90fd\u53ef\u4ee5\u662f $s[i]$ \u548c $s[j]$ \u4e0d\u53d6\uff0c\u4ece\u800c\u4e24\u8005\u90fd\u53ef\u4ee5\u9000\u5316\u6210 $f[i-1][j-1]$<\/p>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/899\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6700\u957f\u516c\u5171\u4e0a\u5347\u5b50\u5e8f\u5217<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$O(n^3)\u4f18\u5316\u5230O(n^2)$<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/274\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6700\u957f\u516c\u5171\u4e0a\u5347\u5b50\u5e8f\u5217<\/a><\/p>\n\n\n\n<p>\u72b6\u6001\u8868\u793a\uff1a$f[i][j]$\uff1a\u8003\u8651a\u7684\u524d $i$ \u4e2a\u5b57\u6bcd\u548cb\u7684\u524d $j-1$ \u4e2a\u5b57\u6bcd\u4e14\u4ee5 $j$ \u7ed3\u5c3e\u7684\u6700\u957f\u516c\u5171\u4e0a\u5347\u5b50\u5e8f\u5217<\/p>\n\n\n\n<p>\u539f\u59cb\u4ee3\u7801<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>for(int i=1;i&lt;=n;i++)\n{\n    for(int j=1;j&lt;=n;j++)\n    {\n        f&#91;i]&#91;j]=f&#91;i-1]&#91;j]; \/\/\u4e0d\u9009\n        if(a&#91;i] == b&#91;j]) \n        {\n            int maxv=1; \/\/\u957f\u5ea6\u4e3a1\n            for(int k=1;k&lt;j;k++) \/\/\u957f\u5ea6\u81f3\u5c11\u4e3a2\n            {\n                if(a&#91;i]==b&#91;k]) maxv=max(maxv, f&#91;i-1]&#91;k] + 1);\n            }\n            f&#91;i]&#91;j]=max(f&#91;i]&#91;j], maxv);\n        }\n    }\n}<\/code><\/pre>\n\n\n\n<p>\u4f18\u5316\u540e\u4ee3\u7801<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>for(int i=1;i&lt;=n;i++)\n{\n    int maxv=1; \/\/\u957f\u5ea6\u4e3a1 maxv\u7ef4\u62a4a&#91;i] &gt; b&#91;k] \u7684\u4e0b\u7684f&#91;i]&#91;k]\u7684\u6700\u5927\u503c\u5c31\u884c\u4e86\n    for(int j=1;j&lt;=n;j++)\n    {\n        f&#91;i]&#91;j]=f&#91;i-1]&#91;j]; \/\/\u4e0d\u9009\n        if(a&#91;i] == b&#91;j]) \n        {\n            f&#91;i]&#91;j]=max(f&#91;i]&#91;j], maxv); \/\/\u627e\u4e00\u4e2a\u524d\u9762\u7684\u6700\u5927\u503c\u9009\n        }\n        if(a&#91;i] &gt; b&#91;j]) maxv=max(maxv, f&#91;i-1]&#91;j] + 1);\n    }\n}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u6700\u5927\u4e0a\u5347\u5b50\u5e8f\u5217<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4ece\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u6362\u4e00\u4e2a\u96c6\u5408\u5c5e\u6027\u5c31\u884c\u4e86\u3002\u957f\u5ea6max\u6539\u4e3a\u52a0\u548cmax<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/1018\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6700\u5927\u4e0a\u5347\u5b50\u5e8f\u5217<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6700\u957f\u56de\u6587\u5b50\u4e32<\/h2>\n\n\n\n<p>\u533a\u95f4DP\uff0c\u6bcf\u6b21\u679a\u4e3e\u533a\u95f4\u957f\u5ea6\u3002\u6ce8\u610f\u5947\u6570\u548c\u5076\u6570\u8981\u5206\u5f00\u5904\u7406\u4e00\u4e0b\u3002<\/p>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/leetcode.cn\/problems\/longest-palindromic-substring\/description\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noreferrer noopener\">\u6700\u957f\u56de\u6587\u5b50\u4e32 &#8211; \u529b\u6263<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6700\u957f\u8fde\u7eed\u4e0d\u91cd\u590d\u5b50\u5e8f\u5217<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u54c8\u5e0c\u8868+\u53cc\u6307\u9488<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/submission\/801\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6700\u957f\u8fde\u7eed\u4e0d\u91cd\u590d\u5b50\u5e8f\u5217<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">01\u80cc\u5305<\/h2>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/2\/\" target=\"_blank\" rel=\"noreferrer noopener\">01\u80cc\u5305<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b8c\u5168\u80cc\u5305<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6bcf\u4e2a\u7269\u54c1\u53ef\u4ee5\u53d6\u65e0\u9650\u6b21<\/li>\n\n\n\n<li>\u539f\u59cb\u4ee3\u7801\u679a\u4e3e\u6b21\u6570\uff0c\u4f46\u662f\u53ef\u4f18\u5316\u3002\u590d\u6742\u5ea6\u4efb\u7136\u662f $O(nm)$<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/3\/\">\u5b8c\u5168\u80cc\u5305\u95ee\u9898<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u591a\u91cd\u80cc\u5305<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7269\u54c1\u6700\u591a\u53ea\u80fd\u53d6\u7279\u5b9a\u6b21\u6570<\/li>\n<\/ul>\n\n\n\n<p>\u7b80\u5355\u7248\u672c\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/4\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u591a\u91cd\u80cc\u5305\u95ee\u9898 I<\/a><\/p>\n\n\n\n<p>\u4e8c\u8fdb\u5236\u4f18\u5316\u7248\u672c\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/4\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u591a\u91cd\u80cc\u5305\u95ee\u9898 II<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5206\u7ec4\u80cc\u5305<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u540c\u4e00\u7ec4\u7684\u7269\u54c1\u6700\u591a\u53ea\u80fd\u90091\u4e2a\uff0c\u590d\u6742\u5ea6 $O(nms)$<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/9\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u5206\u7ec4\u80cc\u5305\u95ee\u9898<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">KMP<\/h2>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/833\/\" target=\"_blank\" rel=\"noreferrer noopener\">KMP\u5b57\u7b26\u4e32<\/a><\/p>\n\n\n\n<p>\u6838\u5fc3\u4ee3\u7801<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/\u6c42next\u6570\u7ec4\nfor(int i=2, j=0;i&lt;=n;i++)\n{\n    while(j &amp;&amp; p&#91;i]!=p&#91;j+1]) j=ne&#91;j];\n    if(p&#91;i]==p&#91;j+1]) j++;\n    ne&#91;i]=j;\n}\n\n\/\/\u5339\u914d\u8fc7\u7a0b\nfor(int i=1, j=0; i&lt;=m; i++)\n{\n    while(j &amp;&amp; s&#91;i]!=p&#91;j+1]) j=ne&#91;j];\n    if(s&#91;i]==p&#91;j+1]) j++;\n    if(j==n) \n    {\n        cout&lt;&lt;i-n&lt;&lt;' ';\n        j=ne&#91;j];\n    }\n}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u5355\u8c03\u6808<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u53ef\u4ee5\u6c42\u6bcf\u4e2a\u6570\u524d\u9762\u6bd4\u5b83\u5c0f\u7684\u6570\u7684\u6700\u8fd1\u7684\u6570<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/833\/\" data-type=\"link\" data-id=\"https:\/\/www.acwing.com\/problem\/content\/833\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u5355\u8c03\u6808<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5355\u8c03\u961f\u5217<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5355\u8c03\u961f\u5217\u76f8\u5bf9\u7528\u5904\u5927\u4e00\u4e9b<\/li>\n\n\n\n<li>\u53ef\u4ee5\u6c42\u6ed1\u52a8\u7a97\u53e3\u6700\u5927\u6700\u5c0f\u503c<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/156\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6ed1\u52a8\u7a97\u53e3<\/a>\uff0c<a href=\"https:\/\/leetcode.cn\/problems\/sliding-window-maximum\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noreferrer noopener\">\u6ed1\u52a8\u7a97\u53e3\u6700\u5927\u503c &#8211; \u529b\u6263<\/a><\/p>\n\n\n\n<p>acwing\u7b80\u5355\u9898\uff0c\u5230\u4e86leetcode\u53d8\u6210\u56f0\u96be\u9898\uff0c2333\ud83d\ude00<\/p>\n\n\n\n<p>\u6838\u5fc3\u4ee3\u7801<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>int hh=0,tt=-1;\nfor(int i=1;i&lt;=n;i++) \/\/\u5355\u8c03\u9012\u589e\u961f\u5217 \u7ef4\u5ea6\u6700\u5c0f\u503c\n{\n    while(hh&lt;=tt &amp;&amp; a&#91;q&#91;tt]] &gt;= a&#91;i]) tt--;\n    q&#91;++tt]=i;\n\n    if(i-q&#91;hh]+1 &gt; m) hh++; \/\/\u6ce8\u610f\u8fd9\u91cc\u662fq&#91;hh]\uff0c\u4e0d\u662fhh\n    if(i&gt;=m) printf(\"%d \", a&#91;q&#91;hh]]);\n}\nputs(\"\");\n    \nhh=0,tt=-1;\nfor(int i=1;i&lt;=n;i++) \/\/\u5355\u8c03\u9012\u51cf\u961f\u5217 \u7ef4\u62a4\u6700\u5927\u503c\n{\n    while(hh&lt;=tt &amp;&amp; a&#91;q&#91;tt]] &lt;= a&#91;i]) tt--;\n    q&#91;++tt]=i;\n        \n    if(i-q&#91;hh]+1 &gt; m) hh++;\n    if(i&gt;=m) printf(\"%d \", a&#91;q&#91;hh]]);\n}<\/code><\/pre>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5308\u7259\u5229\u7b97\u6cd5\uff0c\u590d\u6742\u5ea6\u6700\u9ad8 $O(mn)$\uff0c\u5b9e\u9645\u5f88\u96be\u8fbe\u5230\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/863\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u4e8c\u5206\u56fe\u7684\u6700\u5927\u5339\u914d<\/a><\/p>\n\n\n\n<p>\u6838\u5fc3\u4ee3\u7801<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>int n1,n2,m;\n\nint match&#91;N];\nbool st&#91;N]; \/\/\u8ba9\u5de6\u8fb9\u7684\u7537\u751f\u90fd\u7ee7\u7eed\u53bb\u8003\u8651\u53f3\u8fb9\u8fde\u7ebf\u7684\u6240\u6709\u5973\u751f\uff0c\n\/\/\u5982\u679c\u4e0d\u91cd\u7f6est\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7537\u751f\u5c06\u5c1d\u8bd5\u90fd\u4e0d\u4f1a\u5c1d\u8bd5\u3002\n\/\/\u53ea\u6709st=false\u624d\u4f1a\u7ee7\u7eed\u5c1d\u8bd5\uff0c\u8ba9\u81ea\u5df1\u5fc3\u7cfb\u7684\u5973\u751f\u5c1d\u8bd5\u7eff\u4e86\u5979\u73b0\u5728\u7684\u7537\u751f\u3002\n\/\/\u6e29\u99a8\u63d0\u793a\uff1a\u8fd9\u4e2a\u5339\u914d\u8bf4\u6cd5\u6765\u81eayxc\uff01\n\nbool find(int u)\n{\n    for(int i=h&#91;u];~i;i=ne&#91;i])\n    {\n        int j=e&#91;i];\n        if(!st&#91;j])\n        {\n            st&#91;j]=true;\n            if(!match&#91;j] || find(match&#91;j]))\n            {\n                match&#91;j]=u;\n                return true;\n            }\n        }\n    }\n    \n    return