{"id":136,"date":"2018-10-18T18:19:26","date_gmt":"2018-10-18T10:19:26","guid":{"rendered":"http:\/\/SmokeyDays.top\/wordpress\/?p=136"},"modified":"2018-10-22T12:23:25","modified_gmt":"2018-10-22T04:23:25","slug":"lp2467-sdoi2010-%e5%9c%b0%e7%b2%be%e9%83%a8%e8%90%bd","status":"publish","type":"post","link":"http:\/\/SmokeyDays.top\/wordpress\/2018\/10\/18\/lp2467-sdoi2010-%e5%9c%b0%e7%b2%be%e9%83%a8%e8%90%bd\/","title":{"rendered":"lp2467 SDOI2010 \u5730\u7cbe\u90e8\u843d"},"content":{"rendered":"

\u8fd9\u4e00\u9898\u7684\u9898\u9762\u5f88\u590d\u6742\uff0c\u4f46\u5f62\u5f0f\u5316\u5730\u6982\u62ec\u5219\u5f88\u7b80\u5355\uff1a<\/p>\n

\u5bf9\u4e8e\u4e00\u4e2a\u957f\u5ea6\u4e3an\u7684\u5168\u6392\u5217\uff0c\u6c42\u51fa\u5176\u4e2d\u6709\u591a\u5c11\u6392\u5217A\u6ee1\u8db3\uff0c\u5bf9\u4e8e\u4efb\u610fi\u5c5e\u4e8en\uff0c$$(A_{i}-A{i-1})*(A_{i}-A_{i+1})>=0;$$<\/p>\n

\u7136\u540e\u6211\u4eec\u89c2\u5bdf\u6392\u5217\u7684\u7279\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u5bf9\u4e8e\u6392\u5217A\u4e2d\u7684\u4e00\u4e2a\u5143\u7d20\\(A_{i}\\)\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u5982\u679c\\(A_{i}\\)\u662f\u5c71\u5cf0\uff0c\u90a3\u4e48\u5c06\\(A_{i}\\)\u7684\u503c\u65e0\u8bba\u6dfb\u52a0\u591a\u5c11\uff0c\u90fd\u4e0d\u6539\u53d8\u8fd9\u4e2a\u5e8f\u5217\u7684\u53ef\u5c45\u4f4f\u6027\uff1b\u5bf9\u4e8e\u5c71\u8c37\uff0c\u5219\u53cd\u4e4b\u3002
\n\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e00\u4e2a\u5408\u6cd5\u7684\u6392\u5217\uff0c\u5982\u679c\u6211\u4eec\u8981\u5728\u5b83\u672b\u5c3e\u6dfb\u4e0a\u4e00\u4e2a\u6570\u8ba9\u5b83\u5f62\u6210\u4e00\u4e2a\u65b0\u7684\u5408\u6cd5\u6392\u5217\uff0c\u5bf9\u4e8e\u9664\u4e86\u6700\u540e\u4e00\u4e2a\u6570\u4ee5\u53ca\u8fd9\u4e2a\u6570\u662f\u5c5e\u4e8e\u5c71\u5cf0\u4ee5\u53ca\u5c71\u8c37\u4ee5\u5916\uff0c\u6211\u4eec\u4e0d\u5173\u5fc3\u5176\u4ed6\u7684\u5c5e\u6027\u3002
\n\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u7528\\(f[i][j][k]\\)\u8868\u8fbe\u5f53\u524d\u957f\u5ea6\u4e3ai\uff0c\u6700\u540e\u4e00\u4e2a\u6570\u4e3aj\uff0c\u6700\u540e\u4e00\u4e2a\u6570\u7684\u72b6\u6001\u4e3ak\u7684\u65f6\u5019\u7684\u72b6\u6001\u6570\u3002\u5176\u4e2dk==0\u8868\u793a\u5c71\u8c37\uff0c\u800ck==1\u8868\u793a\u5c71\u5cf0\u3002
\n\u5219\u5f88\u5bb9\u6613\u53ef\u4ee5\u5f97\u5230\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff1a
\n$$f[i][j][k]+=f[i-1][l][k\\ xor\\ 1](k?(0<l<=j-1):(j-1<l<=i))$$
\n\u4f46\u662f\u8fd9\u6837\u5b50\u7684\u590d\u6742\u5ea6\u662fN^3\u7684\uff0c\u5bf9\u4e8e4200\u7684\u6570\u636e\u663e\u7136\u662f\u4e0d\u80fd\u901a\u8fc7\u7684\u3002\u8fd9\u65f6\u5019\u8003\u8651\u4f18\u5316\u3002
