{"id":11,"date":"2026-04-08T19:11:04","date_gmt":"2026-04-08T11:11:04","guid":{"rendered":"https:\/\/blogp.cus-shine.cn\/?p=11"},"modified":"2026-04-08T21:10:29","modified_gmt":"2026-04-08T13:10:29","slug":"%e8%93%9d%e6%a1%a5%e6%9d%af2025b","status":"publish","type":"post","link":"https:\/\/blogp.cus-shine.cn\/index.php\/2026\/04\/08\/%e8%93%9d%e6%a1%a5%e6%9d%af2025b\/","title":{"rendered":"\u84dd\u6865\u676f2025B\u9898\u89e3"},"content":{"rendered":"<h1>\u79fb\u52a8\u8ddd\u79bb<\/h1>\n<h2>\u9898\u76ee\u80cc\u666f<\/h2>\n<p>\u672c\u7ad9\u84dd\u6865\u676f 2025 \u7701\u8d5b\u6d4b\u8bd5\u6570\u636e\u5747\u4e3a\u6d1b\u8c37\u81ea\u9020\uff0c\u4e0e\u5b98\u65b9\u6570\u636e\u53ef\u80fd\u5b58\u5728\u5dee\u5f02\uff0c\u4ec5\u4f9b\u5b66\u4e60\u53c2\u8003\u3002<\/p>\n<h2>\u9898\u76ee\u63cf\u8ff0<\/h2>\n<p>\u5c0f\u660e\u521d\u59cb\u5728\u4e8c\u7ef4\u5e73\u9762\u7684\u539f\u70b9\uff0c\u4ed6\u60f3\u524d\u5f80\u5750\u6807 $(233, 666)$\u3002\u5728\u79fb\u52a8\u8fc7\u7a0b\u4e2d\uff0c\u4ed6\u53ea\u80fd\u91c7\u7528\u4ee5\u4e0b\u4e24\u79cd\u79fb\u52a8\u65b9\u5f0f\uff0c\u5e76\u4e14\u8fd9\u4e24\u79cd\u79fb\u52a8\u65b9\u5f0f\u53ef\u4ee5\u4ea4\u66ff\u3001\u4e0d\u9650\u6b21\u6570\u5730\u4f7f\u7528\uff1a<\/p>\n<ol>\n<li>\u6c34\u5e73\u5411\u53f3\u79fb\u52a8\uff0c\u5373\u6cbf\u7740 $x$ \u8f74\u6b63\u65b9\u5411\u79fb\u52a8\u4e00\u5b9a\u7684\u8ddd\u79bb\u3002<\/li>\n<li>\u6cbf\u7740\u4e00\u4e2a\u5706\u5fc3\u5728\u539f\u70b9 $(0, 0)$\u3001\u4ee5\u4ed6\u5f53\u524d\u4f4d\u7f6e\u5230\u539f\u70b9\u7684\u8ddd\u79bb\u4e3a\u534a\u5f84\u7684\u5706\u7684\u5706\u5468\u79fb\u52a8\uff0c\u79fb\u52a8\u65b9\u5411\u4e0d\u9650\uff08\u5373\u987a\u65f6\u9488\u6216\u9006\u65f6\u9488\u79fb\u52a8\u4e0d\u9650\uff09\u3002<\/li>\n<\/ol>\n<p>\u5728\u8fd9\u79cd\u6761\u4ef6\u4e0b\uff0c\u4ed6\u5230\u8fbe\u76ee\u7684\u5730\u6700\u5c11\u79fb\u52a8\u591a\u5c11\u5355\u4f4d\u8ddd\u79bb\uff1f\u4f60\u53ea\u9700\u8981\u8f93\u51fa\u7b54\u6848\u56db\u820d\u4e94\u5165\u5230\u6574\u6570\u7684\u7ed3\u679c\u3002<\/p>\n<h2>\u9898\u76ee\u89e3\u6790<\/h2>\n<p>\u56e0\u4e3a\u901a\u8fc7\u65cb\u8f6c\u6240\u8d70\u7684\u8def\u7a0b\u4e5f\u7b97\u662f\u5728\u603b\u7684\u79fb\u52a8\u8ddd\u79bb\u91cc\u9762\uff0c\u51ed\u611f\u89c9\uff0c\u53ef\u77e5\u9053\uff0c\u8981\u60f3\u5230\u8fbe\u76ee\u6807\u70b9\u4f4d\uff0c\u6211\u4eec\u53ea\u80fd\u65cb\u8f6c\u4e00\u6b21\uff0c\u8fd9\u6837\u662f\u6700\u4f18\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u9996\u5148\u8d70\uff0c$\\sqrt{223^2+666^2}$\uff0c\u7136\u540e\u518d\u65cb\u8f6c\u5373\u53ef\u5230\u8fbe\u3002<br \/>\n\u4ee3\u7801\u5982\u4e0b\uff1a\u6ce8\u610f\u8f93\u51fa\u8981\u6c42<\/p>\n<pre><code class=\"language-cpp\">\tdouble r=sqrt(233*233+666*666);\n\tr+=r*atan((double)666\/233);\n\tcout&lt;&lt;(int)r;\n<\/code><\/pre>\n<h1>\u5ba2\u6d41\u91cf\u4e0a\u9650<\/h1>\n<h2>\u9898\u76ee\u63cf\u8ff0<\/h2>\n<p>\u4e00\u5bb6\u8fde\u9501\u65c5\u9986\u5728\u5168\u56fd\u62e5\u6709 $2025$ \u4e2a\u5206\u5e97\uff0c\u5206\u522b\u7f16\u53f7\u4e3a $1$ \u81f3 $2025$\u3002\u968f\u7740\u8282\u65e5\u4e34\u8fd1\uff0c\u603b\u90e8\u51b3\u5b9a\u4e3a\u6bcf\u5bb6\u5206\u5e97\u8bbe\u5b9a\u6bcf\u65e5\u5ba2\u6d41\u91cf\u7684\u4e0a\u9650\uff0c\u5206\u522b\u8bb0\u4f5c $A_1, A_2, \\dots , A_{2025}$\u3002\u8fd9\u4e9b\u4e0a\u9650\u5e76\u975e\u968f\u610f\u5206\u914d\uff0c\u800c\u662f\u9700\u8981\u6ee1\u8db3\u4ee5\u4e0b\u7ea6\u675f\u6761\u4ef6\uff1a<\/p>\n<ol>\n<li>$A_1, A_2, \\dots , A_{2025}$ \u5fc5\u987b\u662f $1$ \u81f3 $2025$ \u7684\u4e00\u4e2a\u6392\u5217\uff0c\u5373\u6bcf\u4e2a $A_i$ \u5747\u662f $1$ \u81f3 $2025$ \u4e4b\u95f4\u7684\u6574\u6570\uff0c\u4e14\u6240\u6709 $A_i$ \u4e92\u4e0d\u76f8\u540c\u3002<\/li>\n<li>\u5bf9\u4e8e\u4efb\u610f\u5206\u5e97 $i$ \u548c $j$\uff08$1 \\leq i, j \\leq 2025$\uff0c$i$ \u53ef\u7b49\u4e8e $j$\uff09\uff0c\u5b83\u4eec\u7684\u5ba2\u6d41\u91cf\u4e0a\u9650 $A_i$ \u548c $A_j$ \u7684\u4e58\u79ef\u4e0d\u5f97\u8d85\u8fc7 $i \\times j + 2025$\u3002<\/li>\n<\/ol>\n<p>\u8fd9\u4e9b\u7ea6\u675f\u65e8\u5728\u5e73\u8861\u5404\u5206\u5e97\u5ba2\u6d41\u538b\u529b\uff0c\u786e\u4fdd\u670d\u52a1\u8d28\u91cf\u548c\u8fd0\u8425\u7a33\u5b9a\u6027\u3002<\/p>\n<p>\u73b0\u5728\uff0c\u8bf7\u4f60\u8ba1\u7b97\u8fd9\u6837\u7684\u5206\u914d\u65b9\u6848\u7a76\u7adf\u6709\u591a\u5c11\u79cd\u3002\u7531\u4e8e\u7b54\u6848\u53ef\u80fd\u5f88\u5927\uff0c\u4f60\u53ea\u9700\u8f93\u51fa\u5176\u5bf9 $10^9 + 7$ \u53d6\u4f59\u540e\u7684\u7ed3\u679c\u5373\u53ef\u3002<\/p>\n<h2>\u9898\u76ee\u89e3\u6790<\/h2>\n<p>\u9898\u76ee\u4e2d\u8bf4i\u53ef\u4ee5\u7b49\u4e8ej\uff0c\u90a3\u4e48\u8bf4\u660e\u8fd9\u53ef\u80fd\u662f\u4e2a\u7279\u6b8a\u60c5\u51b5\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4ee5\u4e0b\u5f0f\u5b50<br \/>\n$$A_i^2 \\leq i^2+2025$$<br \/>\n\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u53bb\u66b4\u529b\u6253\u8868<\/p>\n<pre><code class=\"language-cpp\">for(int