poj-1191-棋盘分割

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题目地址

http://poj.org/problem?id=1191

题目大意

解题思路

Code

#include <stdio.h>
#include <iostream>
#include <stdlib.h>
#include <string.h>
#include <queue>
#include <map>
#include <vector>
#include <math.h>
#include <algorithm>
#define INF 0x3fffffff
#define N 80

using namespace std;
typedef long long LL;

int n;
int s[9][9]; //每个格子的分数
int sum[9][9]; //(1,1)到(i,j)的矩形的分数之和
int res[15][9][9][9][9]; //fun的记录表

//(x1,y1)到(x2,y2)的矩形的分数之和
int get_sum(int x1, int y1, int x2, int y2) {
    return sum[x2][y2] - sum[x2][y1-1] - sum[x1-1][y2] + sum[x1-1][y1-1];
}

int fun(int n, int x1, int y1, int x2, int y2) {
    if (res[n][x1][y1][x2][y2] != -1) {
        return res[n][x1][y1][x2][y2];
    }
    if (n == 1) {
        int ans = get_sum(x1, y1, x2, y2);
        res[n][x1][y1][x2][y2] = ans*ans;
        return res[n][x1][y1][x2][y2];
    }
    int MIN = INF;
    for (int x = x1; x < x2; x++) {
        int up = get_sum(x1, y1, x, y2);
        int down = get_sum(x+1, y1, x2, y2);
        int local = min(fun(n-1, x1, y1, x, y2) + down*down, fun(n-1, x+1, y1, x2, y2) + up*up);
        MIN = min(MIN, local);
    }
    for (int y = y1; y < y2; y++) {
        int left = get_sum(x1, y1, x2, y);
        int right = get_sum(x1, y+1, x2, y2);
        int local = min(fun(n-1, x1, y1, x2, y) + right*right, fun(n-1, x1, y+1, x2, y2) + left*left);
        MIN = min(MIN, local);
    }
    res[n][x1][y1][x2][y2] = MIN;
    return MIN;
}

int main() {

#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
#else
    //
#endif
    scanf("%d", &n);
    memset(sum, 0, sizeof(sum));
    memset(res, -1, sizeof(res));
    for (int i = 1; i < 9; i++) {
        int row_sum = 0;
        for (int j = 1; j < 9; j++) {
            scanf("%d", &s[i][j]);
            row_sum += s[i][j];
            sum[i][j] = sum[i-1][j] + row_sum;
        }
    }
    double ans = fun(n, 1, 1, 8, 8) - 1.0 * (sum[8][8]*sum[8][8]) / n;
    ans = sqrt(ans/n);
    printf("%.3f\n", ans);
    return 0;
}

参考

https://d396qusza40orc.cloudfront.net/pkupop/lectures/Week12/W12-03_%E9%80%92%E5%BD%92-%E6%A3%8B%E7%9B%98%E5%88%86%E5%89%B2.pdf