<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 dirX[4] = {1,-1,0,0};
    int dirY[4] = {0,0,-1,1};

    vector<vector<int>> dp;
    int dfs(vector<vector<int>>&matrix, int startX, int startY){
        if(dp[startX][startY])return dp[startX][startY];
        int ans = 1;
        for(int i = 0;i<4;i++){
            int nextx = startX + dirX[i];
            int nexty = startY + dirY[i];
            if(nextx < 0 || nextx >=matrix.size() || nexty < 0 || nexty >=matrix[0].size()) continue;
            if(matrix[nextx][nexty] > matrix[startX][startY]){
                ans = max(ans,dfs(matrix,nextx,nexty)+1);                
            }
        }
        return dp[startX][startY] = ans;
    }

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

        int longestPathDistance = 0;
        for(int i = 0;i<n;i++){
            for(int j = 0;j<m;j++){
                dp.resize(n, vector<int>(m,0));
                int pathDistance = dfs(matrix,i,j);
                longestPathDistance = max(longestPathDistance,pathDistance);

            }
        }

        return longestPathDistance;        
    }
};
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