i=1;i&lt;=2025;i++){\n\t\tcout&lt;&lt;i&lt;&lt;\" \"&lt;&lt;(int)sqrt(i*i+2025)&lt;&lt;endl;\n\t}\n<\/code><\/pre>\n<p>\u53ef\u4ee5\u53d1\u73b0\u5f53$i==1013$\u5f00\u59cb\uff0c\u5f00\u65b9\u4e4b\u540e\u7684\u503c\u5c31\u662f$i$\u672c\u8eab\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff0c\u5728$i\\ge1013$\u65f6\uff0c$A_i==i$\u3002\u6240\u4ee5$A_{1\\sim1012} \\le 1012$<\/p>\n<p>\u5f53$1\\le i\\le1012&lt;j\\le2025$\u65f6\uff0c<\/p>\n<p>$A_i\\times A_j==A_i\\times j$<\/p>\n<p>$A_i\\times A_j\\leq i\\times j+2025$<\/p>\n<p>$A_i\\times j\\le i\\times j+2025$<\/p>\n<p>$A_i\\le i+\\frac{2025}{j}$<\/p>\n<p>$$A_i\\le i+1$$<\/p>\n<p>\u6240\u4ee5\u5bf9\u4e8e$A_i$\u53ef\u4ee5\u9009\u62e9$1\\le A_i\\le i+1$<br \/>\n\u56e0\u4e3a\u6574\u4e2a\u5e8f\u5217\u662f\u4e2a\u6392\u5217\uff0c\u4e0d\u80fd\u6709\u91cd\u590d\u6570\u5b57\u3002<br \/>\n\u6240\u4ee5\u6bcf\u4e2a\u4f4d\u7f6e\u53ea\u6709\u4e24\u79cd\u9009\u62e9,\u603b\u91cf\u4e3a$2^{1012}$<\/p>\n<pre><code class=\"language-cpp\">long long ans=1;\n\tint mod=1e9+7;\n\tfor(int i=1;i&lt;=1012;i++){\n\t\tans*=2;\n\t\tans%=mod;\n\t}\n\tcout&lt;&lt;ans;\n\n<\/code><\/pre>\n<h1>\u53ef\u5206\u89e3\u7684\u6b63\u6574\u6570<\/h1>\n<h1>P12132 [\u84dd\u6865\u676f 2025 \u7701 B] \u53ef\u5206\u89e3\u7684\u6b63\u6574\u6570<\/h1>\n<h2>\u9898\u76ee\u80cc\u666f<\/h2>\n<p>\u672c\u7ad9\u84dd\u6865\u676f 2025 \u7701\u8d5b\u6d4b\u8bd5\u6570\u636e\u5747\u4e3a\u6d1b\u8c37\u81ea\u9020\uff0c\u4e0e\u5b98\u65b9\u6570\u636e\u53ef\u80fd\u5b58\u5728\u5dee\u5f02\uff0c\u4ec5\u4f9b\u5b66\u4e60\u53c2\u8003\u3002<\/p>\n<h2>\u9898\u76ee\u63cf\u8ff0<\/h2>\n<p>\u5b9a\u4e49\u4e00\u79cd\u7279\u6b8a\u7684\u6574\u6570\u5e8f\u5217\uff0c\u8fd9\u79cd\u5e8f\u5217\u7531<strong>\u8fde\u7eed\u9012\u589e\u7684\u6574\u6570<\/strong>\u7ec4\u6210\uff0c\u5e76\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n<ol>\n<li>\u5e8f\u5217\u957f\u5ea6\u81f3\u5c11\u4e3a $3$\u3002<\/li>\n<li>\u5e8f\u5217\u4e2d\u7684\u6570\u5b57\u662f\u8fde\u7eed\u9012\u589e\u7684\u6574\u6570\uff08\u5373\u76f8\u90bb\u5143\u7d20\u4e4b\u5dee\u4e3a $1$\uff09\uff0c\u53ef\u4ee5\u5305\u62ec\u6b63\u6574\u6570\u3001\u8d1f\u6574\u6570\u6216 $0$\u3002<\/li>\n<\/ol>\n<p>\u4f8b\u5982\uff0c$[1, 2, 3]$\u3001$[4, 5, 6, 7]$ \u548c $[\u22121, 0, 1]$ \u662f\u7b26\u5408\u6761\u4ef6\u7684\u5e8f\u5217\uff0c\u800c $[1, 2]$\uff08\u957f\u5ea6\u4e0d\u8db3\uff09\u548c $[1, 2, 4]$\uff08\u4e0d\u8fde\u7eed\uff09\u4e0d\u7b26\u5408\u8981\u6c42\u3002<\/p>\n<p>\u73b0\u7ed9\u5b9a\u4e00\u7ec4\u5305\u542b $N$ \u4e2a\u6b63\u6574\u6570\u7684\u6570\u636e $A_1, A_2, \\dots , A_N$\u3002\u5982\u679c\u67d0\u4e2a $A_i$ \u80fd\u591f\u8868\u793a\u4e3a\u7b26\u5408\u4e0a\u8ff0\u6761\u4ef6\u7684\u8fde\u7eed\u6574\u6570\u5e8f\u5217\u4e2d\u6240\u6709\u5143\u7d20\u7684\u548c\uff0c\u5219\u79f0 $A_i$ \u662f\u53ef\u5206\u89e3\u7684\u3002<\/p>\n<p>\u8bf7\u4f60\u7edf\u8ba1\u8fd9\u7ec4\u6570\u636e\u4e2d\u53ef\u5206\u89e3\u7684\u6b63\u6574\u6570\u7684\u6570\u91cf\u3002<\/p>\n<h2>\u9898\u76ee\u89e3\u6790<\/h2>\n<p>\u4e0d\u96be\u53d1\u73b0\uff0c\u5f53\u4f60\u9009\u62e9-1,0,1\u65f6\uff0c\u5c31\u5df2\u7ecf\u6ee1\u8db3\u5e8f\u5217\u957f\u5ea6\u4e3a3\uff0c\u8fd9\u65f6\u5019\u518d\u90092\uff0c\u5c31\u80fd\u6ee1\u8db3\u6761\u4ef6\uff0c\u7c7b\u6bd4\u53d1\u73b0\uff0c$x\\ge 2$\u90fd\u662f\u6709\u5e8f\u5217\u53ef\u4ee5\u6ee1\u8db3\u6761\u4ef6\u7684\uff0c\u53ea\u6709\u5f53$x==1$\u65f6\u6ca1\u6709\u6ee1\u8db3\u6761\u4ef6\u7684\u5e8f\u5217\u3002<\/p>\n<pre><code class=\"language-cpp\">int n;\n\tcin&gt;&gt;n;\n\tint ans=0;\n\tfor(int i=1;i&lt;=n;i++){\n\t\tint x;\n\t\tcin&gt;&gt;x;\n\t\tif(x==1){\n\t\t\tcontinue;\n\t\t}\n\t\tans++;\n\t}\n\tcout&lt;&lt;ans;\n<\/code><\/pre>\n<h1>\u4ea7\u503c\u8c03\u6574<\/h1>\n<h2>\u9898\u76ee\u63cf\u8ff0<\/h2>\n<p>\u504f\u8fdc\u7684\u5c0f\u9547\u4e0a\uff0c\u4e09\u5144\u5f1f\u5171\u540c\u7ecf\u8425\u7740\u4e00\u5bb6\u5c0f\u578b\u77ff\u4e1a\u516c\u53f8\u201c\u5144\u5f1f\u77ff\u4e1a\u201d\u3002\u516c\u53f8\u65d7\u4e0b\u6709\u4e09\u5ea7\u77ff\u5c71\uff1a\u91d1\u77ff\u3001\u94f6\u77ff\u548c\u94dc\u77ff\uff0c\u5b83\u4eec\u7684\u521d\u59cb\u4ea7\u503c\u5206\u522b\u7528\u975e\u8d1f\u6574\u6570 $A$\u3001$B$ \u548c $C$ \u8868\u793a\u3002\u8fd9\u4e9b\u77ff\u5c71\u7684\u4ea7\u51fa\u662f\u5c0f\u9547\u7ecf\u6d4e\u7684\u6838\u5fc3\uff0c\u652f\u6491\u7740\u4e09\u5144\u5f1f\u548c\u8bb8\u591a\u77ff\u5de5\u5bb6\u5ead\u7684\u751f\u8ba1\u3002<\/p>\n<p>\u7136\u800c\uff0c\u5404\u77ff\u5c71\u7684\u4ea7\u503c\u6ce2\u52a8\u5267\u70c8\uff0c\u6709\u65f6\u91d1\u77ff\u6536\u76ca\u9ad8\u800c\u94f6\u77ff\u3001\u94dc\u77ff\u4f4e\u8ff7\uff0c\u6709\u65f6\u5219\u76f8\u53cd\u3002\u8fd9\u79cd\u4e0d\u7a33\u5b9a\u6027\u8ba9\u516c\u53f8\u6536\u5165\u96be\u4ee5\u9884\u6d4b\uff0c\u4e5f\u5e38\u5f15\u53d1\u5144\u5f1f\u95f4\u7684\u4e89\u6267\u3002\u4e3a\u4e86\u7a33\u5b9a\u7ecf\u8425\uff0c\u4e09\u5144\u5f1f\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u516c\u5e73\u7684\u4ea7\u503c\u8c03\u6574\u7b56\u7565\uff0c\u6bcf\u5e74\u6267\u884c\u4e00\u6b21\uff0c\u6bcf\u6b21\u8c03\u6574\u65f6\uff0c\u5c06\u6839\u636e\u5f53\u524d\u7684\u4ea7\u503c $A$\u3001$B$\u3001$C$\uff0c\u8ba1\u7b97\u65b0\u4ea7\u503c\uff1a<\/p>\n<ol>\n<li>\u91d1\u77ff\u65b0\u4ea7\u503c\uff1a$A'=\\lfloor \\dfrac{B+C}{2} \\rfloor$\uff1b<\/li>\n<li>\u94f6\u77ff\u65b0\u4ea7\u503c\uff1a$B'=\\lfloor \\dfrac{A+C}{2} \\rfloor$\uff1b<\/li>\n<li>\u94dc\u77ff\u65b0\u4ea7\u503c\uff1a$C'=\\lfloor \\dfrac{A+B}{2} \\rfloor$\uff1b<\/li>\n<\/ol>\n<p>\u5176\u4e2d\uff0c$\\lfloor \\rfloor$ \u8868\u793a\u5411\u4e0b\u53d6\u6574\u3002\u4f8b\u5982\uff0c$\\lfloor 3.7\\rfloor = 3$\uff0c$\\lfloor 5.2\\rfloor = 5$\u3002<\/p>\n<p>\u8ba1\u7b97\u51fa $A'$\u3001$B'$\u3001$C'$ \u540e\uff0c\u540c\u65f6\u66f4\u65b0\uff1a$A$ \u53d8\u4e3a $A'$\uff0c$B$ \u53d8\u4e3a $B'$\uff0c$C$ \u53d8\u4e3a $C'$\uff0c\u4f5c\u4e3a\u4e0b\u4e00\u5e74\u8c03\u6574\u7684\u57fa\u7840\u3002<\/p>\n<p>\u4e09\u5144\u5f1f\u8ba4\u4e3a\u8fd9\u4e2a\u65b9\u6cd5\u80fd\u5e73\u8861\u4ea7\u503c\u6ce2\u52a8\uff0c\u4e8e\u662f\u8ba1\u5212\u8fde\u7eed\u6267\u884c $K$ \u6b21\u8c03\u6574\u3002\u73b0\u5728\uff0c\u8bf7\u4f60\u5e2e\u4ed6\u4eec\u8ba1\u7b97\uff0c\u7ecf\u8fc7 $K$ \u6b21\u8c03\u6574\u540e\uff0c\u91d1\u77ff\u3001\u94f6\u77ff\u548c\u94dc\u77ff\u7684\u4ea7\u503c\u5206\u522b\u662f\u591a\u5c11\u3002<\/p>\n<h3>\u8bc4\u6d4b\u7528\u4f8b\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/h3>\n<ul>\n<li>\u5bf9\u4e8e $30%$ \u7684\u8bc4\u6d4b\u7528\u4f8b\uff0c$1 \\leq T \\leq 100$\uff0c$1 \\leq A, B, C, K \\leq 10^5$\u3002<\/li>\n<li>\u5bf9\u4e8e $100%$ \u7684\u8bc4\u6d4b\u7528\u4f8b\uff0c$1 \\leq T \\leq 10^5$\uff0c$1 \\leq A, B, C, K \\leq 10^9$\u3002<\/li>\n<\/ul>\n<h2>\u9898\u76ee\u5206\u6790<\/h2>\n<p>\u6839\u636e100%\u7684\u5927\u5c0f\uff0c\u6b63\u5e38\u505a\u7684\u590d\u6742\u5ea6\u4e3a$O(TK)$,\u8fd9\u4e2a\u6570\u503c\u5230\u4e86<code>1e14<\/code>\uff0c\u5f88\u660e\u663e\u4f1a\u8d85\u65f6\uff0c\u6211\u4eec\u5176\u5b9e\u53ef\u4ee5\u6253\u8868\u770b\u4e00\u770b\u6709\u6ca1\u6709\u89c4\u5f8b\uff0c\u50cf\u8fd9\u79cd\u4e92\u76f8\u5236\u7ea6\u7684\uff0c\u4f1a\u6700\u7ec8\u53d6\u5411\u540c\u4e00\u4e2a\u6570\u3002<br \/>\n\u6211\u4eec\u6253\u8868\u6295\u5165\u4e00\u4e0b\u6570\u636e1 1000000000 2000000000 3000000000 1000\uff0c\u4ee5\u53ca1 1000000000 2000000000 3000000000 