<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:
    map <pair<int,int>,int> cache;
    int backtrack(int r,int c, int prevNum,vector<vector<int>>& matrix) {
        if (r < 0 || c < 0 || r>=matrix.size()||c>= matrix[0].size() || matrix[r][c] <= prevNum) {
            return 0;
        }
        if (cache.find({r,c}) !=cache.end()) {
            return cache[{r,c}];
        }
        vector <int> dirs;
        dirs.push_back(backtrack(r-1,c,matrix[r][c],matrix));
        dirs.push_back(backtrack(r+1,c,matrix[r][c],matrix));
        dirs.push_back(backtrack(r,c-1,matrix[r][c],matrix));
        dirs.push_back(backtrack(r,c+1,matrix[r][c],matrix));
        cache[{r,c}] = 1 + *max_element(dirs.begin(),dirs.end());
        return cache[{r,c}];
    }
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int res = 1;
        for (int i =0;i< matrix.size();i++) {
            for (int j = 0;j < matrix[0].size();j++) {
                res = max(res,backtrack(i,j,INT_MIN,matrix));
            }
        }
        return res;
    }
};
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