0329. Longest Increasing Path in a Matrix.md

---

class Solution {
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        vector<vector<int>> dp(m, vector<int>(n, -1));
        pair<int, int> dirs[] = {{-1,0},{1,0},{0,-1},{0,1}};
        int res = 0;

        function<int(int, int)> dfs = [&](int i, int j) -> int {
            if(dp[i][j] != -1) return dp[i][j];
            int maxLength = 1;
            for (auto [di, dj] : dirs) {
                int x = i + di;
                int y = j + dj;
                if(x >= 0 && x < m && y >= 0 && y < n && matrix[x][y] > matrix[i][j]) {
                    maxLength = max(maxLength, dfs(x, y) + 1);
                }
            }
            dp[i][j] = maxLength;
            return maxLength;
        };

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

        return res;
    }
};

Time Complexity: O(M*N)
Space Complexity: O(M*N)