100\uff0c\u4f1a\u53d1\u73b0\u5176\u5728100\u6b21\u4e4b\u5185$a,b,c$\u5c31\u4f1a\u8d8b\u4e8e\u540c\u4e00\u4e2a\u6570\uff0c\u6240\u4ee5\u6211\u4eec\u6709\u4e86\u5982\u4e0b\u4ee3\u7801<\/p>\n<pre><code class=\"language-cpp\">#define int long long\nsigned main(){\n\tint t;\n\tcin&gt;&gt;t;\n\twhile(t--){\n\t\tint a,b,c,d;\n\t\tcin&gt;&gt;a&gt;&gt;b&gt;&gt;c&gt;&gt;d;\n\t\tint na,nb,nc;\n\t\td=min((long long)100,d);\n\t\tfor(int i=1;i&lt;=d;i++){\n\t\t\tna=(b+c)\/2;\n\t\t\tnb=(a+c)\/2;\n\t\t\tnc=(a+b)\/2;\n\t\t\ta=na,b=nb,c=nc;\n\t\t}\n\t\tcout&lt;&lt;a&lt;&lt;\" \"&lt;&lt;b&lt;&lt;\" \"&lt;&lt;c&lt;&lt;endl;\n\t}\n}\n<\/code><\/pre>\n<h1>\u753b\u5c55\u5e03\u7f6e<\/h1>\n<h2>\u9898\u76ee\u63cf\u8ff0<\/h2>\n<p>\u753b\u5c55\u7b56\u5c55\u4eba\u5c0f\u84dd\u548c\u52a9\u7406\u5c0f\u6865\u4e3a\u5373\u5c06\u4e3e\u529e\u7684\u753b\u5c55\u51c6\u5907\u4e86 $N$ \u5e45\u753b\u4f5c\uff0c\u5176\u827a\u672f\u4ef7\u503c\u5206\u522b\u4e3a $A_1, A_2, \\dots , A_N$\u3002\u4ed6\u4eec\u9700\u8981\u4ece\u8fd9 $N$ \u5e45\u753b\u4e2d\u6311\u9009 $M$ \u5e45\uff0c\u5e76\u6309\u7167\u4e00\u5b9a\u987a\u5e8f\u5e03\u7f6e\u5728\u5c55\u5385\u7684 $M$ \u4e2a\u4f4d\u7f6e\u4e0a\u3002\u5982\u679c\u968f\u610f\u6311\u9009\u548c\u6392\u5217\uff0c\u827a\u672f\u4ef7\u503c\u7684\u53d8\u5316\u53ef\u80fd\u4f1a\u8fc7\u4e8e\u7a81\u5140\uff0c\u5bfc\u81f4\u89c2\u4f17\u7684\u89c2\u5c55\u4f53\u9a8c\u4e0d\u591f\u6d41\u7545\u3002<\/p>\n<p>\u4e3a\u4e86\u4f18\u5316\u5e03\u7f6e\uff0c\u4ed6\u4eec\u67e5\u9605\u4e86\u300a\u753b\u5c55\u5e03\u7f6e\u6307\u5357\u300b\u3002\u6307\u5357\u6307\u51fa\uff0c\u7406\u60f3\u7684\u753b\u5c55\u5e94\u4f7f\u89c2\u4f17\u5728\u6b23\u8d4f\u753b\u4f5c\u65f6\uff0c\u827a\u672f\u4ef7\u503c\u7684\u8fc7\u6e21\u5c3d\u91cf\u5e73\u7f13\u3002\u6307\u5357\u5efa\u8bae\uff0c\u9009\u62e9\u5e76\u6392\u5217 $M$ \u5e45\u753b\uff0c\u5e94\u4f7f\u827a\u672f\u4ef7\u503c\u7684\u53d8\u5316\u7a0b\u5ea6\u901a\u8fc7\u4e00\u4e2a\u6570\u503c $L$ \u6765\u8861\u91cf\uff0c\u4e14\u8be5\u503c\u8d8a\u5c0f\u8d8a\u597d\u3002\u6570\u503c $L$ \u7684\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<p>$$L=\\sum_{i=1}^{M-1} |B_{i+1}^2-B_i^2|$$<\/p>\n<p>\u5176\u4e2d $B_i$ \u8868\u793a\u5c55\u5385\u7b2c $i$ \u4e2a\u4f4d\u7f6e\u4e0a\u753b\u4f5c\u7684\u827a\u672f\u4ef7\u503c\u3002<\/p>\n<p>\u73b0\u5728\uff0c\u4ed6\u4eec\u5e0c\u671b\u901a\u8fc7\u7cbe\u5fc3\u6311\u9009\u548c\u6392\u5217\u8fd9 $M$ \u5e45\u753b\u4f5c\uff0c\u4f7f $L$ \u8fbe\u5230\u6700\u5c0f\u503c\uff0c\u4ee5\u63d0\u5347\u753b\u5c55\u7684\u6574\u4f53\u534f\u8c03\u6027\u3002\u8bf7\u4f60\u5e2e\u4ed6\u4eec\u8ba1\u7b97\u51fa\u8fd9\u4e2a\u6700\u5c0f\u503c\u662f\u591a\u5c11\u3002<\/p>\n<h2>\u9898\u76ee\u89e3\u6790<\/h2>\n<p>\u5c06\u6570\u503cL\u7684\u516c\u5f0f\u8fdb\u884c\u5206\u6790\uff0c\u53d1\u73b0\u4ee5\u4e0b\u7ed3\u8bba<br \/>\n$$L=|B_{i+M-1}^2-B_i^2|$$<br \/>\n\u6240\u4ee5\u6211\u4eec\u76f4\u63a5\u5bf9\u8bfb\u5165\u7684\u6bcf\u4e2a\u6570\u8fdb\u884c\u5e73\u65b9\uff0c\u7136\u540e\u5728\u8fdb\u884c\u6392\u5e8f\uff0c\u4e4b\u540e\u901a\u8fc7\u5faa\u73af\u641c\u7d22\u7b54\u6848\u3002<br \/>\n\u6ce8\u610f\u6570\u636e\u8303\u56f4\uff0c\u5e73\u65b9\u4f1a<strong>\u7206<\/strong>$int$\u5927\u5c0f\uff0c\u9700\u8981\u5f00<strong>long long<\/strong>\u3002<\/p>\n<pre><code class=\"language-cpp\">const int MAXN=1e6+10;\n#define int long long\nint a[MAXN];\nsigned main(){\n\tint n,m;\n\tcin&gt;&gt;n&gt;&gt;m;\n\tfor(int i=1;i&lt;=n;i++){\n\t\tcin&gt;&gt;a[i];\n\t\ta[i]*=a[i];\n\t}\n\tsort(a+1,a+n+1);\n\tint ans=1e17;\n\tfor(int i=1;i&lt;=n-m+1;i++){\n\t\tans=min(ans,a[i+m-1]-a[i]);\n\t} \n\tcout&lt;&lt;ans&lt;&lt;endl;\n}\n<\/code><\/pre>\n<h1>\u6c34\u8d28\u68c0\u6d4b<\/h1>\n<h2>\u9898\u76ee\u63cf\u8ff0<\/h2>\n<p>\u5c0f\u660e\u9700\u8981\u5728\u4e00\u6761 $2 \\times n$ \u7684\u6cb3\u5e8a\u4e0a\u94fa\u8bbe\u6c34\u8d28\u68c0\u6d4b\u5668\u3002\u5728\u4ed6\u94fa\u8bbe\u4e4b\u524d\uff0c\u6cb3\u5e8a\u4e0a\u5df2\u7ecf\u5b58\u5728\u4e00\u4e9b\u68c0\u6d4b\u5668\u3002\u5982\u679c\u4e24\u4e2a\u68c0\u6d4b\u5668\u4e0a\u4e0b\u6216\u8005\u5de6\u53f3\u76f8\u90bb\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u68c0\u6d4b\u5668\u5c31\u662f\u4e92\u76f8\u8fde\u901a\u7684\u3002\u8fde\u901a\u5177\u6709\u4f20\u9012\u6027\uff0c\u5373\u5982\u679c $A$ \u548c $B$ \u8fde\u901a\uff0c$B$ \u548c $C$ \u8fde\u901a\uff0c\u90a3\u4e48 $A$ \u548c $C$ \u4e5f\u8fde\u901a\u3002\u73b0\u5728\u4ed6\u9700\u8981\u5728\u6cb3\u5e8a\u4e0a\u589e\u52a0\u94fa\u8bbe\u4e00\u4e9b\u68c0\u6d4b\u5668\u4f7f\u5f97\u6240\u6709\u7684\u68c0\u6d4b\u5668\u90fd\u4e92\u76f8\u8fde\u901a\u3002\u4ed6\u60f3\u77e5\u9053\u6700\u5c11\u9700\u8981\u589e\u52a0\u94fa\u8bbe\u591a\u5c11\u4e2a\u68c0\u6d4b\u5668\uff1f<\/p>\n<h3>\u8bc4\u6d4b\u7528\u4f8b\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/h3>\n<p>\u5bf9\u4e8e $100%$ \u7684\u8bc4\u6d4b\u7528\u4f8b\uff0c\u4fdd\u8bc1 $n \\leq 1000000$\u3002<\/p>\n<h2>\u9898\u76ee\u89e3\u6790<\/h2>\n<p><a href=\"https:\/\/www.luogu.com.cn\/article\/73itpj0d\" target=\"_blank\"  