uva 10891

dp

状态转移方程:d(i,j)=sum(i,j)-min{d(i+1,j),d(i+2,j)...d(j,j),d(i,j-1),d(i,j-2)...d(i,i),0}
可化为d(i,j)=sum(i,j)-min{f(i+1,j),g(i,j-1),0}

#include <iostream>#include <cstring>#include <cstdio>using namespace std;const int maxn=100+10;int arr[maxn];int f[maxn][maxn],d[maxn][maxn],s[maxn],g[maxn][maxn];int n;int min(int a,int b)  { return a<b?a:b; }int main(){while(scanf("%d",&n)&&n){int i,j,k;s[0]=0;for(i=1;i<=n;i++) { scanf("%d",&arr[i]); s[i]=s[i-1]+arr[i]; }for(i=1;i<=n;i++) f[i][i]=g[i][i]=d[i][i]=arr[i];for(i=2;i<=n;i++){for(j=1;j+i-1<=n;j++){k=j+i-1;int tem=min(f[j+1][k],g[j][k-1]);d[j][k]=s[k]-s[j-1]-min(tem,0);f[j][k]=min(d[j][k],f[j+1][k]);g[j][k]=min(d[j][k],g[j][k-1]);}}printf("%d\n",2*d[1][n]-s[n]);}return 0;}