<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 h;
    int w;
    vector<vector<int>> dp;
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        h = matrix.size();
        w = matrix[0].size();
        int globalMax = INT_MIN;
        dp.assign(h, vector<int>(w, -1));
        for(int row=0; row<h; row++) {
            for(int col=0; col<w; col++) {
                globalMax = max(globalMax, dfs(row, col, matrix, -1));
            }
        }
        return globalMax;
    }

    int dfs(int row, int col, vector<vector<int>>& matrix, int prev) {
        if(!inBound(row, col) || matrix[row][col] <= prev) {
            return 0;
        }
        if(dp[row][col] != -1) {
            return dp[row][col];
        }
        int tmp = matrix[row][col];
        int left = dfs(row, col-1, matrix, tmp);
        int right = dfs(row, col+1, matrix, tmp);
        int up = dfs(row-1, col, matrix, tmp);
        int bot = dfs(row+1, col, matrix, tmp);
        return dp[row][col] = 1+max({left, right, up, bot});
    } 

    bool inBound(int& row, int& col) {
        return 0<=row && row<h && 0<=col && col<w;
    }
};
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