\n\u6211\u4eec\u53d1\u73b0\u6c42\u548c\u7684\u4e1c\u897f\u662f\u4e00\u6bb5\u533a\u95f4\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u524d\u7f00\u4f18\u5316\u3002
\n\u8fd9\u6837\u5b50\u5c31\u5c06\u590d\u6742\u5ea6\u4ece\\(n^3\\)\u964d\u4f4e\u5230\u4e86\\(n^2\\)\uff0c\u4e8e\u662f\u53ef\u4ee5\u901a\u8fc7\u3002
\n\u4f46\u662f\u8fd9\u6837\u5b50\u9700\u8981\u7684\u7a7a\u95f4\u662f3E7\u7684\uff0c\u5bf9\u4e8e128MB\u7684\u7a7a\u95f4\u662f\u975e\u5e38\u5371\u9669\u7684\uff0c\u8fd9\u65f6\u5019\u8003\u8651\u6eda\u52a8\u6570\u7ec4\u4f18\u5316\uff0c\u8fd9\u6837\u662f\u53ef\u4ee5\u901a\u8fc7\u7684\u3002<\/p>\n

#include<iostream>\r\n#include<cstdio>\r\nusing namespace std;\r\nlong long n,p,f[4205][2],pre[4205][2];\r\nvoid init(){\r\n    scanf(\"%lld%lld\",&n,&p);\r\n    int l,r;\r\n    f[1][1]=f[1][0]=pre[1][0]=pre[1][1]=1;\r\n    for(int i=2;i<=n;++i){\r\n        pre[i][0]=pre[i-1][0],pre[i][1]=pre[i-1][1];\r\n        for(int j=1;j<=i;++j){\r\n            for(int k=0;k<=1;++k){\r\n                l=k?0:j-1;\r\n                r=k?j-1:i;\r\n                f[j][k]=(pre[r][k^1]-pre[l][k^1]+p)%p;\r\n\/\/                printf(\"(%d,%d)[%d,%d]%lld|\",l,r,pre[l][k^1],pre[r][k^1],f[j][k]);\r\n            }\r\n\/\/            printf(\" \");\r\n        }\r\n        pre[0][0]=pre[0][1]=0;\r\n        for(int j=1;j<=i;++j){\r\n            pre[j][0]=(pre[j-1][0]+f[j][0])%p;\r\n            pre[j][1]=(pre[j-1][1]+f[j][1])%p;\r\n        }\r\n\/\/        puts(\"\");\r\n    }\r\n    long long ans=(pre[n][0]+pre[n][1])%p;\r\n    printf(\"%lld\",ans);\r\n}\r\nint main(){\r\n    init();\r\n    return 0;\r\n}<\/code><\/pre>\n
 <\/p>\n
Q\uff1a\u4e3a\u4ec0\u4e48\u8fd9\u4e2a\u65b9\u7a0b\u4e0d\u4f1a\u91cd\u590d\u7edf\u8ba1\u5462\uff1f
\n\u5982\u679c\u53ea\u5173\u5fc3\u4e0a\u4e00\u4e2a\u5143\u7d20\u7684\u5927\u5c0f\uff0c\u6392\u5217\u4e2d\u7684\u5143\u7d20\u53ef\u80fd\u91cd\u590d\u51fa\u73b0\u4e86\u3002<\/p>\n
A\uff1a\u4e0d\u4f1a\u91cd\u590d\u7edf\u8ba1\uff0c\u611f\u6027\u8bc1\u660e\u5982\u4e0b\uff1a<\/p>\n
\u9996\u5148\u6211\u4eec\u5047\u5b9a\u5bf9\u4e8e\u4e0a\u4e00\u4e2aA\uff0c\u4f7f\u5f97\uff1a<\/p>\n
$$ |A|==i-1 $$<\/p>\n
\u5e76\u6ca1\u6709\u91cd\u590d\u7edf\u8ba1\u3002
\n\u90a3\u4e48\u6211\u4eec\u63d2\u5165\u4e00\u4e2a\u65b0\u7684\u5143\u7d20\\(i\\)\u65f6\uff0c\u4ea7\u751f\u7684\u65b0\u5e8f\u5217\u5fc5\u7136\u662f \u672c\u8d28\u4e0d\u540c \u7684\u3002
\n\u6211\u4eec\u5bf9\u4e8e\\(A_{i-1}\\)\u662f\u5c71\u5cf0\u548c\u5c71\u8c37\u5206\u522b\u8ba8\u8bba\u3002