false;\n}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u533a\u95f4\u95ee\u9898<\/h2>\n\n\n\n<p>\u533a\u95f4\u9009\u70b9\uff1ahttps:\/\/www.acwing.com\/problem\/content\/907\/<\/p>\n\n\n\n<p>\u6700\u5927\u4e0d\u76f8\u4ea4\u533a\u95f4\u6570\u91cf\uff1ahttps:\/\/www.acwing.com\/problem\/content\/910\/<\/p>\n\n\n\n<p>\u533a\u95f4\u5206\u7ec4\uff1ahttps:\/\/www.acwing.com\/problem\/content\/908\/<\/p>\n\n\n\n<p>\u533a\u95f4\u8986\u76d6\uff1ahttps:\/\/www.acwing.com\/problem\/content\/909\/<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">\u6570\u8bba\uff08latex\u4fee\u597d\u518d\u5199\uff09<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u7b5b\u8d28\u6570<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5 \u590d\u6742\u5ea6 $O(nlog(log(n)))$<\/li>\n\n\n\n<li>\u6b27\u62c9\u7b5b\uff0c\u6bcf\u4e2a\u5408\u6570\u53ea\u4f1a\u88ab\u6700\u5c0f\u8d28\u56e0\u5b50\u7b5b\u53bb $O(n)$<\/li>\n<\/ol>\n\n\n\n<p>\u6b27\u62c9\u7b5b\u6838\u5fc3\u4ee3\u7801\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>int euler(int n)\/\/\u6b27\u62c9\u7b5b\u6cd5\n{\n    int cnt=0;\n    for(int i=2;i&lt;=n;i++)\n    {\n        if(!st&#91;i]) primes&#91;cnt++]=i;\n        for(int j=0;primes&#91;j]&lt;=n\/i;j++) \/\/primes&#91;j] * i &lt;= n \u597d\u7406\u89e3\u4e9b\uff0c\u4f46\u662f\u9632\u6b62\u6ea2\u51fa\n        {\n            st&#91;primes&#91;j]*i]=true;\n            if(i%primes&#91;j]==0) break;\n        }\n    }\n    return cnt;\n}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u5feb\u901f\u5e42<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u672c\u8d28\u4e0a\u8ddf\u591a\u91cd\u80cc\u5305\u7684\u4e8c\u8fdb\u5236\u4f18\u5316\u76f8\u4f3c\uff0c\u90fd\u662f\u4e8c\u8fdb\u5236\u4f18\u5316\u3002\u8fd8\u6709\u6811\u72b6\u6570\u7ec4\u4e5f\u662f\u8fd9\u7c7b\u601d\u60f3<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/877\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u5feb\u901f\u5e42<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6c42\u7ec4\u5408\u6570<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6570\u636e\u8303\u56f4 $2000$ \u5de6\u53f3\uff0c\u76f4\u63a5\u9012\u63a8\uff0c\u590d\u6742\u5ea6 $O(n^2)$<\/li>\n\n\n\n<li>\u6570\u636e\u8303\u56f4 $1e6$ \u5de6\u53f3\uff0c\u524d\u7f00\u548c\u9012\u63a8\uff0c\u6a21\u6570\u4e3a\u8d28\u6570\u7528\u8d39\u9a6c\u5c0f\u5b9a\u7406\u6c42\u9006\u5143\u3002\u6700\u540e\u7528\u6570\u5b66\u4e0a\u7684\u7ec4\u5408\u6570\u65b9\u6cd5\u76f4\u63a5\u6c42<\/li>\n\n\n\n<li>\u6570\u636e\u8303\u56f4 $1e18$\uff0c\u65e0\u6cd5\u76f4\u63a5\u7b97\uff0c\u4f46\u662f\u5728\u53d6\u6a21\u7684\u6761\u4ef6\u4e0b\u6709\u5362\u5361\u65af\u5b9a\u7406\u3002$$C^{n}_{m}=C^{n\\%p}_{m\\%p} \\cdot C^{\\lfloor \\frac{n}{p} \\rfloor}_{\\lfloor \\frac{m}{p} \\rfloor} \\% p$$<\/li>\n<\/ol>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.acwing.com\/problem\/content\/887\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6c42\u7ec4\u5408\u6570 I<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.acwing.com\/problem\/content\/888\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6c42\u7ec4\u5408\u6570 