POJ - 1191 / NOI 1999 棋盤分割 記憶化搜索DP

思路

代碼

#include <iostream>
#include <cstring>
#include <algorithm>
#include <cstdio>
#include <cmath>

using namespace std;

const int N = 15, M = 9;

int n;
double f[M][M][M][M][N];
int s[M][M];
double X;

int get_sum(int x1, int y1, int x2, int y2)
{
	return s[x2][y2] - s[x1 - 1][y2] - s[x2][y1 - 1] + s[x1 - 1][y1 - 1];
}

double get(int x1, int y1, int x2, int y2)
{
	double sum = get_sum(x1, y1, x2, y2);
	sum = sum - X;
	return sum * sum / n;
}

double dfs(int x1, int y1, int x2, int y2, int k)
{
	double &u = f[x1][y1][x2][y2][k];
	if(k == 1) return u = get(x1, y1, x2, y2);
	if(u > 0)	return u;
	
	u = 1e9;
	for(int i = x1; i < x2; i++)
	{
		u = min(u, get(i + 1, y1, x2, y2) + dfs(x1, y1, i, y2, k - 1));
		u = min(u, get(x1, y1, i, y2) + dfs(i + 1, y1, x2, y2, k - 1));
	}
	for(int i = y1; i < y2; i++)
	{
		u = min(u, get(x1, y1, x2, i) + dfs(x1, i + 1, x2, y2, k - 1));
		u = min(u, get(x1, i + 1, x2, y2) + dfs(x1, y1, x2, i, k - 1));
	}
	return u;
}

int main()
{
	cin >> n;
	for(int i = 1; i <= 8; i++)
		for(int j = 1; j <= 8; j++)
		{
			cin >> s[i][j];
			s[i][j] += s[i - 1][j] + s[i][j - 1] - s[i - 1][j - 1];
		}
	memset(f, -1, sizeof f);
	X = (double)s[8][8] / n;
	printf("%.3lf", sqrt(dfs(1, 1, 8, 8, n)));
	return 0;	
}