{"id":45,"date":"2025-01-11T22:50:54","date_gmt":"2025-01-11T14:50:54","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=45"},"modified":"2025-01-11T22:50:54","modified_gmt":"2025-01-11T14:50:54","slug":"b-gamegame-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e5%8d%9a%e5%bc%88","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=45","title":{"rendered":"B. GameGame \u89e3\u6790(\u601d\u7dad\u3001\u535a\u5f08)"},"content":{"rendered":"\n<div class=\"wp-block-jetpack-markdown\"><h1>Codeforce 1383 B. GameGame \u89e3\u6790(\u601d\u7dad\u3001\u535a\u5f08)<\/h1>\n<p>\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF1383B<br>\n<a href=\"https:\/\/codeforces.com\/problemset\/problem\/1383\/B\">\u984c\u76ee\u9023\u7d50<\/a><\/p>\n<blockquote>\n<p><strong>\u984c\u76ee<\/strong><br>\n\u5169\u500b\u4eba\u5728\u73a9\u904a\u6232\uff0c\u6709\u4e00\u500b\u9577\u5ea6\u70ba$n$\u7684\u6578\u5217$a$\uff0c\u6bcf\u6b21\u6bcf\u500b\u4eba\u9078\u4e00\u500b\u6578\u5b57\u548c\u76ee\u524d\u81ea\u5df1\u7684\u5206\u6578XOR(\u521d\u59cb\u70ba0\u5206)\uff0c\u6700\u5f8c\u62ff\u5230\u6700\u591a\u5206\u6578\u7684\u4eba\u8d0f\uff0c\u6c42\u8ab0\u6703\u8d0f?<\/p>\n<\/blockquote>\n<h3>\u524d\u8a00<\/h3>\n<p>\u535a\u5f08\u7684\u984c\u76ee\u4e00\u76f4\u4e0d\u662f\u5f88\u6703\u505a\uff0c\u9019\u6b21\u9019\u984c\u6709\u500b\u6211\u5e73\u6642\u53ef\u80fd\u4e0d\u6703\u60f3\u5230\u7684\u65b0\u60f3\u6cd5:\u53ef\u4ee5\u5617\u8a66\u8b93\u5176\u4e2d\u4e00\u500b\u73a9\u5bb6\u8ddf\u96a8\u53e6\u4e00\u500b\u73a9\u5bb6\u505a\u52d5\u4f5c\uff0c\u5982\u679c\u88ab\u8ddf\u96a8\u7684\u90a3\u500b\u73a9\u5bb6\u6700\u5f8c\u6703\u8f38\uff0c\u90a3\u9ebc\u8ddf\u96a8\u7684\u90a3\u500b\u73a9\u5bb6\u5c31\u6703\u8d0f\u3002\u9019\u662f\u56e0\u70ba\u6211\u5011\u7d66\u51fa\u4e86\u4e00\u500b\u660e\u78ba\u7684\u79fb\u52d5\u65b9\u6cd5\u3002<\/p>\n<h3>\u60f3\u6cd5<\/h3>\n<p>\u9996\u5148\u8981\u77e5\u9053\u4e00\u4ef6\u4e8b:\u5982\u679c\u4e00\u500b\u73a9\u5bb6\u80fd\u5920\u4f7f\u5f97\u5206\u6578\u6709\u6700\u9ad8\u4f4d\u7684bit\uff0c\u4e26\u4e14\u53e6\u5916\u4e00\u500b\u4eba\u6c92\u6709\uff0c\u90a3\u9ebc\u5c31\u8d0f\u4e86\u3002\u9019\u662f\u56e0\u70ba\u5728\u53f3\u908a\u7684bit\u4e0d\u7ba1\u6709\u591a\u5c11\uff0c\u90fd\u6bd4\u4e0d\u4e0a\u6700\u5de6\u908a\u7684bit(\u6b63\u5f0f\u4f86\u8aaa:$2^n&gt;\\sum\\limits_{i=0}^{n-1}2^i\\ \\forall n\\in\\mathbb{N}_{\\ge1}$)\u3002<br>\n\u90a3\u9ebc\u6211\u5011\u53ef\u4ee5\u5148\u7d71\u8a08\u5c0d\u65bcbit\u6709\u5e7e\u500b\u5143\u7d20\u6709\u9019\u500bbit\uff0c\u63a5\u8457\u6211\u5011\u5f9e\u6700\u5de6\u908a\u7684bit\u958b\u59cb\u300c\u8003\u616e\u300d:<br>\n\u5206\u70ba\u5169\u7a2e\u60c5\u6cc1:<\/p>\n<ol>\n<li>\n<p>\u9019\u500bbit\u6709\u5076\u6578\u500b\uff0c\u90a3\u9ebc\u7531\u65bc\u5169\u500b\u73a9\u5bb6\u53ea\u67092\u7a2e\u62ff\u7684\u65b9\u6cd5<\/p>\n<ul>\n<li>\u5076\u5076<\/li>\n<li>\u5947\u5947<\/li>\n<\/ul>\n<p>\u4e0d\u7ba1\u73a9\u5bb6\u600e\u9ebc\u62ff\uff0c\u9019\u500bbit\u6700\u5f8c\u7684\u72c0\u614b\u90fd\u662f\u4e00\u6a23\u7684\uff0c\u6240\u4ee5\u6211\u5011\u53ef\u4ee5\u5b8c\u5168\u4e0d\u7528\u8003\u616e\u9019\u500bbit\u3002<\/p>\n<\/li>\n<li>\n<p>\u9019\u500bbit\u6709\u5947\u6578\u500b\uff0c\u4e5f\u5c31\u662f\u73a9\u5bb6\u8981\u53bb\u6436\u9019\u500bbit: \u9996\u5148\u53e6$x=$\u6709\u9019\u500bbit\u7684\u5143\u7d20\u7684\u6578\u91cf\uff0c$y=n-x$\u4e5f\u5c31\u662f\u5269\u4e0b\u7684\u6578\u5b57\u7684\u6578\u91cf(\u9019\u500bbit\u662f$0$)\u3002\u7531\u65bc\u73a9\u5bb6\u5011\u62ff\u4e86$4$\u500b$1$\u7b49\u540c\u65bc\u6c92\u6709\u6539\u8b8a\u72c0\u614b\uff0c\u56e0\u6b64\u6709\u4ee5\u4e0b\u7684\u5206\u985e:<\/p>\n<ol>\n<li>$x\\mod 4=1$ and $y\\mod 2=0$: \u5148\u624b\u5148\u62ff\u4e00\u500b$1$\uff0c\u63a5\u8457\u5b8c\u5168\u7167\u642c\u5f8c\u624b\u7684\u884c\u52d5\u3002\u5982\u6b64\u6613\u767c\u73fe\u5148\u624b\u6703\u8d0f\u3002<\/li>\n<li>$x\\mod 4=1$ and $y\\mod 2=1$: \u5148\u624b\u5148\u62ff\u4e00\u500b$1$\uff0c\u63a5\u8457\u5b8c\u5168\u7167\u642c\u5f8c\u624b\u7684\u884c\u52d5\uff0c\u76f4\u5230\u5f8c\u624b\u62ff\u8d70\u4e86\u6700\u5f8c\u4e00\u500b$0$\uff0c\u90a3\u9ebc\u63a5\u8457\u5c31\u5269\u4e0b\u8981\u62ff\u5076\u6578\u500b$1$\uff0c\u4e26\u4e14\u662f\u5148\u624b\u5148\u62ff\u3002\u7531\u65bc\u662f$x\\mod 4=1$\uff0c\u6240\u4ee5\u6700\u5f8c\u662f\u5148\u624b\u8d0f\u3002<\/li>\n<li>$x\\mod 4=3$ and $y\\mod 2=0$: \u5f8c\u624b\u5b8c\u5168\u7167\u642c\u5148\u624b\u7684\u884c\u52d5\uff0c\u6700\u5f8c\u5148\u624b\u4e00\u5b9a\u6703\u62ff\u5230\u5076\u6578\u500b$1$\uff0c\u6240\u4ee5\u5f8c\u624b\u8d0f\u3002<\/li>\n<li>$x\\mod 4=3$ and $y\\mod 2=1$: \u5148\u624b\u5148\u62ff\u4e00\u500b$0$\uff0c\u90a3\u9ebc\u5c31\u662f3.\u7684\u60c5\u6cc1\u4e86\uff0c\u5148\u624b\u8d0f\u3002<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h3>\u7a0b\u5f0f\u78bc:<\/h3>\n<pre><code class=\"language-cpp=\">const int _n=1e5+10;  \nint t,n,a[_n],cnt[32];  \nmain(void) {cin.tie(0);ios_base::sync_with_stdio(0);  \n  cin&gt;&gt;t;while(t--){  \n    cin&gt;&gt;n;rep(i,0,n)cin&gt;&gt;a[i]; memset(cnt,0,sizeof cnt);  \n    rep(j,0,30)rep(i,0,n)cnt[j]+=((a[i]&amp;(1&lt;&lt;j))?1:0);  \n    per(i,0,30){  \n      if(cnt[i]%2==0)continue;  \n      int x=cnt[i],y=n-x;  \n      if(x%4==3 and y%2==0){cout&lt;&lt;&quot;LOSE\\n&quot;;goto A;}  \n      else {cout&lt;&lt;&quot;WIN\\n&quot;;goto A;}  \n    }cout&lt;&lt;&quot;DRAW\\n&quot;;  \n    A:;  \n  }  \n  return 0;  \n}  \n<\/code><\/pre>\n<p>\u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b<br>\n<a href=\"https:\/\/codeforces.com\/contest\/1383\/submission\/90386752\">Submission<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[3],"tags":[10,9,18,8],"class_list":["post-45","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-18","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>B. 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