II<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.acwing.com\/problem\/content\/889\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6c42\u7ec4\u5408\u6570 III<\/a><\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u535a\u5f08\u8bba<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8303\u56f4\u5f88\u5e7f\uff0c\u4e0d\u9650\u4e8e\u8bb0\u5fc6\u5316\u641c\u7d22+\u601d\u7ef4<\/li>\n<\/ul>\n\n\n\n<p>\u6682\u65f6\u4e0d\u505a\u63cf\u8ff0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7ea6\u6570\u4e2a\u6570<\/h2>\n\n\n\n<p>\u8bbe\u4e00\u4e2a\u6570 $N = (p_1^{x_1})(p_2^{x_2})(p_3^{x_3})\u2026(p_k^{x_k})$\uff0c\u5176\u4e2d $p_i$ \u4e3a\u8d28\u6570\u3002<\/p>\n\n\n\n<p>\u5219 $N$ \u7684<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7ea6\u6570\u4e2a\u6570\u4e3a\uff1a$(x_1+1)(x_2+1)(x_3+1)\u2026(x_k+1)$\uff0c<\/li>\n\n\n\n<li>\u7ea6\u6570\u4e4b\u548c\u4e3a\uff1a$(p_1^0+p_1^1+\u2026+p_1^{x_1})\u2217\u2026\u2217(p_k^0+p_k^1+\u2026+p_k^{c_k})$<\/li>\n<\/ol>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/872\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u7ea6\u6570\u4e2a\u6570<\/a><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>unordered_map&lt;int,int&gt;primes;\nwhile(n--)\n{\n    int x; cin&gt;&gt;x;\n\n    for(int i=2;i&lt;=x\/i;i++)\/\/\u5206\u89e3\u8d28\u56e0\u5b50\n    {\n        while(x%i==0)\n        {\n            primes&#91;i]++;\n            x\/=i;\n        }\n    }\n\n    if(x&gt;1) primes&#91;x]++;\n}\n\nlong long res=1;\nfor(auto prime:primes) res=res*(prime.second+1)%mod;\n<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u7ea6\u6570\u4e4b\u548c<\/h2>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/873\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u7ea6\u6570\u4e4b\u548c<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6b27\u62c9\u51fd\u6570<\/h2>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/875\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6b27\u62c9\u51fd\u6570<\/a><\/p>\n\n\n\n<p>\u5b9a\u4e49\uff1a\u5bf9\u4e8e\u6b63\u6574\u6570 $n$\uff0c\u6b27\u62c9\u51fd\u6570\u662f\u5c0f\u4e8e\u6216\u7b49\u4e8e $n$ \u7684\u6b63\u6574\u6570\u4e2d\u4e0e $n$ \u4e92\u8d28\u7684\u6570\u7684\u6570\u76ee\uff0c\u8bb0\u4f5c $varphi n\uff0c  \\varphi(1)=1$<\/p>\n\n\n\n<p>\u6b27\u62c9\u51fd\u6570 $\\phi(n)$ \u662f\u79ef\u6027\u51fd\u6570\uff0c\u5373\u5f53 $m$ \u4e0e $n$ \u4e92\u8d28\u65f6\uff1a$\\varphi(mn) = \\varphi(m) \\cdot \\varphi(n)$<br>\u6839\u636e\u552f\u4e00\u5206\u89e3\u5b9a\u7406\u77e5 $n = p_1^{a_1} p_2^{a_2} \\cdots p_x^{a_x}$<br>\u56e0\u6b64\uff1a$\\varphi(n) = \\varphi(p_1^{a_1}) \\cdot \\varphi(p_2^{a_2}) \\cdots \\varphi(p_x^{a_x})$<br><strong>\u7d20\u6570\u5e42\u7684\u6b27\u62c9\u51fd\u6570<\/strong><br>\u5bf9\u4e8e\u7d20\u6570\u5e42\uff08\u7d20\u6570\u7684\u6b63\u6574\u6570\u6b21\u5e42\uff09 $p_k^{a_k}$\uff1a<br>$$<br>\\varphi(p_k^{a_k}) = p_k^{a_k} &#8211; p_k^{a_k-1} = p_k^{a_k}(1 &#8211; \\frac{1}{p_k})<br>$$<br> <strong>\u4e00\u822c\u516c\u5f0f<\/strong><br>\u6700\u7ec8\u6b27\u62c9\u51fd\u6570\u516c\u5f0f\u4e3a\uff1a<br>$$<br>\\varphi(n) = n \\cdot \\prod_{i=1}^{x} {(1 &#8211; \\frac{1}{p_i})}<br>$$<br><\/p>\n\n\n\n<p>\u7b5b\u6cd5\u6c42\u6b27\u62c9\u51fd\u6570 <a href=\"https:\/\/www.acwing.com\/problem\/content\/876\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u7b5b\u6cd5\u6c42\u6b27\u62c9\u51fd\u6570<\/a><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e8b\u5b9e\u4e0a\u6b27\u62c9\u7b5b\u53ef\u4ee5\u6c42\u5f88\u591a\u4e1c\u897f\uff0c\u4e0d\u53ea\u662f\u6b27\u62c9\u51fd\u6570<\/li>\n<\/ul>\n\n\n\n<p>\u6682\u65f6\u7565&#8230;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6982\u7387\u4e0e\u6570\u5b66\u671f\u671b<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u672c\u8d28\u4e0a\u662f\u6982\u7387dp<\/li>\n<\/ul>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a href=\"https:\/\/www.acwing.com\/problem\/content\/219\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u7eff\u8c46\u86d9\u7684\u5f52\u5bbf<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u535a\u5f08\u8bba<\/h2>\n\n\n\n<p><strong>\u516c\u5e73\u7ec4\u5408\u6e38\u620fICG\u200b<\/strong>\u200b<br>\u82e5\u4e00\u4e2a\u6e38\u620f\u6ee1\u8db3\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7531\u4e24\u540d\u73a9\u5bb6\u4ea4\u66ff\u884c\u52a8\uff1b<\/li>\n\n\n\n<li>\u5728\u6e38\u620f\u8fdb\u7a0b\u7684\u4efb\u610f\u65f6\u523b\uff0c\u53ef\u4ee5\u6267\u884c\u7684\u5408\u6cd5\u884c\u52a8\u4e0e\u8f6e\u5230\u54ea\u540d\u73a9\u5bb6\u65e0\u5173\uff1b<\/li>\n\n\n\n<li>\u4e0d\u80fd\u884c\u52a8\u7684\u73a9\u5bb6\u5224\u8d1f\uff1b<br>\u5219\u79f0\u8be5\u6e38\u620f\u4e3a\u4e00\u4e2a\u516c\u5e73\u7ec4\u5408\u6e38\u620f\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u200b<strong>\u200b<\/strong>\u4e3e\u4f8b\u8bf4\u660e\u200b\u200b<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>NIM\u535a\u5f08\u5c5e\u4e8e\u516c\u5e73\u7ec4\u5408\u6e38\u620f\u3002<\/li>\n\n\n\n<li>\u56f4\u68cb\u7b49\u57ce\u5efa\u68cb\u7c7b\u6e38\u620f\u4e0d\u5c5e\u4e8e\u516c\u5e73\u7ec4\u5408\u6e38\u620f\uff0c\u56e0\u4e3a\u56f4\u68cb\u4ea4\u6218\u53cc\u65b9\u5206\u522b\u53ea\u80fd\u843d\u9ed1\u5b50\u548c\u767d\u5b50\uff08\u884c\u52a8\u53d7\u9650\uff09\uff0c\u4e14\u80dc\u8d1f\u5224\u5b9a\u590d\u6742\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5148\u624b\u5fc5\u80dc\u72b6\u6001\uff08\u5148\u624b\u62ff\u5b8c\u4ee5\u540e\u8ba9\u5269\u4e0b\u7684\u72b6\u6001\u662f\u5148\u624b\u5fc5\u8d25\u72b6\u6001\uff0c\u90a3\u5c31\u5c31\u662f\u5fc5\u80dc\u72b6\u6001\uff09<\/p>\n\n\n\n<p>\u5148\u624b\u5fc5\u8d25\u72b6\u6001\uff08\u4e0d\u7ba1\u600e\u4e48\u64cd\u4f5c\uff0c\u90fd\u662f\u8f93\uff09<\/p>\n\n\n\n<p><strong>\u8bc1\u660e\u8fc7\u7a0b<\/strong>\uff1a<\/p>\n\n\n\n<p>\u82e5$a_1, a_2, &#8230; ,a_n$ \u90fd\u4e3a $0$\uff0c\u5219\u8f93\u6389\u6bd4\u8d5b\uff0c\u4e14\u5176\u5f02\u6216\u548c\u4e5f\u4e3a0\u3002<\/p>\n\n\n\n<p>\u5fc5\u80dc\u6001\uff1a\u5f02\u6216\u548c\u4e0d\u4e3a0\uff0c\u7136\u540e\u5728\u7b2c $i$ \u5806\u53d6 $a_i-(a_i \\oplus