{"id":184,"date":"2010-03-23T17:00:00","date_gmt":"2010-03-23T09:00:00","guid":{"rendered":"http:\/\/localhost\/?p=184"},"modified":"2010-03-23T17:00:00","modified_gmt":"2010-03-23T09:00:00","slug":"scoi2005_the_largest_sub-matrix","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/wjmzbmr\/?p=184","title":{"rendered":"[SCOI2005]\u6700\u5927\u5b50\u77e9\u9635"},"content":{"rendered":"\n

[SCOI2005]\u6700\u5927\u5b50\u77e9\u9635<\/p>\n

Time Limit:10000MS Memory Limit:165536K
Total Submit:26 Accepted:13
Case Time Limit:1000MS<\/p>\n

Description <\/strong><\/p>\n

\u8fd9\u91cc\u6709\u4e00\u4e2an*m\u7684\u77e9\u9635\uff0c\u8bf7\u4f60\u9009\u51fa\u5176\u4e2dk\u4e2a\u5b50\u77e9\u9635\uff0c\u4f7f\u5f97\u8fd9\u4e2ak\u4e2a\u5b50\u77e9\u9635\u5206\u503c\u4e4b\u548c\u6700\u5927\u3002\u6ce8\u610f\uff1a\u9009\u51fa\u7684k\u4e2a\u5b50\u77e9\u9635\u4e0d\u80fd\u76f8\u4e92\u91cd\u53e0\u3002 <\/p>\n

Input <\/strong><\/p>\n

\u7b2c\u4e00\u884c\u4e3an,m,k\uff081\u2264n\u2264100,1\u2264m\u22642,1\u2264k\u226410\uff09\uff0c\u63a5\u4e0b\u6765n\u884c\u63cf\u8ff0\u77e9\u9635\u6bcf\u884c\u4e2d\u7684\u6bcf\u4e2a\u5143\u7d20\u7684\u5206\u503c(\u6bcf\u4e2a\u5143\u7d20\u7684\u5206\u503c\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc732767)\u3002 <\/p>\n

Output <\/strong><\/p>\n

\u53ea\u6709\u4e00\u884c\u4e3ak\u4e2a\u5b50\u77e9\u9635\u5206\u503c\u4e4b\u548c\u6700\u5927\u4e3a\u591a\u5c11\u3002 <\/p>\n

Sample Input <\/strong><\/p>\n<\/p>\n

Sample Output <\/strong><\/p>\n<\/p>\n

Source
\u8fd9\u4e2a\u660e\u663e\u8981DP\uff0c\u4e00\u7ef4\u7684\u592a\u6c34\u5c31\u4e0d\u8bf4\u4e86\u3002
\u4e8c\u7ef4\u7684\u8bdd\uff0c\u9996\u5148\u9884\u5904\u7406\u51fa\u5b50\u77e9\u9635\u7684\u548c\u6bd4\u8f83\u65b9\u4fbf\u3002
\u8bbeDp(i,a1,a2)\u4e3ai\u4e2a\u77e9\u5f62\uff0c\u7b2c1\u52171..a1\uff0c\u7b2c\u4e8c\u52171..a2\u7684\u6700\u5927\u4ef7\u503c\uff0c
\u90a3\u4e48\u5982\u679c\u7b2c\u4e00\u5217\u7684a1\u4e0d\u653e\u7684\u8bdd\uff0c\u662fDp(i,a1-1,a2)\u3002\u3002\u3002
\u5982\u679c\u7b2c\u4e8c\u5217\u7684a2\u4e0d\u653e\u7684\u8bdd\uff0c\u662fDp(i,a1,a2-1)\u3002\u3002\u3002
\u5982\u679c\u653e\u7684\u8bdd\u679a\u4e3e\u4e0a\u4e00\u4e2a\u72b6\u6001\u662fO\uff08n\uff09\u7684\u3002
\u7136\u540e\u53ea\u6709\u5728a1==a2\u7684\u65f6\u5019\u624d\u679a\u4e3e\u5bbd\u5ea6\u4e3a2\u7684\u77e9\u9635\u7684\u60c5\u51b5\u5c31\u53ef\u4ee5\u4e86\u3002\u3002
\u4e0d\u8fc7\u7ec6\u8282\u5f88\u8981\u7d27\uff0c\u6211WA\u4e86\u534a\u5929\uff0c\u8fd9\u6837\u4e0b\u53bb\u600e\u4e48\u884c\u554a\u3002\u6bd4\u8d5b\u8003\u5230\u7684\u8bdd\u80af\u5b9a\u60b2\u5267\u7684\u56e7\u3002\u3002
Code\uff1a
<\/strong><\/p>\n

