<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> memo;
    int helper(vector<vector<int>>& matrix, int x, int y, int prev) {
        if (memo.count(make_pair(x * matrix[0].size() + y, prev))) return memo[make_pair(x * matrix[0].size() + y, prev)];
        if (x >= matrix.size() || x < 0 || y >= matrix[0].size() || y < 0 || matrix[x][y] <= prev) {
            return 0;
        } else {
            int up = helper(matrix, x - 1, y, matrix[x][y]);
            int down = helper(matrix, x + 1, y, matrix[x][y]);
            int right = helper(matrix, x, y + 1, matrix[x][y]);
            int left = helper(matrix, x, y - 1, matrix[x][y]);

            memo[make_pair(x * matrix[0].size() + y, prev)] = 1 + max(up, max(down, max(right, left)));
            return memo[make_pair(x * matrix[0].size() + y, prev)];
        }
    }

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int ans = 0;
        for (int i = 0; i < matrix.size(); i++) {
            for (int j = 0; j < matrix[i].size(); j++) {
                ans = max(ans, helper(matrix, i, j, -1));
            }
        }

        return ans;
    }
};
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