<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:

    struct pos {
        int i;
        int j;
        int depth;
    };

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

        vector<vector<int>> dp(n, vector<int>(m, 1));

        for(int i=0; i<n; i++) {
            for(int j=0; j<m; j++) {
                dp[i][j] = dfs(i, j, 1, matrix, dp);
            }
        }

        int maxDepth = 0;
        for(int i=0; i<n; i++) {
            for(int j=0; j<m; j++) {
                maxDepth = max(maxDepth, dp[i][j]);
            }
        }

        return maxDepth;
    }

    int dfs(int i, int j, int depth, vector<vector<int>>& matrix, vector<vector<int>>& dp) {

        if(dp[i][j] > 1) {
            return dp[i][j];
        }

        vector<int> vert = {-1, 0, 1, 0};
        vector<int> horz = {0, -1, 0, 1};

        int maxDepth = 1;

        for(int v=0; v<4; v++) {
        
            if(i + vert[v] >= 0 && i + vert[v] < matrix.size() &&
                j + horz[v] >= 0 && j + horz[v] < matrix[0].size() &&
                matrix[i + vert[v]][j + horz[v]] > matrix[i][j]) {
                
                maxDepth = max(maxDepth, 1 + dfs(i + vert[v], j + horz[v], depth, matrix, dp));
                
            }
            
        }
        
        dp[i][j] = maxDepth;
        return maxDepth;
    }
};
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