#include<iostream>#include<cstring>using namespace std;const int maxn=100+10,maxk=10+1,inf=~0U>>2;int n,m,k;\/\/solve 1inline void Renew(int&x,int c){ x=max(x,c);}void Solve1(){ int Dp[maxk][maxn]={0}; int A[maxn]={0}; for(int i=1;i<=n;i++)cin>>A[i],A[i]+=A[i-1]; for(int i=1;i<=k;i++) { for(int j=0;j<=n;j++) { int&x=Dp[i][j];x=-inf; if(j)x=Dp[i][j-1]; for(int o=0;o<j;o++) { Renew(x,Dp[i-1][o]+A[j]-A[o]); } } } cout<<Dp[k][n]<<endl;}\/\/solve 2void Solve2(){ int Dp[maxk][maxn][maxn]={0}; int A[2][maxn]={0},S[maxn]={0}; for(int j=1;j<=n;j++) for(int i=0;i<2;i++) cin>>A[i][j],S[j]+=A[i][j],A[i][j]+=A[i][j-1]; for(int j=1;j<=n;j++) S[j]+=S[j-1]; for(int i=1;i<=k;i++) for(int a1=0;a1<=n;a1++) for(int a2=0;a2<=n;a2++) { int&x=Dp[i][a1][a2];x=-inf; if(a1) { Renew(x,Dp[i][a1-1][a2]); for(int o=0;o<a1;o++) Renew(x,Dp[i-1][o][a2]+A[0][a1]-A[0][o]); } if(a2) { Renew(x,Dp[i][a1][a2-1]); for(int o=0;o<a2;o++) Renew(x,Dp[i-1][a1][o]+A[1][a2]-A[1][o]); } if(a1==a2) { for(int o=0;o<a1;o++) Renew(x,Dp[i-1][o][o]+S[a1]-S[o]); } } cout<<Dp[k][n][n]<<endl;}int main(){ \/\/freopen("in","r",stdin); cin>>n>>m>>k; if(m==1)Solve1(); else Solve2();}93 2 21 -32 3-2 3 <\/p>\n","protected":false},"excerpt":{"rendered":"

[SCOI2005]\u6700\u5927\u5b50\u77e9\u9635 Time Limit:10000MS Memory Limit:165536KTotal Submit:26 Accepted:13 Case Time Limit:1000MS Description \u8fd9\u91cc\u6709\u4e00\u4e2an*m\u7684\u77e9\u9635\uff0c\u8bf7\u4f60\u9009\u51fa\u5176\u4e2dk\u4e2a\u5b50\u77e9\u9635\uff0c\u4f7f\u5f97\u8fd9\u4e2ak\u4e2a\u5b50\u77e9\u9635\u5206\u503c\u4e4b\u548c\u6700\u5927\u3002\u6ce8\u610f\uff1a\u9009\u51fa\u7684k\u4e2a\u5b50\u77e9\u9635\u4e0d\u80fd\u76f8\u4e92\u91cd\u53e0\u3002 Input \u7b2c\u4e00\u884c\u4e3an,m,k\uff081\u2264n\u2264100,1\u2264m\u22642,1\u2264k\u226410\uff09\uff0c\u63a5\u4e0b\u6765n\u884c\u63cf\u8ff0\u77e9\u9635\u6bcf\u884c\u4e2d\u7684\u6bcf\u4e2a\u5143\u7d20\u7684\u5206\u503c(\u6bcf\u4e2a\u5143\u7d20\u7684\u5206\u503c\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc732767)\u3002 Output \u53ea\u6709\u4e00\u884c\u4e3ak\u4e2a\u5b50\u77e9\u9635\u5206\u503c\u4e4b\u548c\u6700\u5927\u4e3a\u591a\u5c11\u3002 Sample Input Sample Output Source \u8fd9\u4e2a\u660e\u663e\u8981DP\uff0c\u4e00\u7ef4\u7684\u592a\u6c34\u5c31\u4e0d\u8bf4\u4e86\u3002\u4e8c\u7ef4\u7684\u8bdd\uff0c\u9996\u5148\u9884\u5904\u7406\u51fa\u5b50\u77e9\u9635\u7684\u548c\u6bd4\u8f83\u65b9\u4fbf\u3002\u8bbeDp(i,a1,a2)\u4e3ai\u4e2a\u77e9\u5f62\uff0c\u7b2c1\u52171..a1\uff0c\u7b2c\u4e8c\u52171..a2\u7684\u6700\u5927\u4ef7\u503c\uff0c\u90a3\u4e48\u5982\u679c\u7b2c\u4e00\u5217\u7684a1\u4e0d\u653e\u7684\u8bdd\uff0c\u662fDp(i,a1-1,a2)\u3002\u3002\u3002\u5982\u679c\u7b2c\u4e8c\u5217\u7684a2\u4e0d\u653e\u7684\u8bdd\uff0c\u662fDp(i,a1,a2-1)\u3002\u3002\u3002\u5982\u679c\u653e\u7684\u8bdd\u679a\u4e3e\u4e0a\u4e00\u4e2a\u72b6\u6001\u662fO\uff08n\uff09\u7684\u3002\u7136\u540e\u53ea\u6709\u5728a1==a2\u7684\u65f6\u5019\u624d\u679a\u4e3e\u5bbd\u5ea6\u4e3a2\u7684\u77e9\u9635\u7684\u60c5\u51b5\u5c31\u53ef\u4ee5\u4e86\u3002\u3002\u4e0d\u8fc7\u7ec6\u8282\u5f88\u8981\u7d27\uff0c\u6211WA\u4e86\u534a\u5929\uff0c\u8fd9\u6837\u4e0b\u53bb\u600e\u4e48\u884c\u554a\u3002\u6bd4\u8d5b\u8003\u5230\u7684\u8bdd\u80af\u5b9a\u60b2\u5267\u7684\u56e7\u3002\u3002Code\uff1a #include<iostream>#include<cstring>using namespace std;const int maxn=100+10,maxk=10+1,inf=~0U>>2;int n,m,k;\/\/solve 1inline void Renew(int&x,int c){ x=max(x,c);}void Solve1(){ int Dp[maxk][maxn]={0}; int A[maxn]={0}; for(int i=1;i<=n;i++)cin>>A[i],A[i]+=A[i-1]; for(int i=1;i<=k;i++) { for(int j=0;j<=n;j++) { int&x=Dp[i][j];x=-inf; if(j)x=Dp[i][j-1]; for(int o=0;o<j;o++) { Renew(x,Dp[i-1][o]+A[j]-A[o]); } } } […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/184"}],"collection":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=184"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/184\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}