CF-1198D (二維DP)

題目鏈接：https://codeforc.es/problemset/problem/1198/D

給你一個n*n(n<51)的棋盤，棋盤上有黑格有白格，每次可以花費max(w,h)的價值，將一個w*h的矩陣塗白，問你將這個棋盤塗白的最小花費是多少？

解題思路：

定義dp[x1][y1][x2][y2]爲將(x1,y1)-(x2,y2)爲對角線的矩陣染成白色的最小花費，這樣子不斷分解子問題直到大小爲1的時候直接判斷該格子是黑是白就可以了。

#include<iostream>
#include<cstdio>
#include<queue>
#include<cstring>
#include<unordered_map>
using namespace std;
const int maxn = 55;
const long long inf = 0x3f3f3f3f3f3f3f3f;

char mp[maxn][maxn];
int dp[maxn][maxn][maxn][maxn];

int dfs(int x1, int y1, int x2, int y2)
{
    if(x1==x2&&y1==y2) return dp[x1][y1][x2][y2] = (mp[x1][y2] == '#');
    if(dp[x1][y1][x2][y2]!=-1) return dp[x1][y1][x2][y2];
    dp[x1][y1][x2][y2] = max(x2-x1,y2-y1)+1;
    for(int i = x1; i < x2; i++)
    {
        dp[x1][y1][x2][y2] = min(dp[x1][y1][x2][y2],dfs(x1,y1,i,y2)+dfs(i+1,y1,x2,y2));
    }
    for(int i = y1; i < y2; i++)
    {
        dp[x1][y1][x2][y2] = min(dp[x1][y1][x2][y2],dfs(x1,y1,x2,i)+dfs(x1,i+1,x2,y2));
    }
    return dp[x1][y1][x2][y2];

}

int main()
{
    int n;
    scanf("%d", &n);
    for(int i = 1; i <= n; i++)
        scanf("%s", mp[i]+1);
    memset(dp,-1,sizeof(dp));
    int ans = dfs(1,1,n,n);
    printf("%d\n", ans);
    return 0;
}