<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 longestIncreasingPath(vector<vector<int>>& matrix) {
        if(matrix.empty()||matrix[0].empty()) return 0;
        int m=matrix.size(), n=matrix[0].size(), res=0;
        vector<vector<int>> len(m, vector<int>(n));
        for(int i=0; i<m; ++i) {
            for(int j=0; j<n; ++j) {
                res=max(res, helper(matrix, i, j, len));
            }
        }
        return res;
    }
    int helper(const vector<vector<int>>& matrix, int row, int col, vector<vector<int>>& len) {
        if(len[row][col]) return len[row][col];
        const vector<pair<int,int>> dirs={{-1,0},{1,0},{0,-1},{0,1}};
        int m=matrix.size(), n=matrix[0].size();
        for(const auto &d:dirs) {
              int x=row+d.first, y=col+d.second;
              if(x>=0&&x<m&&y>=0&&y<n&&matrix[row][col]<matrix[x][y]) len[row][col]=max(len[row][col], helper(matrix, x, y, len));
        }
        return ++len[row][col];
    }
};
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