<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 {
    const vector< vector<int> > directions = {{1,0}, {-1, 0}, {0,1}, {0,-1}};
    int dfs(vector<vector<int>>& matrix, int i, int j, int n, int m, vector<vector<int>> &dp) {
        if(dp[i][j]!=0) {
            return dp[i][j];
        } 
        for(auto dir: directions) {
            if(isValid(i + dir[0], j + dir[1], n, m) && matrix[i + dir[0]][j + dir[1]] > matrix[i][j])
                dp[i][j] = max(dp[i][j],  1 + dfs(matrix, i + dir[0], j + dir[1], n, m, dp));
        }
        return dp[i][j];
    }
    bool isValid(int i, int j , int n , int m) {
        if(i < 0 || j < 0 || i >= n || j >= m) {
            return false;
        }
        return true;
    }
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int n = matrix.size();
        if(n==0) return 0;
        int m = matrix[0].size();
        int ans = INT_MIN;
        vector < vector < int> > dp(n, vector<int> (m, 0));
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < m; j++) {
                ans = max(ans, dfs(matrix, i, j, n , m, dp));
            }
        }
        return ans + 1 ;
    }
};
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