http://acm.nankai.edu.cn/p1137.html
http://172.20.16.106/JudgeOnline/showproblem?problem_id=1036
//7562 liyunsong B Accepted     G++   2009-04-17 12:57:36 
#include<iostream>
using namespace std;
const int N = 101;
int dpmax[2*N][2*N];//dpmax[i][j]表示從第i對石子開始連續順時針合并j堆的最大耗費  
int dpmin[2*N][2*N];//dpmin[i][j]表示從第i對石子開始連續順時針合并j堆的最小耗費
int mins[2*N][2*N];
int maxs[2*N][2*N];
int num[2*N]; 

int main()
{
    int n,i,j,k,r;
    while(cin>>n)
    {
        int t;
        for(i=1;i<=n;i++)
            scanf("%d",&num[i]);

        if(n==1)
        {
            printf("0\n0\n");
            continue;
        }    

        for(i=1;i<=n;i++)
            num[i+n] = num[i];

        for(i=1;i<=2*n;i++)
            for(j=1;j<=2*n;j++)
            {
                dpmin[i][j] = 10000000;
                dpmax[i][j] = 0;
            }

        for(i=1;i<=2*n;i++)
        {
            dpmin[i][1] = dpmax[i][1] = 0;
            dpmin[i][i] = dpmax[i][i] = 0;
            mins[i][i] = maxs[i][i] = num[i];
        }

        for(r = 2;r<=n;r++)//合并堆數
        {
            for(i=1;i<2*n-r+1;i++)//起點
            {
                j = i+r-1;
                dpmin[i][j] = dpmin[i+1][j] + num[i] + mins[i+1][j];
                mins[i][j] = num[i] + mins[i+1][j];
                dpmax[i][j] = dpmax[i+1][j] + num[i] + maxs[i+1][j];
                maxs[i][j] = num[i] + maxs[i+1][j];
                for(k=i+1;k<j;k++)
                {
                    t = mins[i][k] + mins[k+1][j] + dpmin[i][k] + dpmin[k+1][j];
                    if(t < dpmin[i][j])
                    {
                        dpmin[i][j] = t;
                        mins[i][j] = mins[i][k] + mins[k+1][j];
                    }

                    t = maxs[i][k] + maxs[k+1][j] + dpmax[i][k] + dpmax[k+1][j];
                    if(t > dpmax[i][j])
                    {
                        dpmax[i][j] = t;
                        maxs[i][j] = maxs[i][k] + maxs[k+1][j];
                    }
                }
            }
        }
        int MAX = dpmax[1][n];
        int MIN = dpmin[1][n];
        for(i=2;i<=n;i++)
        {
            if(MAX < dpmax[i][i+n-1])
                MAX = dpmax[i][i+n-1];
            if(MIN > dpmin[i][i+n-1])
                MIN = dpmin[i][i+n-1];
        }
        printf("%d\n%d\n",MIN,MAX);
    }
    return 0;
}