{"id":76858,"date":"2026-02-23T13:34:35","date_gmt":"2026-02-23T05:34:35","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/76858.html"},"modified":"2026-02-23T13:34:35","modified_gmt":"2026-02-23T05:34:35","slug":"%e6%89%93%e5%8d%a1%e4%bf%a1%e5%a5%a5%e5%88%b7%e9%a2%98%ef%bc%882859%ef%bc%89%e7%94%a8c%e5%ae%9e%e7%8e%b0%e4%bf%a1%e5%a5%a5%e9%a2%98-p4910-%e5%b8%95%e7%a7%8b%e8%8e%89%e7%9a%84%e6%89%8b%e7%8e%af","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/76858.html","title":{"rendered":"\u6253\u5361\u4fe1\u5965\u5237\u9898\uff082859\uff09\u7528C++\u5b9e\u73b0\u4fe1\u5965\u9898 P4910 \u5e15\u79cb\u8389\u7684\u624b\u73af"},"content":{"rendered":"

P4910 \u5e15\u79cb\u8389\u7684\u624b\u73af<\/h2>\n

\u9898\u76ee\u80cc\u666f<\/h3>\n

\u5e15\u79cb\u8389\u662f\u857e\u7c73\u8389\u4e9a\u5f88\u65e9\u7ed3\u8bc6\u7684\u670b\u53cb，\u73b0\u5728\u4f4f\u5728\u7ea2\u9b54\u9986\u5730\u4e0b\u7684\u5927\u56fe\u4e66\u9986\u91cc\u3002\u4e0d\u4ec5\u64c5\u957f\u8bb8\u591a\u9b54\u6cd5，\u8fd8\u6bcf\u5929\u90fd\u4f1a\u5f00\u53d1\u51fa\u65b0\u7684\u9b54\u6cd5\u3002\u53ea\u662f\u8eab\u4f53\u6bd4\u8f83\u5f31，\u56e0\u4e3a\u54ee\u5598，\u4f1a\u5728\u548f\u5531\u7b26\u5361\u65f6\u9047\u5230\u9ebb\u70e6\u3002<\/p>\n

\u5979\u6240\u7528\u7684\u5c5e\u6027\u9b54\u6cd5，\u4e3b\u8981\u662f\u751f\u547d\u548c\u89c9\u9192\u7684\u201c\u6728\u201d，\u53d8\u5316\u548c\u6d3b\u52a8\u7684\u201c\u706b\u201d，\u57fa\u7840\u548c\u4e0d\u52a8\u7684\u201c\u571f\u201d，\u679c\u5b9e\u548c\u4e30\u6536\u7684\u201c\u91d1\u201d，\u5bc2\u9759\u548c\u51c0\u5316\u7684\u201c\u6c34\u201d，\u673a\u52a8\u548c\u653b\u51fb\u7684\u201c\u65e5\u201d，\u88ab\u52a8\u548c\u9632\u5fa1\u7684\u201c\u6708\u201d\u4e03\u79cd\u5c5e\u6027<\/p>\n

\u6ca1\u6709\u7a97\u6237\u7684\u56fe\u4e66\u9986\u6216\u8bb8\u5145\u6ee1\u4e86\u7070\u5c18，\u4e0d\u8fc7\u5979\u8ba4\u4e3a\u5728\u4e66\u65c1\u8fb9\u624d\u662f\u81ea\u5df1，\u6240\u4ee5\u5979\u4e0d\u80fd\u4ece\u4e66\u7684\u65c1\u8fb9\u79bb\u5f00\u3002\u8fd9\u6837\u5df2\u7ecf\u4e00\u767e\u5e74\u4e86\u3002<\/p>\n

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

\u7ecf\u8fc7\u6570\u5e74\u9b54\u6cd5\u7684\u6c89\u6dc0，\u5e15\u79cb\u8389\u5c06\u5979\u90a3\u6d69\u701a\u65e0\u8fb9\u7684\u9b54\u6cd5\u7684\u4e00\u90e8\u5206\u6d53\u7f29\u5230\u4e86\u4e00\u4e9b\u7279\u8d28\u7684\u73e0\u5b50\u4e2d\u3002<\/p>\n

