{"id":90671,"date":"2026-08-05T19:49:02","date_gmt":"2026-08-05T11:49:02","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/90671.html"},"modified":"2026-08-05T19:49:02","modified_gmt":"2026-08-05T11:49:02","slug":"%e6%8e%a8%e8%8d%90%e9%a2%98%e7%9b%ae%ef%bc%9a%e6%b4%9b%e8%b0%b7-p12792-nerc-2022-cactus-meets-torus","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/90671.html","title":{"rendered":"\u63a8\u8350\u9898\u76ee\uff1a\u6d1b\u8c37 P12792 [NERC 2022] Cactus Meets Torus"},"content":{"rendered":"

\u63a8\u8350\u9898\u76ee：\u6d1b\u8c37 P12792 [NERC 2022] Cactus Meets Torus<\/h2>\n

\u9898\u76ee\u63cf\u8ff0<\/h3>\n

Alice \u6709\u4e00\u4e2a\u6f02\u4eae\u7684\u4ed9\u4eba\u638c\u56fe，\u5979\u60f3\u628a\u5b83\u753b\u5728\u4e00\u5f20\u7eb8\u4e0a\u3002Eve \u5a01\u80c1\u8bf4\u8981\u62ff\u8d70\u8fd9\u4e2a\u4ed9\u4eba\u638c\u56fe\u7684\u4e00\u4e2a\u73af，\u5e76\u6cbf\u7740\u8fd9\u4e2a\u73af\u4e0a\u7684\u6240\u6709\u8fb9\u628a\u7eb8\u526a\u5f00\u3002\u8fd9\u6837\u4e00\u6765，\u8fd9\u5f20\u7eb8\u5c31\u4f1a\u88ab\u5206\u6210\u4e24\u90e8\u5206，Alice \u4f1a\u56e0\u6b64\u800c\u96be\u8fc7\u3002\u5e78\u8fd0\u7684\u662f，Barbara \u521a\u521a\u7ed9\u4e86 Alice \u4e00\u4e2a\u7eb8\u8d28\u73af\u9762\u2014\u2014\u4e00\u5f20\u5c06\u9876\u8fb9\u548c\u5e95\u8fb9\u3001\u5de6\u8fb9\u548c\u53f3\u8fb9\u5206\u522b\u8fde\u63a5\u8d77\u6765\u4e14\u6ca1\u6709\u626d\u66f2\u7684\u7eb8\u3002\u5728\u73af\u9762\u4e0a，\u6709\u65f6\u4f60\u53ef\u4ee5\u6cbf\u7740\u4e00\u4e2a\u73af\u7684\u6240\u6709\u8fb9\u526a\u5f00\u7eb8，\u4f46\u5b83\u4ecd\u7136\u4f1a\u4fdd\u6301\u4e3a\u4e00\u6574\u5757\u3002\u8bf7\u5e2e\u52a9 Alice \u5224\u65ad\u5979\u662f\u5426\u80fd\u5c06\u5979\u7684\u4ed9\u4eba\u638c\u56fe\u753b\u5728\u4e00\u4e2a\u73af\u9762\u4e0a，\u4f7f\u5f97 Eve \u65e0\u6cd5\u6cbf\u7740\u4efb\u4f55\u4e00\u4e2a\u73af\u526a\u5f00\u7eb8\u5e76\u628a\u73af\u9762\u5206\u6210\u4e24\u4e2a\u4e0d\u76f8\u8fde\u7684\u90e8\u5206\u3002<\/p>\n

\u4ed9\u4eba\u638c\u56fe (Cactus) \u662f\u4e00\u4e2a\u8fde\u901a\u7684\u65e0\u5411\u56fe，\u5176\u4e2d\u6bcf\u6761\u8fb9\u6700\u591a\u53ea\u5c5e\u4e8e\u4e00\u4e2a\u7b80\u5355\u73af\u3002\u76f4\u89c2\u5730\u8bf4，\u4ed9\u4eba\u638c\u56fe\u662f\u6811\u7684\u4e00\u79cd\u63a8\u5e7f，\u5141\u8bb8\u5b58\u5728\u4e00\u4e9b\u73af\u3002\u4ed9\u4eba\u638c\u56fe\u4e2d\u4e0d\u5141\u8bb8\u5b58\u5728\u91cd\u8fb9（\u4e00\u5bf9\u9876\u70b9\u4e4b\u95f4\u7684\u591a\u6761\u8fb9）\u548c\u81ea\u73af（\u8fde\u63a5\u4e00\u4e2a\u9876\u70b9\u5230\u5176\u81ea\u8eab\u7684\u8fb9）\u3002<\/p>\n

