<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 calculate(vector<vector<int>>& matrix, vector<vector<int>>& visited, int i, int j, int m, int n) {
        
        if(visited[i][j] != -1)
            return visited[i][j];
        int curr = matrix[i][j];
        int up = 0;
        int down = 0;
        int left = 0;
        int right = 0;
        if(i-1 >= 0 && matrix[i-1][j] > curr)
            up = 1 + calculate(matrix, visited, i-1, j, m, n);
        if(j-1 >= 0 && matrix[i][j-1] > curr)
            left = 1 + calculate(matrix, visited, i, j-1, m, n);
        if(i+1 < m && matrix[i+1][j] > curr)
            down = 1 + calculate(matrix, visited, i+1, j, m, n);
        if(j+1 < n && matrix[i][j+1] > curr)
            right = 1 + calculate(matrix, visited, i, j+1, m, n);
        visited[i][j] = max(up, max(left, max(down, right)));
        return visited[i][j];
    }

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        int ans = 0;
        vector<vector<int>> visited(202, vector<int>(202,-1));
        for (int i=0;i<m;i++) {
            for (int j=0;j<n;j++){
                ans = max(ans, calculate(matrix, visited, i, j, m, n));
            }
        }
        return ans+1;
    }
};
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