{"id":310,"date":"2018-11-01T21:31:00","date_gmt":"2018-11-01T13:31:00","guid":{"rendered":"http:\/\/SmokeyDays.top\/wordpress\/?p=310"},"modified":"2018-11-07T16:36:22","modified_gmt":"2018-11-07T08:36:22","slug":"lp3959-noip2017-%e5%ae%9d%e8%97%8f","status":"publish","type":"post","link":"http:\/\/SmokeyDays.top\/wordpress\/2018\/11\/01\/lp3959-noip2017-%e5%ae%9d%e8%97%8f\/","title":{"rendered":"lp3959 NOIP2017 \u5b9d\u85cf"},"content":{"rendered":"

\u6211\u4eec\u9996\u5148\uff0c\u5982\u679c\u4e24\u4e2a\u70b9\u4e4b\u95f4\u6709\u8fde\u591a\u6761\u8fb9\uff0c\u80af\u5b9a\u53ea\u6709\u6700\u77ed\u7684\u90a3\u6761\u6700\u4f18\u3002
\n\u90a3\u4e48\u6211\u4eec\u8fdb\u884c\u72b6\u538b\uff0c\u5bf9\u4e8e\u67d0\u4e00\u4e2a\u72b6\u6001\\(S_{0}\\)\uff0c\u6211\u4eec\u7ef4\u62a4\u5b83\u7684\u6240\u6709\u62d3\u5c55\u7684\u96c6\u5408\\(T_{S_{1}}\\)
\n\u7136\u540e\uff0c\u8bb0\\(f_{i,k}\\)\u8868\u793a\uff0c\u5f53\u524d\u72b6\u6001\u4e3a\\(i\\)\uff0c\u5f53\u524d\u7684\u6df1\u5ea6\u4e3a\\(k\\)\u65f6\u7684\u6700\u5c0f\u82b1\u8d39\u3002
\n\u8fd9\u6837\u62d3\u5c55\uff0c\u6bcf\u4e00\u6b21\u62d3\u5c55\u90fd\u76f8\u5f53\u4e8e\u628a\u6df1\u5ea6\u52a0\u6df1\u4e86\u4e00\u5c42\uff0c\u56e0\u6b64\u5c31\u53ef\u4ee5\u4e0d\u8981\u82b1\u8d39\u592a\u591a\u7684\u7cbe\u529b\u53bb\u8003\u8651\\(k\\)\u5bf9\u8d21\u732e\u7684\u5f71\u54cd\u3002
\n\u800c\uff0c\u4ece\u67d0\u4e00\u4e2a\u6839\u5f00\u59cb\u62d3\u5c55\uff0c\u5373\u76f8\u5f53\u4e8e\\(f_{(1<<i),0}\\)
\n\u4e8e\u662f\u6211\u4eec\u4fbf\u53ef\u4ee5\u5f00\u59cbDP\u3002\u6bcf\u4e00\u6b21\u62d3\u5c55\u90fd\u4f1a\u5c06\u53ef\u884c\u96c6\u5408\u7eb3\u5165\u8303\u56f4\u3002\u8fd9\u6837\u62d3\u5c55\u7684\u82b1\u8d39\u4e5f\u662f\u53ef\u4ee5\u88ab\u8f7b\u677e\u8ba1\u7b97\u51fa\u6765\u7684\u3002<\/p>\n

#include<iostream>\r\n#include<cstdio>\r\n#include<cstring>\r\nusing namespace std;\r\n#define Min(_A,_B) ((_A)<(_B)?(_A):(_B))\r\nint n,m,f[1<<12][12],usf[1<<12];\r\nint mp[15][15];\r\nvoid init(){\r\n    scanf(\"%d%d\",&n,&m);\r\n    int u,v,w;\r\n    memset(mp,0x3f,sizeof(mp));\r\n    for(int i=1;i<=m;++i){\r\n        scanf(\"%d%d%d\",&u,&v,&w);\r\n        --u,--v; \r\n        mp[u][v]=Min(mp[u][v],w);\r\n        mp[v][u]=Min(mp[v][u],w);\r\n    }\r\n    const int MAX=1<<n;\r\n    for(int i=1;i<MAX;++i){\r\n        for(int j=0;j<n;++j){\r\n            if((i|(1<<j))!=i){\r\n                continue;\r\n            }\r\n            for(int k=0;k<n;++k){\r\n                if(mp[j][k]!=0x3f3f3f3f){\r\n                    usf[i]|=(1<<k);\r\n                }\r\n            }\r\n        }\r\n    }\r\n    memset(f,0x3f,sizeof(f));\r\n    for(int i=0;i<n;++i){\r\n        mp[i][i]=0;\r\n        f[1<<i][0]=0;\r\n    }\r\n    long long sm,nw,x;\r\n    for(int i=2;i<MAX;++i){\r\n        for(int j=i-1;j;j=(j-1)&i){\r\n            if(((usf[i]|j)!=usf[i])){\r\n                continue;\r\n            }\r\n            sm=0,nw=i^j;\r\n            for(int k=0;k<n;++k){\r\n                if((nw>>k)&1){\r\n                    x=0x3f3f3f3f;\r\n                    for(int l=0;l<n;++l){\r\n                        if((j>>l)&1){\r\n                            x=Min(x,mp[l][k]);\r\n                        }\r\n                    }\r\n                    sm+=x;\r\n                }\r\n            }\r\n            for(int k=1;k<n;++k){\r\n                f[i][k]=Min(f[i][k],f[j][k-1]+sm*k);\r\n            }\r\n        }\r\n    }\r\n    int ans=0x3f3f3f3f;\r\n    for(int i=0;i<n;++i){\r\n        ans=Min(ans,f[MAX-1][i]);\r\n    }\r\n    printf(\"%d\\n\",ans);\r\n}\r\nint main(){\r\n    init();\r\n    return 0;\r\n}<\/code><\/pre>\n
 <\/p>\n","protected":false},"excerpt":{"rendered":"
\u6211\u4eec\u9996\u5148\uff0c\u5982\u679c\u4e24\u4e2a\u70b9\u4e4b\u95f4\u6709\u8fde\u591a\u6761\u8fb9\uff0c\u80af\u5b9a\u53ea\u6709\u6700\u77ed\u7684\u90a3\u6761\u6700\u4f18\u3002 \u90a3\u4e48\u6211\u4eec\u8fdb\u884c\u72b6\u538b\uff0c\u5bf9\u4e8e\u67d0\u4e00\u4e2a\u72b6\u6001\\(S_{0}\\ … <\/p>\n
\u7ee7\u7eed\u9605\u8bfb\u201clp3959 NOIP2017 \u5b9d\u85cf\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":[10,34,37,30,35,31,8,39,6,5],"tags":[],"_links":{"self":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/310"}],"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=310"}],"version-history":[{"count":2,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/310\/revisions"}],"predecessor-version":[{"id":364,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/310\/revisions\/364"}],"wp:attachment":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/media?parent=310"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/categories?post=310"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/tags?post=310"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}