Leetcode 329. 矩阵中的最长递增路径 记忆化搜索

地址 https://leetcode-cn.com/problems/longest-increasing-path-in-a-matrix/

给定一个整数矩阵，找出最长递增路径的长度。

对于每个单元格，你可以往上，下，左，右四个方向移动。 你不能在对角线方向上移动或移动到边界外（即不允许环绕）。

示例 1:

输入: nums = 
[
  [9,9,4],
  [6,6,8],
  [2,1,1]
] 
输出: 4 
解释: 最长递增路径为 [1, 2, 6, 9]。
示例 2:

输入: nums = 
[
  [3,4,5],
  [3,2,6],
  [2,2,1]
] 
输出: 4 
解释: 最长递增路径是 [3, 4, 5, 6]。注意不允许在对角线方向上移动。

解答先后尝试dfs bfs均以TLE失败

class Solution {
public:

    int ans = 1;
    vector<vector<int>> vis;
    void dfs(int x, int y, int step,const vector<vector<int>>& matrix)
    {
        int m = matrix.size(); int n = matrix[0].size();
        int addx[4] = { 1,-1,0,0 };
        int addy[4] = { 0,0,1,-1 };

        for (int i = 0; i < 4; i++) {
            int newx = x + addx[i];
            int newy = y + addy[i];

            if (newx >= 0 && newx < m && newy >= 0 && newy < n && vis[newx][newy] < (step+1) &&
                matrix[x][y] < matrix[newx][newy]) {
                int back = vis[newx][newy];
                vis[newx][newy] = step + 1;
                ans = max(ans, step + 1);
                dfs(newx,newy,step+1,matrix);
                vis[newx][newy] = back;
            }
        }
    }

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        if (matrix.empty() || matrix[0].empty()) return 0;
        int m = matrix.size(); int n = matrix[0].size();

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                
                vis = vector<vector<int>>(m, vector<int>(n));
                vis[i][j] = 1;
                dfs(i,j,1,matrix);
            }
        }
    
        return ans;
    }
};

class Solution {
public:
    queue<vector<int>> q;
    vector<vector<int>> vis;
    int ans = 1;

    void bfs(int x, int y,int m,int n,const vector<vector<int>>& matrix) {
        while (!q.empty()) q.pop();
        int addx[4] = { 1,-1,0,0 };
        int addy[4] = { 0,0,1,-1 };
        vis = vector<vector<int>>(m, vector<int>(n));

        q.push({x,y,1});
        
        while (!q.empty()) {
            int tx = q.front()[0];
            int ty = q.front()[1];
            int step = q.front()[2]+1;
            q.pop();

            for (int i = 0; i < 4; i++) {
                int newx = tx + addx[i];
                int newy = ty + addy[i];
                if (newx >= 0 && newx < m&& newy >= 0 && newy < n && matrix[newx][newy] > matrix[tx][ty] &&
                    vis[newx][newy] < step) 
                {
                    vis[newx][newy] = step;
                    q.push({ newx,newy,step });
                    ans = max(ans, step);
                }
            }
        }
    }

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size(); int n = matrix[0].size();
        if (m == 0 || n == 0) return 0;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                bfs(i,j,m,n, matrix);
            }
        }
        return ans;
    }
};

 

记忆化搜索解决问题 

class Solution {
public:
    int ans = 0;
    vector<vector<int>> dp;

    int dfs(int x, int y, const vector<vector<int>>& matrix) {
        if (dp[x][y] != 0) return dp[x][y];
        int m = matrix.size(); int n = matrix[0].size();
        int addx[4] = { 1,-1,0,0 };
        int addy[4] = { 0,0,1,-1 };

        for (int i = 0; i < 4; i++) {
            int newx = x + addx[i];
            int newy = y + addy[i];

            if (newx >= 0 && newx < m && newy >= 0 && newy < n && matrix[newx][newy] > matrix[x][y]) {
                dp[x][y] = max(dp[x][y], dfs(newx, newy, matrix)+1);
            }
        }

        return dp[x][y];
    }

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        if (matrix.empty() || matrix[0].empty()) return 0;
        int m = matrix.size(); int n = matrix[0].size();
        dp = vector<vector<int>>(m, vector<int>(n));

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                ans = max(ans, dfs(i,j,matrix));
            }
        }

        return ans+1;
    }
};