【CodeForces】【321E】Ciel and Gondolas

DP优化/四边形不等式

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　　这题……跟邮局那题简直一模一样吧……好水的E题……

　　设dp[i][j]表示前 i 艘“gondola”坐了前 j 个人，那么方程即为$dp(i,j)=min\{ dp[i-1][k]+w[k][j] \} (i\leq k\leq j)$

　　很明显$w(l,r)=\sum_{i=l}^r \sum_{j=l}^r u(i,j) /2$是满足四边形不等式的……那么根据决策单调性直接搞就行了……

 //CF 321E
 #include<vector>
 #include<cstdio>
 #include<cstdlib>
 #include<cstring>
 #include<iostream>
 #include<algorithm>
 #define rep(i,n) for(int i=0;i<n;++i)
 #define F(i,j,n) for(int i=j;i<=n;++i)
 #define D(i,j,n) for(int i=j;i>=n;--i)
 using namespace std;
 //#define debug
 int getint(){
     int v=,sign=; char ch=getchar();
     while(ch<''||ch>'') {if (ch=='-') sign=-; ch=getchar();}
     while(ch>=''&&ch<='') {v=v*+ch-''; ch=getchar();}
     return v*sign;
 }
 typedef long long LL;
 const int N=,INF=~0u>>;
 /*******************tamplate********************/
 LL u[][],n,m,w[][],dp[][];
 int s[][];
 int main(){
 #ifndef ONLINE_JUDGE
     freopen("input.txt","r",stdin);
 //    freopen("output.txt","w",stdout);
 #endif
     n=getint(); m=getint();
     F(i,,n) F(j,,n) u[i][j]=getint();
     F(i,,n) F(j,,n) u[i][j]+=u[i-][j]+u[i][j-]-u[i-][j-];

     F(i,,n) F(j,i+,n) w[i][j]=u[j][j]-u[i-][j]-u[j][i-]+u[i-][i-];

     #ifdef debug
     F(i,,n) {F(j,,n) printf("%3d",w[i][j]);puts("");}
     #endif
     F(i,,m) F(j,,n) dp[i][j]=INF;
     F(i,,n){
         dp[][i]=w[][i];
         s[][i]=;
     }
     F(i,,m){
         s[i][n+]=n;
         D(j,n,i)
             F(k,s[i-][j],s[i][j+])
                 if (dp[i-][k]+w[k+][j]<dp[i][j]){
                     s[i][j]=k;
                     dp[i][j]=dp[i-][k]+w[k+][j];
                 }
     }
     printf("%I64d\n",dp[m][n]/);
     return ;
 }