x)$\u4e2a\u77f3\u5b50\uff0c\u8f6c\u4e3a\u5fc5\u8d25\u6001\u7559\u7ed9\u5bf9\u624b<\/p>\n\n\n\n<p>\u5fc5\u8d25\u6001\uff1a\u5f02\u6216\u548c\u4e3a0\uff0c\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u5fc5\u7136\u8f6c\u4e3a\u5fc5\u80dc\u6001\u7559\u7ed9\u5bf9\u624b<\/p>\n\n\n\n<p>\u8bc1\u660e1\uff1a\u5fc5\u80dc\u6001\u5fc5\u7136\u53ef\u4ee5\u8f6c\u4e3a\u5fc5\u53d8\u6001\u3002\u8bbe\u76ee\u524d\u7684\u5f02\u6216\u548c\u4e3a $x$\uff0c\u5219 $x&gt;0$ \u4e14\u5fc5\u7136\u6709x\u7684\u6700\u9ad8\u4f4d\u4e3a $1$\uff0c\u8bbe\u4e3a $i$\u3002\u90a3\u4e48\u5728 $a_{1\\sim n}$ \u4e2d\u5fc5\u7136\u5b58\u5728\u67d0\u4e00\u4e2a\u5806\uff0c\u5176\u7b2c $i$ \u4f4d\u4e3a $1$\u3002\u5219 $a_i \\oplus x&lt;a_i$\uff0c\u7136\u540e\u5728\u8fd9\u4e00\u5806\u91cc\u53d6\u8d70 $a_i-(a_i \\oplus x)$ \u4e2a\u77f3\u5b50\uff0c\u8fd9\u4e00\u5806\u5c31\u53d8\u6210 $a_i \\oplus x$\u3002\u73b0\u5728\u7684\u5f02\u6216\u548c\u66f4\u65b0\u4e3a $a_1\\oplus a_2 \\oplus &#8230; \\oplus (a_i \\oplus x) \\oplus &#8230;\\oplus a_n=0$ \uff08\u76f8\u5f53\u4e8e\u539f\u5148\u7684\u5f02\u6216\u548c $x$ \u591a\u5f02\u6216\u4e86\u4e00\u4e2a $x$\uff0c\u53d8\u4e3a $0$\uff09\u3002<\/p>\n\n\n\n<p>\u8bc1\u660e2\uff1a\u5fc5\u8d25\u6001\u968f\u673a\u53d6\u4e00\u4e2a\u5fc5\u7136\u53d8\u6210\u5fc5\u8d25\u6001\u3002\u8fd9\u4e2a\u663e\u7136\u6613\u89c1\u3002\u4ece\u5f02\u6216\u548c\u4e3a $0$ \u7684\u77f3\u5b50\u5806\u4e2d\u968f\u673a\u53d6\u6570\uff0c\u5fc5\u7136\u5bfc\u81f4\u73b0\u5728\u7684\u5f02\u6216\u548c\u4e3a $0$ \u5f02\u6216\u4e0a\u53d6\u51fa\u7684\u6570\u3002\u5219\u5fc5\u7136\u4e0d\u4e3a $0$\u3002\u6b64\u65f6\u8f6c\u4e3a\u5fc5\u80dc\u6001\u3002<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>\u6a21\u677f\u9898\uff1a<a rel=\"noreferrer noopener\" href=\"https:\/\/www.acwing.com\/problem\/content\/893\/\" target=\"_blank\">Nim\u6e38\u620f<\/a><\/p>\n\n\n\n<p>\u82e5$a_1\\oplus a_2 \\oplus &#8230; \\oplus a_n=0$\uff0c\u4e3a\u5148\u624b\u5fc5\u8d25\u72b6\u6001\uff0c\u53cd\u4e4b\u4e3a\u5148\u624b\u5fc5\u80dc<\/p>\n\n\n\n<p>\u6e38\u620f\u4ee3\u7801\uff08\u548c\u522b\u4eba\u5bf9\u6218\uff09\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include &lt;bits\/stdc++.h&gt;\n#define x first\n#define y second\n#define all(x) x.begin(),x.end()\n#define rep(i, l, r) for (int i = l; i &lt;= r; i++)\n#define nep(i, r, l) for (int i = r; i &gt;= l; i--)\nusing namespace std;\ntypedef long long LL;\ntypedef unsigned long long ULL;\ntypedef pair&lt;int,int&gt; PII;\ntypedef pair&lt;LL,int&gt; PLI;\nconst int INF=0x3f3f3f3f,MOD=998244353,P=131,N=15, M=110;\n\nint e&#91;M],h&#91;N],ne&#91;M],idx;\n\nvoid add(int a, int b)\n{\n\te&#91;idx]=b, ne&#91;idx]=h&#91;a], h&#91;a]=idx++;\n}\n\n\nint a&#91;N], n;\n\nbool check()\n{\n    rep(i,1,n) if(a&#91;i]) return true;\n    return false;\n}\n\nvoid get()\n{\n    int x=0;\n    rep(i,1,n) x ^= a&#91;i];\n    if(x==0)\n    {\n        cout&lt;&lt;\"\u5f53\u524d\u5904\u4e8e\u5fc5\u8d25\u6001\"&lt;&lt;endl;\n        rep(i,1,n)\n        {\n            if(a&#91;i])\n            {\n                a&#91;i]--;\n                printf(\"\u89e3\u7b54\uff1a\u7b2c%d\u5806\u62ff\u51fa1\u4e2a\u77f3\u5b50\\n\", i);\n                return;\n            }\n        }\n    }\n    else cout&lt;&lt;\"\u5f53\u524d\u5904\u4e8e\u5fc5\u80dc\u6001\"&lt;&lt;endl;\n\n    for(int i=31;i&gt;=0;i--)\n    {\n        if(x&gt;&gt;i&amp;1)\n        {\n            rep(j,1,n) if(a&#91;j] &gt;&gt; i &amp; 1)\n            {\n                printf(\"\u89e3\u7b54\uff1a\u7b2c%d\u5806\u62ff\u51fa%d\u4e2a\u77f3\u5b50\\n\", j, a&#91;j] - (a&#91;j] ^ x));\n                a&#91;j] ^= x;\n                break;\n            }\n            break;\n        }\n    }\n}\n\nvoid adver()\n{\n    cout&lt;&lt;\"\u8bf7\u8f93\u5165\u5bf9\u65b9\u64cd\u4f5c\u7684\u300a\u5806\u7f16\u53f7\u300b\u548c\u300a\u53d6\u8d70\u7684\u6570\u91cf\u300b\uff1a\";\n    int kk, cnt; cin&gt;&gt;kk&gt;&gt;cnt;\n    a&#91;kk]-=cnt;\n}\n\nint main()\n{\n    cout&lt;&lt;\"\u8bf7\u8f93\u5165\u77f3\u5b50\u300a\u5806\u6570\u300b\uff1a\";\n    cin&gt;&gt;n;\n    cout&lt;&lt;\"\u8bf7\u8f93\u5165\u300a\u6bcf\u4e00\u5806\u77f3\u5b50\u7684\u6570\u91cf\u300b\uff0c\u4ee5\u7a7a\u683c\u5206\u5f00\uff1a\";\n    rep(i,1,n) cin&gt;&gt;a&#91;i];\n    cout&lt;&lt;\"\u6211\u662f\u5148\u624b\uff0c\u8f93\u5165\u300a1\u300b\uff0c\u5426\u5219\u8f93\u5165\u300a0\u300b\"&lt;&lt;endl;\n    int t; cin&gt;&gt;t;\n\n    if(!t) adver();\n    while(check())\n    {\n        cout&lt;&lt;\"-------------------------------------------\"&lt;&lt;endl;\n        cout&lt;&lt;\"\u73b0\u5728\u7684\u77f3\u5b50\u6570\u91cf\u4fe1\u606f\uff1a\"&lt;&lt;endl;\n        rep(i,1,n) cout&lt;&lt;a&#91;i]&lt;&lt;' '; cout&lt;&lt;endl;\n\n        get();\n        if(!check()) \n        {\n            cout&lt;&lt;\"\u62ff\u5b8c\u6b64\u6b21\uff0c\u5bf9\u624b\u8f93\u4e86\"&lt;&lt;endl;\n            break;\n        }\n        adver();\n        if(!check())\n        {\n            cout&lt;&lt;\"\u5bf9\u624b\u62ff\u5b8c\u6b64\u6b21\uff0c\u6211\u8f93\u4e86\"&lt;&lt;endl;\n        }\n    }\n    return 0;\n}\n<\/code><\/pre>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u624b\u6495\u7ecf\u5178\u7b97\u6cd5 \u5feb\u901f\u6392\u5e8f \u6838\u5fc3\u4ee3\u7801\uff1a \u7406\u89e3\u70b91\uff1a\u5982\u679c\uff0cl++\u7684\u65f6\u5019\u52a0\u5230 r \u7684\u4f4d\u7f6e\u3002\u7531\u4e0a\u4e00\u8f6e\u77e5\uff0cr \u7684\u4f4d\u7f6ea[r [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[41],"tags":[],"class_list":["post-457","post","type-post","status-publish","format-standard","hentry","category-tech"],"_links":{"self":[{"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/posts\/457","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/comments?post=457"}],"version-history":[{"count":24,"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/posts\/457\/revisions"}],"predecessor-version":[{"id":561,"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/posts\/457\/revisions\/561"}],"wp:attachment":[{"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/media?parent=457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/categories?post=457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vcoco.top\/index.php\/wp-json\/wp\/v2\/tags?post=457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}