\u7531\u4e8e\u5e15\u79cb\u8389\u7231\u597d\u548c\u5e73，\u5979\u53ea\u628a\u8c61\u5f81\u751f\u547d\u548c\u89c9\u9192\u7684\u6728\u5c5e\u6027\u9b54\u6cd5\u548c\u679c\u5b9e\u548c\u4e30\u6536\u7684\u91d1\u5c5e\u6027\u9b54\u6cd5\u653e\u5165\u4e86\u73e0\u5b50\u4e2d\u3002<\/p>\n

\u5979\u8ba4\u4e3a\u5149\u8981\u8fd9\u4e9b\u73e0\u5b50\u6ca1\u6709\u4ec0\u4e48\u7528\u5904，\u4e8e\u662f\u5979\u60f3\u5c06\u8fd9\u4e9b\u73e0\u5b50\u4e32\u6210\u9b54\u6cd5\u624b\u73af，\u8fd9\u6837\u5c31\u597d\u770b\u591a\u4e86\u3002\u4e8e\u662f，\u5979\u62ff\u51fa\u6765\u7528\u6765\u4e32\u8fd9\u4e9b\u73e0\u5b50\u7684\u7ebf – \u96fe\u96e8\u7075\u5f84\u3002<\/p>\n

\u5979\u5c06\u8fd9\u4e9b\u73e0\u5b50\u4e32\u5230\u4e00\u8d77\u4e4b\u540e\u53d1\u73b0\u4e86\u4e00\u4e9b\u6027\u8d28：\u53ea\u8981\u76f8\u90bb\u73e0\u5b50\u95f4\u7684\u4e24\u4e2a\u73e0\u5b50\u4e2d\u6709\u4e00\u4e2a\u662f\u91d1\u5c5e\u6027\u7684，\u90a3\u4e48\u5b83\u4eec\u4e4b\u95f4\u7684\u96fe\u96e8\u7075\u5f84\u7684\u989c\u8272\u5c31\u4e3a\u91d1\u8272\u3002<\/p>\n

\u5e15\u79cb\u8389\u60f3\u8981\u4e00\u4e2a\u5168\u90fd\u662f\u91d1\u8272\u7684\u624b\u73af，\u800c\u4e14\u5979\u8fd8\u60f3\u77e5\u9053\u4e00\u5171\u6709\u591a\u5c11\u79cd\u65b9\u6848\u3002\u7531\u4e8e\u5979\u8fd8\u8981\u7814\u7a76\u65b0\u7684\u9b54\u6cd5，\u5979\u5c31\u628a\u8fd9\u4ef6\u4e8b\u4ea4\u7ed9\u4e86\u4f60\u3002\u7531\u4e8e\u5979\u7684\u9b54\u6cd5\u6d69\u701a\u65e0\u8fb9，\u5979\u6709\u65e0\u7a77\u7684\u73e0\u5b50\u3002<\/p>\n

\u5979\u5e76\u4e0d\u60f3\u770b\u7740\u597d\u51e0\u5341\u4f4d\u7684\u6570\u5b57，\u4e8e\u662f\u4f60\u9700\u8981\u5bf9 10000000071000000007<\/span><\/span>1000000007<\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u53d6\u6a21\u3002<\/p>\n

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

\u8f93\u5165\u5305\u542b\u591a\u7ec4\u6570\u636e\u3002<\/p>\n

\u7b2c\u4e00\u884c\u4e00\u4e2a\u6b63\u6574\u6570 TT<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span> ，\u8868\u793a\u6570\u636e\u7ec4\u6570\u3002<\/p>\n

\u4e4b\u540e\u6bcf\u7ec4\u6570\u636e\u6709\u4e00\u4e2a nn<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u4ee3\u8868\u6728\u5c5e\u6027\u73e0\u5b50\u548c\u91d1\u5c5e\u6027\u73e0\u5b50\u7684\u603b\u4e2a\u6570\u3002<\/p>\n

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

\u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e，\u8f93\u51fa\u53d6\u6a21\u540e\u7684\u65b9\u6848\u6570\u3002<\/p>\n