\n\u5982\u679c\\(A_{i-1}\\)\u662f\u5c71\u5cf0\uff0c\u90a3\u4e48\u65b0\u63d2\u5165\u7684\u5143\u7d20\uff0c\u5fc5\u7136\u6bd4\\(A_{i-1}\\)\u5c0f\uff0c\u5e76\u4e14\u4e00\u5b9a\u662f\u7531\u5c06\u5e8f\u5217\u4e2d\u5927\u7b49\u4e8e\u3010\u67d0\u4e2a\u5c0f\u4e8e\u7b49\u4e8e\\(A_{i-1}\\)\u7684\u4e00\u4e2a\u6570\\(l\\)\u3011\u7684\u6240\u6709\u6570\u63d0\u5347\u4e00\uff0c\u7136\u540e\u5c06\u65b0\u63d2\u5165\u7684\u5143\u7d20\u5b9a\u4e49\u4e3a\\(l\\)\u3002
\n\u8fd9\u65f6\u5019\uff0c\\(i-1\\)\u4f4d\u4e0a\u7684\u6570\u662f\\(A_{i-1}+1\\)\uff0c\u800c\\(i\\)\u4f4d\u4e0a\u7684\u6570\u5219\u662f\\(l\\)\u3002
\n\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6700\u540e\u4e24\u4f4d\u662f\\(A_{i-1}+1\\)\u4e0e\\(l\\)\u3002\u663e\u7136\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u672c\u6765\u5df2\u6709\u7684\\(A_{i-1}\\)\uff0c\u5b83\u4eec\u5728\u65b0\u7684\u5e8f\u5217\u4e2d\u90fd\u4f1a\u52a0\u4e14\u4ec5\u52a01\u3002
\n\u8fd9\u6837\uff0c\u6240\u6709\u65b0\u589e\u7684\u7ec4\u5408\u7684\u6700\u540e\u4e24\u4f4d\u90fd\u662f \u672c\u8d28\u4e0d\u540c \u7684\uff0c\u56e0\u6b64\u5e8f\u5217\u672c\u8d28\u4e0d\u540c\u3002
\n\u5bf9\u4e8e\u5c71\u8c37\uff0c\u60c5\u51b5\u7c7b\u540c\u4e8e\u5c71\u5cf0\uff0c\u540c\u6837\u53ef\u4ee5\u8bc1\u660e\u4e0d\u4f1a\u4ea7\u751f\u91cd\u590d\u7684\u540e\u4e24\u4f4d\uff0c\u8fdb\u800c\u4e0d\u4f1a\u4ea7\u751f\u672c\u8d28\u76f8\u540c\u7684\u6570\u5217\u3002<\/p>\n
\u800c\u5bf9\u4e8e $$|A|==1$$ \uff0c\u7ed3\u679c\u663e\u7136\u662f1\uff0c\u6ca1\u6709\u91cd\u590d\u7edf\u8ba1\u3002
\n\u4ece\u800c\u5f52\u7eb3\u5f97\u51fa\u5168\u90e8\u90fd\u6ca1\u6709\u91cd\u590d\u7edf\u8ba1\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u8fd9\u4e00\u9898\u7684\u9898\u9762\u5f88\u590d\u6742\uff0c\u4f46\u5f62\u5f0f\u5316\u5730\u6982\u62ec\u5219\u5f88\u7b80\u5355\uff1a \u5bf9\u4e8e\u4e00\u4e2a\u957f\u5ea6\u4e3an\u7684\u5168\u6392\u5217\uff0c\u6c42\u51fa\u5176\u4e2d\u6709\u591a\u5c11\u6392\u5217A\u6ee1\u8db3\uff0c\u5bf9\u4e8e\u4efb\u610fi\u5c5e … <\/p>\n
\u7ee7\u7eed\u9605\u8bfb\u201clp2467 SDOI2010 \u5730\u7cbe\u90e8\u843d\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[8,9,5],"tags":[],"_links":{"self":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/136"}],"collection":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/comments?post=136"}],"version-history":[{"count":4,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/136\/revisions"}],"predecessor-version":[{"id":196,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/136\/revisions\/196"}],"wp:attachment":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/media?parent=136"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/categories?post=136"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/tags?post=136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}