<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 {
    vector<vector<int>> memo;
    int compute(vector<vector<int>> &matrix, int i, int j) {
        if(i >= memo.size() || j >= memo[0].size()) return 0;
        if(memo[i][j] != -1) return memo[i][j];
        vector<int> ans;
        if(i+1 < memo.size() && matrix[i+1][j] > matrix[i][j]) ans.push_back(compute(matrix, i+1, j));
        if(i > 0 && matrix[i-1][j] > matrix[i][j]) ans.push_back(compute(matrix, i-1, j));
        if(j+1 < memo[0].size() && matrix[i][j+1] > matrix[i][j]) ans.push_back(compute(matrix, i, j+1));
        if(j > 0 && matrix[i][j-1] > matrix[i][j]) ans.push_back(compute(matrix, i, j-1));
        if(ans.empty()) memo[i][j] = 1;
        else memo[i][j] = *max_element(ans.begin(), ans.end()) + 1;
        // cout << matrix[i][j] << " " << memo[i][j] << endl;
        return memo[i][j];
    }
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        memo = vector<vector<int>>(m, vector<int>(n, -1));
        for(int i = 0; i<m; i++) {
            for(int j = 0; j<n; j++) compute(matrix, i, j);
        }
        int ans = 0;
        for(int i = 0; i < m; i++) ans = max(ans, *max_element(memo[i].begin(), memo[i].end()));
        return ans;
    }
};
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