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

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

2
\n5
\n20<\/p>\n

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

11
\n15127<\/p>\n

\u8f93\u5165\u8f93\u51fa\u6837\u4f8b #2<\/h3>\n

\u8f93\u5165 #2<\/h4>\n

3
\n9
\n99
\n999<\/p>\n

\u8f93\u51fa #2<\/h4>\n

76
\n281781445
\n445494875<\/p>\n

\u8f93\u5165\u8f93\u51fa\u6837\u4f8b #3<\/h3>\n

\u8f93\u5165 #3<\/h4>\n

5
\n123
\n1234
\n12345
\n123456
\n1234567<\/p>\n

\u8f93\u51fa #3<\/h4>\n

528790589
\n200102666
\n537707871
\n262341000
\n534036342<\/p>\n

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

\u8fd9\u91cc\u7ed9\u51fa n=5n = 5<\/span><\/span>n<\/span><\/span>=<\/span><\/span><\/span><\/span>5<\/span><\/span><\/span><\/span><\/span> \u65f6，\u6837\u4f8b\u7684\u89e3\u91ca：<\/p>\n

\u4f7f\u7528 1,2,3,4,51, 2, 3, 4, 5<\/span><\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span> \u6765\u4ee3\u8868\u5404\u4e2a\u73e0\u5b50\u3002<\/p>\n

\u53ef\u884c\u7684\u65b9\u6848\u662f（\u5176\u4e2d\u7684\u6570\u5b57\u4ee3\u8868\u67d3\u6210\u91d1\u5143\u7d20\u7684\u73e0\u5b50\u5e8f\u53f7）：<\/p>\n

{1,3,5},{1,2,4},{1,3,4},{2,3,5},{2,4,5}\\\\{1, 3, 5\\\\}, \\\\{1, 2, 4\\\\}, \\\\{1, 3, 4\\\\}, \\\\{2, 3, 5\\\\}, \\\\{2, 4, 5\\\\}<\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>5<\/span>}<\/span>,<\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>4<\/span>}<\/span>,<\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>4<\/span>}<\/span>,<\/span><\/span>{<\/span>2<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>5<\/span>}<\/span>,<\/span><\/span>{<\/span>2<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>5<\/span>}<\/span><\/span><\/span><\/span><\/span><\/p>\n

{1,2,3,4},{1,2,3,5},{1,2,4,5},{1,3,4,5},{2,3,4,5}\\\\{1, 2, 3, 4\\\\}, \\\\{1, 2, 3, 5\\\\}, \\\\{1, 2, 4, 5\\\\}, \\\\{1, 3, 4, 5\\\\}, \\\\{2, 3, 4, 5\\\\}<\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>4<\/span>}<\/span>,<\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>5<\/span>}<\/span>,<\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>5<\/span>}<\/span>,<\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>5<\/span>}<\/span>,<\/span><\/span>{<\/span>2<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>5<\/span>}<\/span><\/span><\/span><\/span><\/span><\/p>\n

{1,2,3,4,5}\\\\{1, 2, 3, 4, 5\\\\}<\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>5<\/span>}<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5bf9\u4e8e 20%20\\\\%<\/span><\/span>20%<\/span><\/span><\/span><\/span><\/span> \u7684\u6570\u636e，\u6709 1\u2264n\u2264101 \\\\le n \\\\le 10<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>10<\/span><\/span><\/span><\/span><\/span> ；<\/p>\n

\u5bf9\u4e8e 40%40\\\\%<\/span><\/span>40%<\/span><\/span><\/span><\/span><\/span> \u7684\u6570\u636e，\u6709 1\u2264n\u22641021 \\\\le n \\\\le 10^2<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> ；<\/p>\n

\u5bf9\u4e8e 60%60\\\\%<\/span><\/span>60%<\/span><\/span><\/span><\/span><\/span> \u7684\u6570\u636e，\u6709 1\u2264n\u22641061\\\\le n \\\\le 10^6<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> ；<\/p>\n

\u5bf9\u4e8e 90%90\\\\%<\/span><\/span>90%<\/span><\/span><\/span><\/span><\/span> \u7684\u6570\u636e，\u6709 1\u2264n\u22641091 \\\\le n \\\\le 10^9<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> ；<\/p>\n

\u5bf9\u4e8e\u5168\u90e8\u7684\u6570\u636e，\u6709 1\u2264T\u226410,1\u2264n\u226410181\\\\le T \\\\le 10, 1\\\\le n \\\\le 10^{18}<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>T<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>10<\/span>,<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>18<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

