递归-棋盘分割（算法基础 第3周）

递归-棋盘分割

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <iomanip>
using namespace std;

int s[9][9];  //每个格子的分数
int sum[9][9];   //从(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

int calSum(int x1, int y1, int x2, int y2) {    //(x1, y1)到(x2, y2)的矩形的分数之和
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) {
int t, a, b, c, e, MIN=10000000;
if(res
[x1][y1][x2][y2] != -1)
return res
[x1][y1][x2][y2];
if (n==1) {
t=calSum(x1, y1, x2, y2);
res
[x1][y1][x2][y2] = t*t;
return t*t;
}
for (a=x1; a<x2; a++) {
c=calSum(a+1, y1, x2, y2);
e=calSum(x1, y1, a, y2);
t=min(fun(n-1, x1, y1, a, y2)+c*c, fun(n-1, a+1, y1, x2, y2)+e*e);
if(MIN>t) MIN=t;
}
for (b=y1; b<y2; b++) {
c=calSum(x1, b+1, x2, y2);
e=calSum(x1, y1, x2, b);
t=min(fun(n-1, x1, y1, x2, b)+c*c, fun(n-1, x1, b+1, x2, y2)+e*e);
if(MIN>t) MIN=t;
}
res
[x1][y1][x2][y2]=MIN;
return MIN;
}

int main() {
memset(sum, 0, sizeof(sum));
memset(res, -1, sizeof(res));  //初始化记录表
int n;
cin>>n;
for(int i=1; i<9; i++) {
for (int j=1, rowsum=0; j<9; j++) {
cin >> s[i][j];
rowsum += s[i][j];
sum[i][j] += sum[i-1][j]+rowsum;
}
}
double result = n*fun(n, 1, 1, 8, 8)-sum[8][8]*sum[8][8];
cout << setiosflags(ios::fixed) << setprecision(3) << sqrt(result/(n*n)) << endl;
return 0;
}