POJ-1088 滑雪（DP，二维LIS，记忆化）2017寒假集训

题意：给你一个R*C的矩阵，每个元素代表这一小格的h，只能往上下左右四个方向走，每次只能往高度小于当前格h的方向走，求能走的最长路径

数据范围：1 <= R,C <= 100 , 0 <= h <= 10000

思路：裸LIS，只不过是二维的，感觉这种走迷宫，矩阵形状的写记忆化比递推方便而且自然

dp[ i ][ j ] = max(dp[ i-1 ][ j ], dp[ i+1 ][ j ], dp[ i ][ j-1 ], dp[ i ][ j+1 ]) + 1

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

const int mx = 110;
int a[mx][mx], dp[mx][mx];
int dr[] = {-1, 0, 1, 0};
int dc[] = {0, -1, 0, 1};
int n, m;

int dfs(int r, int c){
    int sum = 1;
    if (dp[r][c] > 0) return dp[r][c];
    for (int i = 0; i < 4; i++){
        int x = r+dr[i];
        int y = c+dc[i];
        if (x <= 0 || x > n || y <= 0 || y > m) continue;
        if (a[x][y] > a[r][c])
            sum = max(sum, dfs(x, y)+1);
    }
    return dp[r][c] = sum;
}

int main(){
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++)
            scanf("%d", &a[i][j]);
    int ans = 0;
    for (int i = 1; i <= n; i++){
        for (int j = 1; j <= m; j++){
            dp[i][j] = dfs(i, j);
            ans = max(ans, dp[i][j]);
        }
    }
    printf("%d
", ans);
    return 0;
}