<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:
    vector<vector<int>>dp;
    bool checkPath(vector<vector<int>>&matrix, int x, int y, int prevx, int prevy)
    {
        if(prevx >= matrix.size() || prevx < 0 || prevy >= matrix[0].size() || prevy < 0)
            return 0;
        
        if(matrix[x][y] >= matrix[prevx][prevy])
            return 0;
        
        return 1;
    }
    
    int dfs(vector<vector<int>>& matrix, int x, int y)
    {
        vector<int> pathx = {0, 0, 1, -1};
        vector<int> pathy = {1, -1, 0, 0};
        
        if(dp[x][y] != INT_MIN)
            return dp[x][y];
        
        int val = 0;
        for(int i = 0; i<4; i++)
        {
            if(checkPath(matrix, x, y, x + pathx[i], y + pathy[i]))
                val = max(val, dfs(matrix, x+pathx[i], y+pathy[i]));
        }
        return dp[x][y] = 1+val;
    }
    
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        dp = vector<vector<int>>(matrix.size(), vector<int>(matrix[0].size(), INT_MIN));
        int val = 0;
        for(int i = 0; i<matrix.size(); i++)
        {
            for(int j = 0; j<matrix[0].size(); j++)
            {
                val = max(val, dfs(matrix, i, j));
            }
        }
        return val;
    }
};
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