\u6211\u4eec\u8bf4\u4e00\u4e2a\u56fe\u88ab\u753b\u5728\u4e00\u5f20\u7eb8\u4e0a，\u5982\u679c\u6bcf\u4e2a\u9876\u70b9\u662f\u8fd9\u5f20\u7eb8\u4e0a\u7684\u4e00\u4e2a\u70b9，\u6bcf\u6761\u8fb9\u662f\u5176\u5bf9\u5e94\u9876\u70b9\u4e4b\u95f4\u7684\u7ebf\u6bb5，\u5e76\u4e14\u8fd9\u4e9b\u7ebf\u6bb5\u53ea\u5728\u5b83\u4eec\u7684\u7aef\u70b9\u5904\u76f8\u4ea4\u3002\u5728\u73af\u9762\u4e0a，\u7ebf\u6bb5\u53ef\u4ee5\u7a7f\u8fc7\u7eb8\u7684\u8fb9\u754c\u4efb\u610f\u6b21\u6570\u3002<\/p>\n

\u8f93\u5165\u683c\u5f0f<\/h3>\n

\u8f93\u5165\u5305\u542b\u4e00\u4e2a\u6216\u591a\u4e2a\u72ec\u7acb\u7684\u6d4b\u8bd5\u7528\u4f8b\u3002<\/p>\n

\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u7684\u7b2c\u4e00\u884c\u5305\u542b\u4e24\u4e2a\u6574\u6570 <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u548c <\/p>\n

m<\/p>\n

m<\/p>\n

<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> (<\/p>\n

1<\/p>\n

\u2264<\/p>\n

n<\/p>\n

\u2264<\/p>\n

10<\/p>\n

5<\/p>\n

1 \\\\le n \\\\le 10^5<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>; <\/p>\n

0<\/p>\n

\u2264<\/p>\n

m<\/p>\n

\u2264<\/p>\n

10<\/p>\n

5<\/p>\n

0 \\\\le m \\\\le 10^5<\/p>\n

<\/span><\/span>0<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>m<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)，\u5176\u4e2d <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u662f\u56fe\u4e2d\u9876\u70b9\u7684\u6570\u91cf\u3002\u9876\u70b9\u7f16\u53f7\u4ece <\/p>\n

1<\/p>\n

1<\/p>\n

<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5230 <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u3002\u56fe\u7684\u8fb9\u7531\u4e00\u7ec4\u8fb9\u4e0d\u91cd\u590d\u7684\u8def\u5f84\u8868\u793a，\u5176\u4e2d <\/p>\n

m<\/p>\n

m<\/p>\n

<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u662f\u8fd9\u4e9b\u8def\u5f84\u7684\u6570\u91cf\u3002<\/p>\n

\u63a5\u4e0b\u6765\u7684 <\/p>\n

m<\/p>\n

m<\/p>\n

<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u884c，\u6bcf\u884c\u63cf\u8ff0\u4e86\u56fe\u4e2d\u7684\u4e00\u6761\u8def\u5f84\u3002\u4e00\u6761\u8def\u5f84\u4ee5\u4e00\u4e2a\u6574\u6570 <\/p>\n

s<\/p>\n

i<\/p>\n

s_i<\/p>\n

<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> (<\/p>\n

2<\/p>\n

\u2264<\/p>\n

s<\/p>\n

i<\/p>\n

\u2264<\/p>\n

1000<\/p>\n

2 \\\\le s_i \\\\le 1000<\/p>\n

<\/span><\/span>2<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1000<\/span><\/span><\/span><\/span><\/span>) \u5f00\u59cb，\u540e\u9762\u8ddf\u7740 <\/p>\n

s<\/p>\n

i<\/p>\n

s_i<\/p>\n

<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e2a\u4ece <\/p>\n

1<\/p>\n

1<\/p>\n

<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5230 <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u7684\u6574\u6570\u3002\u8fd9 <\/p>\n

s<\/p>\n

i<\/p>\n

s_i<\/p>\n

<\/span><\/span>s<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e2a\u6574\u6570\u8868\u793a\u8def\u5f84\u4e0a\u7684\u9876\u70b9\u3002\u8def\u5f84\u4e2d\u76f8\u90bb\u7684\u9876\u70b9\u662f\u4e0d\u540c\u7684\u3002\u8def\u5f84\u53ef\u4ee5\u591a\u6b21\u7ecf\u8fc7\u540c\u4e00\u4e2a\u9876\u70b9，\u4f46\u5728\u6574\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u4e2d，\u6bcf\u6761\u8fb9\u90fd\u6070\u597d\u88ab\u904d\u5386\u4e00\u6b21\u3002\u56fe\u4e2d\u6ca1\u6709\u91cd\u8fb9（\u4efb\u610f\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u6700\u591a\u53ea\u6709\u4e00\u6761\u8fb9）\u3002<\/p>\n

