<p>Given an <code>m x n</code> integers <code>matrix</code>, return <em>the length of the longest increasing path in </em><code>matrix</code>.</p>

<p>From each cell, you can either move in four directions: left, right, up, or down. You <strong>may not</strong> move <strong>diagonally</strong> or move <strong>outside the boundary</strong> (i.e., wrap-around is not allowed).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/05/grid1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> matrix = [[9,9,4],[6,6,8],[2,1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest increasing path is <code>[1, 2, 6, 9]</code>.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/27/tmp-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> matrix = [[3,4,5],[3,2,6],[2,2,1]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>The longest increasing path is <code>[3, 4, 5, 6]</code>. Moving diagonally is not allowed.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[1]]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= matrix[i][j] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution {
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        if(m == 0) return 0;
        int n = matrix[0].size();
        vector<vector<int>> memo(m, vector<int>(n, -1));
        int max_len = 0;
        
        for(int r = 0; r < m; r++){
            for(int c = 0; c < n; c++){
                max_len = max(max_len, dfs(r, c, m, n, matrix, memo));
            }
        }
        
        return max_len;
    }
    
    int dfs(int r, int c, int m, int n, vector<vector<int>>& matrix, vector<vector<int>>& memo){
        if(memo[r][c] != -1) return memo[r][c];
        
        vector<int> dirR = {-1, 0, 0, 1};
        vector<int> dirC = {0, -1, 1, 0};
        int max_len = 1;
        
        for(int i = 0; i < 4; i++){
            int newR = r + dirR[i];
            int newC = c + dirC[i];
            if(isValid(newR, newC, m, n) && matrix[r][c] < matrix[newR][newC])
                max_len = max(max_len, 1 + dfs(newR, newC, m, n, matrix, memo));
        }

        memo[r][c] = max_len;
        
        return max_len;
    }
    
    bool isValid(int r, int c, int rows, int cols){
        return (r >= 0 && r < rows && c >= 0 && c < cols);
    }
};
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