C++\u5b9e\u73b0<\/h3>\n

#<\/span>include<\/span> <iostream><\/span><\/span>
\n#<\/span>include<\/span> <cstdio><\/span><\/span>
\nusing<\/span> namespace<\/span> std;<\/span>
\nconst<\/span> int<\/span> N =<\/span> 1e6<\/span> +<\/span> 5<\/span>,<\/span> mod =<\/span> 1e9<\/span> +<\/span> 7<\/span>;<\/span>
\nint<\/span> n,<\/span> dp[<\/span>N]<\/span>[<\/span>2<\/span>]<\/span>;<\/span>
\nvoid<\/span> calc<\/span>(<\/span>)<\/span>
\n{<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 2<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span>
\ndp[<\/span>i]<\/span>[<\/span>0<\/span>]<\/span> =<\/span> dp[<\/span>i –<\/span> 1<\/span>]<\/span>[<\/span>1<\/span>]<\/span>,<\/span>
\ndp[<\/span>i]<\/span>[<\/span>1<\/span>]<\/span> =<\/span> (<\/span>dp[<\/span>i –<\/span> 1<\/span>]<\/span>[<\/span>0<\/span>]<\/span> +<\/span> dp[<\/span>i –<\/span> 1<\/span>]<\/span>[<\/span>1<\/span>]<\/span>)<\/span> %<\/span> mod;<\/span>
\n}<\/span>
\nvoid<\/span> solve<\/span>(<\/span>)<\/span>
\n{<\/span>
\nlong<\/span> long<\/span> ans =<\/span> 0<\/span>;<\/span>
\nscanf<\/span>(<\/span>"%d"<\/span>,<\/span> &<\/span>n)<\/span>;<\/span><\/p>\n

dp[<\/span>1<\/span>]<\/span>[<\/span>0<\/span>]<\/span> =<\/span> 1<\/span>,<\/span> dp[<\/span>1<\/span>]<\/span>[<\/span>1<\/span>]<\/span> =<\/span> 0<\/span>;<\/span>
\ncalc<\/span>(<\/span>)<\/span>,<\/span> ans =<\/span> (<\/span>ans +<\/span> dp[<\/span>n]<\/span>[<\/span>1<\/span>]<\/span>)<\/span> %<\/span> mod;<\/span> <\/p>\n

dp[<\/span>1<\/span>]<\/span>[<\/span>0<\/span>]<\/span> =<\/span> 0<\/span>,<\/span> dp[<\/span>1<\/span>]<\/span>[<\/span>1<\/span>]<\/span> =<\/span> 1<\/span>;<\/span>
\ncalc<\/span>(<\/span>)<\/span>,<\/span> ans =<\/span> (<\/span>ans +<\/span> dp[<\/span>n]<\/span>[<\/span>0<\/span>]<\/span> +<\/span> dp[<\/span>n]<\/span>[<\/span>1<\/span>]<\/span>)<\/span> %<\/span> mod;<\/span> <\/p>\n

cout <<<\/span> ans <<<\/span> '\\\\n'<\/span>;<\/span>
\n}<\/span>
\nint<\/span> main<\/span>(<\/span>)<\/span>
\n{<\/span>
\nios::<\/span>sync_with_stdio<\/span>(<\/span>false<\/span>)<\/span>;<\/span>
\nint<\/span> T;<\/span>
\nscanf<\/span>(<\/span>"%d"<\/span>,<\/span> &<\/span>T)<\/span>;<\/span>
\nwhile<\/span> (<\/span>T—<\/span>)<\/span> solve<\/span>(<\/span>)<\/span>;<\/span>
\nreturn<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u540e\u7eed<\/h3>\n

\u63a5\u4e0b\u6765\u6211\u4f1a\u4e0d\u65ad\u7528C++\u6765\u5b9e\u73b0\u4fe1\u5965\u6bd4\u8d5b\u4e2d\u7684\u7b97\u6cd5\u9898\u3001GESP\u8003\u7ea7\u7f16\u7a0b\u9898\u5b9e\u73b0\u3001\u767d\u540d\u5355\u8d5b\u4e8b\u8003\u9898\u5b9e\u73b0，\u8bb0\u5f55\u65e5\u5e38\u7684\u7f16\u7a0b\u751f\u6d3b\u3001\u6bd4\u8d5b\u5fc3\u5f97，\u611f\u5174\u8da3\u7684\u8bf7\u5173\u6ce8，\u6211\u540e\u7eed\u5c06\u7ee7\u7eed\u5206\u4eab\u76f8\u5173\u5185\u5bb9<\/p>\n","protected":false},"excerpt":{"rendered":"

P4910 \u5e15\u79cb\u8389\u7684\u624b\u73af
\n\u9898\u76ee\u80cc\u666f
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