[AcWing 901] 滑雪

记忆化搜索

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点击查看代码

#include<iostream>
#include<cstring>

using namespace std;

const int N = 310;
int n, m;
int h[N][N];
int f[N][N];
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
int dp(int x, int y)
{
    int &v = f[x][y];
    if (v != -1)    return v;
    v = 1;
    for (int i = 0; i < 4; i ++) {
        int a = x + dx[i], b = y + dy[i];
        if (a > 0 && a <= n && b > 0 && b <= m && h[a][b] < h[x][y])
            v = max(v, dp(a, b) + 1);
    }
    return v;
}
int main()
{
    cin >> n >> m;
    for (int i = 1; i <= n; i ++)
        for (int j = 1; j <= m; j ++)
            cin >> h[i][j];
    memset(f, -1, sizeof f);
    int res = 0;
    for (int i = 1; i <= n; i ++)
        for (int j = 1; j <= m; j ++)
            res = max(res, dp(i, j));
    cout << res << endl;
    return 0;
}

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1. 状态表示
   $f[i][j]$ 表示所有从 $(i,j)$ 开始滑的路径的最大值
2. 状态转移
   枚举 $f[i][j]$ 的上下左右四个方向，需要枚举的条件：没有越过边界，高度小于 $h[i][j]$
   $f[i][j] = 1 + max(f[i-1][j],f[i+1][j],f[i][j-1],f[i][j+1])$