\u6240\u6709\u6d4b\u8bd5\u7528\u4f8b\u7ed3\u675f\u540e\u7684\u6700\u540e\u4e00\u884c\u5305\u542b\u4e24\u4e2a\u96f6\u3002\u5b83\u4e0d\u5b9a\u4e49\u4e00\u4e2a\u6d4b\u8bd5\u7528\u4f8b，\u4ec5\u4ec5\u662f\u6807\u8bb0\u8f93\u5165\u7684\u7ed3\u675f，\u4e0d\u9700\u8981\u4efb\u4f55\u8f93\u51fa\u3002<\/p>\n

\u8f93\u5165\u4e2d\u7684\u6240\u6709\u56fe\u90fd\u662f\u4ed9\u4eba\u638c\u56fe\u3002\u5728\u6574\u4e2a\u8f93\u5165\u4e2d，\u6240\u6709 <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u7684\u603b\u548c\u4ee5\u53ca\u6240\u6709 <\/p>\n

m<\/p>\n

m<\/p>\n

<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u7684\u603b\u548c\u5747\u4e0d\u8d85\u8fc7 <\/p>\n

10<\/p>\n

5<\/p>\n

10^5<\/p>\n

<\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u8f93\u51fa\u683c\u5f0f<\/h3>\n

\u5bf9\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b，\u6309\u7167\u5b83\u4eec\u5728\u8f93\u5165\u4e2d\u51fa\u73b0\u7684\u987a\u5e8f\u8f93\u51fa\u7b54\u6848\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b，\u5982\u679c\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u4ed9\u4eba\u638c\u56fe\u753b\u5728\u73af\u9762\u4e0a，\u5219\u5728\u5355\u884c\u4e2d\u8f93\u51fa Yes，\u5426\u5219\u8f93\u51fa No\u3002<\/p>\n

\u8f93\u5165\u8f93\u51fa\u6837\u4f8b #1<\/h3>\n

\u8f93\u5165 #1<\/h4>\n

6 1
\n8 1 2 3 1 4 5 6 4
\n10 2
\n9 1 2 3 1 10 4 5 6 4
\n5 7 8 9 7 10
\n0 0<\/p>\n

\u8f93\u51fa #1<\/h4>\n

Yes
\nNo<\/p>\n

\u8bf4\u660e\/\u63d0\u793a<\/h3>\n

\u5c06\u7b2c\u4e00\u4e2a\u6837\u4f8b\u4e2d\u7684\u4ed9\u4eba\u638c\u56fe\u753b\u5728\u73af\u9762\u4e0a\u7684\u4e00\u79cd\u65b9\u5f0f\u5982\u56fe\u7247\u6240\u793a\u3002<\/p>\n

\"\"<\/p>\n

\u7ffb\u8bd1\u7531 gemini2.5pro \u5b8c\u6210<\/p>\n","protected":false},"excerpt":{"rendered":"

\u63a8\u8350\u9898\u76ee：\u6d1b\u8c37 P12792 [NERC 2022] Cactus Meets Torus
\n\u9898\u76ee\u63cf\u8ff0
\nAlice \u6709\u4e00\u4e2a\u6f02\u4eae\u7684\u4ed9\u4eba\u638c\u56fe，\u5979\u60f3\u628a\u5b83\u753b\u5728\u4e00\u5f20\u7eb8\u4e0a\u3002Eve \u5a01\u80c1\u8bf4\u8981\u62ff\u8d70\u8fd9\u4e2a\u4ed9\u4eba\u638c\u56fe\u7684\u4e00\u4e2a\u73af，\u5e76\u6cbf\u7740\u8fd9\u4e2a\u73af\u4e0a\u7684\u6240\u6709\u8fb9\u628a\u7eb8\u526a\u5f00\u3002\u8fd9\u6837\u4e00\u6765，\u8fd9\u5f20\u7eb8\u5c31\u4f1a\u88ab\u5206\u6210\u4e24\u90e8\u5206，Alice \u4f1a\u56e0\u6b64\u800c\u96be\u8fc7\u3002\u5e78\u8fd0\u7684\u662f，Barbara \u521a\u521a\u7ed9\u4e86 Alice \u4e00\u4e2a\u7eb8\u8d28\u73af\u9762\u2014\u2014\u4e00\u5f20\u5c06\u9876\u8fb9\u548c\u5e95\u8fb9\u3001\u5de6\u8fb9\u548c\u53f3\u8fb9\u5206\u522b\u8fde\u63a5<\/p>\n","protected":false},"author":2,"featured_media":90670,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[1813,248,1578,427,1649],"topic":[],"class_list":["post-90671","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-1813","tag-248","tag-1578","tag-427","tag-1649"],"yoast_head":"\n\u63a8\u8350\u9898\u76ee\uff1a\u6d1b\u8c37 P12792 [NERC 2022] Cactus Meets Torus - 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