rel=\"nofollow\" >\u770b\u8fd9\u7bc7\u9898\u89e3\u5427<\/a><\/p>\n<pre><code class=\"language-cpp\">\tstring str1,str2;\n\tcin&gt;&gt;str1&gt;&gt;str2;\n\tint n=str1.length();\n\tint ans=0;\n\tint r=0;\n\tfor(int i=0;i&lt;n;i++){\n\t\tif(str1[i]=='#'||str2[i]=='#'){\n\t\t\tr=i;\/\/\u8fd9\u4e2a\u53ef\u4ee5\u7b5b\u6389\u8fd9\u79cd\u60c5\u51b5\n      \/\/#.....\n      \/\/#.....\n\t\t}\n\t}\n\tfor(int i=0;i&lt;r;i++){\n\t\tif(str1[i]=='#'&amp;&amp;str2[i]=='.'){\n\t\t\tif(str1[i+1]=='.'){\n\t\t\t\tstr1[i+1]='#';\n\t\t\t\tans++;\n\t\t\t}\n\t\t}\n\t\tif(str1[i]=='.'&amp;&amp;str2[i]=='#'){\n\t\t\tif(str2[i+1]=='.'){\n\t\t\t\tstr2[i+1]='#';\n\t\t\t\tans++;\n\t\t\t}\n\t\t}\n\t\tif(str1[i+1]=='.'&amp;&amp;str2[i+1]=='.'&amp;&amp;str1[i]=='#'&amp;&amp;str2[i]=='#'){\n\t\t\tfor(int j=i+1;j&lt;=r;j++){\n\t\t\t\tif(str1[j]=='#'){\n\t\t\t\t\tstr1[i+1]='#';\n\t\t\t\t\tans++;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t\tif(str2[j]=='#'){\n\t\t\t\t\tstr2[i+1]='#';\n\t\t\t\t\tans++; \n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\tcout&lt;&lt;ans&lt;&lt;endl;;\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u79fb\u52a8\u8ddd\u79bb \u9898\u76ee\u80cc\u666f \u672c\u7ad9\u84dd\u6865\u676f 2025 \u7701\u8d5b\u6d4b\u8bd5\u6570\u636e\u5747\u4e3a\u6d1b\u8c37\u81ea\u9020\uff0c\u4e0e\u5b98\u65b9\u6570\u636e\u53ef\u80fd\u5b58\u5728\u5dee\u5f02\uff0c\u4ec5\u4f9b\u5b66\u4e60\u53c2\u8003\u3002 \u9898\u76ee\u63cf\u8ff0 \u5c0f\u660e\u521d\u59cb\u5728\u4e8c &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[2],"tags":[3,4,5],"class_list":["post-11","post","type-post","status-publish","format-standard","hentry","category-2","tag-3","tag-4","tag-5"],"_links":{"self":[{"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/posts\/11","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/comments?post=11"}],"version-history":[{"count":11,"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/posts\/11\/revisions"}],"predecessor-version":[{"id":22,"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/posts\/11\/revisions\/22"}],"wp:attachment":[{"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/media?parent=11"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/categories?post=11"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogp.cus-shine.cn\/index.php\/wp-json\/wp\/v2\/tags?post=11"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}