poj1191

#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
using namespace std;

int n;
int sum;
int dp[16][9][9][9][9];
int g[9][9][9][9];
int mp[9][9];
double ave;

void init(){
    sum=0;
    scanf("%d",&n);
    for(int i=0;i<8;i++){
        for(int j=0;j<8;j++){
            scanf("%d",&mp[i][j]);
            sum+=mp[i][j];
        }
    }

    ave = sum*1.0/n;

	for(int x=0;x<9;x++)
	for(int y=0;y<9;y++){
		for(int xx=x;xx<9;xx++)
		for(int yy=y;yy<9;yy++){
			int ans=0;
			for(int i=x;i<=xx;i++)
			for(int j=y;j<=yy;j++){
				ans+=mp[i][j];
			}
			g[x][y][xx][yy]=ans*ans;
		}
	}
}

int DP(int k,int x,int y,int xx,int yy)
{
	int i,ans=0;
	if(dp[k][x][y][xx][yy]>=0) return dp[k][x][y][xx][yy];
	if(k==n-1) return g[x][y][xx][yy];
	dp[k][x][y][xx][yy]=1<<29;
	for(i=x;i<xx;i++){
		ans=min(DP(k+1,x,y,i,yy)+g[i+1][y][xx][yy],DP(k+1,i+1,y,xx,yy)+g[x][y][i][yy]);
        dp[k][x][y][xx][yy]=min(ans,dp[k][x][y][xx][yy]);
	}
	for(i=y;i<yy;i++){
		ans=min(DP(k+1,x,y,xx,i)+g[x][i+1][xx][yy],DP(k+1,x,i+1,xx,yy)+g[x][y][xx][i]);
		dp[k][x][y][xx][yy]=min(ans,dp[k][x][y][xx][yy]);
	}
	return dp[k][x][y][xx][yy];
}

int main(){
    init();
	memset(dp,-1,sizeof(dp));
	DP(0,0,0,7,7);
	printf("%.3f\n",sqrt((dp[0][0][0][7][7])*1.0/n-ave*ave));
	return 0;
}

#include<iostream>  
#include<cmath>  
#include<cstdio>  
#include<cstdlib>  
#include<cstring>  
#include<algorithm>  
using namespace std;  
  
int n;  
long double d[16][9][9][9][9];  
long double s[9][9][9][9];  
double map[9][9];  
int count_map[9][9];  
long double sum;  
long double ave;  
const int m = 8;  
const double INF = 0x7f7f7f7f;  
  
double count(int i,int j,int i2,int j2)  
{  
    double ans = count_map[i2][j2] - count_map[i2][j-1] - count_map[i-1][j2] + count_map[i-1][j-1];  
    return ans*ans;  
}  
  
void init()  
{  
    int i,j;  
    sum = 0;  
    memset(count_map,0,sizeof(count_map));  
    for(i=1;i<=8;i++)  
    {  
        for(j=1;j<=8;j++)  
        {  
            scanf("%lf",&map[i][j]);  
            sum+=map[i][j];  
  
            count_map[i][j] =   count_map[i][j-1]   +  
                                count_map[i-1][j]   -  
                                count_map[i-1][j-1] +  
                                map[i][j];  
        }  
    }  
  
    ave = sum*1.0/n;  
    int i2,j2;  
  
    for(i=1;i<=m;i++)  
    {  
        for(j=1;j<=m;j++)  
        {  
            for(i2=i;i2<=m;i2++)  
            {  
                for(j2 = j;j2<=m;j2++)  
                {  
                    s[i][j][i2][j2] = count(i,j,i2,j2);  
                    d[0][i][j][i2][j2] = s[i][j][i2][j2];  
                }  
            }  
        }  
    }  
}  
  
void dp()  
{  
    int k,i,j,i2,j2;  
  
    for(k=1;k<n;k++)  
    {  
        for(i=1;i<=m;i++)  
        {  
            for(j=1;j<=m;j++)  
            {  
                for(i2=i;i2<=m;i2++)  
                {  
                    for(j2 = j;j2<=m;j2++)  
                    {  
                        d[k][i][j][i2][j2] = INF;  
  
                       
                        int t;  
                        for( t = i;t<i2;t++)  
                            d[k][i][j][i2][j2] =    min(d[k][i][j][i2][j2],  
                                                        min(d[k-1][i][j][t][j2] + s[t+1][j][i2][j2],  
                                                            s[i][j][t][j2] + d[k-1][t+1][j][i2][j2]));  
                       
                        for( t = j;t<j2;t++)  
                            d[k][i][j][i2][j2] =    min(d[k][i][j][i2][j2],  
                                                        min(d[k-1][i][j][i2][t] + s[i][t+1][i2][j2],  
                                                            s[i][j][i2][t] + d[k-1][i][t+1][i2][j2]));  
                    }  
                }  
            }  
        }  
    }  
}  
  
  
  
int main()  
{  
    while(scanf("%d",&n) != EOF)  
    {  
        init();  
        dp();  
        long double ans = d[n-1][1][1][m][m]*1.0/n - ave*ave;  
        printf("%.3f\n",(double)sqrt(ans));  
    }  
    return 0;  
}