<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:
    bool isValid(int i, int j, vector<vector<int>> &matrix) {
        int n = matrix.size();
        int m = matrix[0].size();
        return (i >= 0 && i < n && j >= 0 && j < m);
    }

    int solve(int i, int j, vector<vector<int>> &dis, vector<vector<int>> &matrix) {
        if (dis[i][j] != 1) return dis[i][j];

        vector<int> row = {1, 0, -1, 0};
        vector<int> col = {0, 1, 0, -1};

        int temp = 0;
        for (int k = 0; k < 4; k++) {
            int nrow = i + row[k];
            int ncol = j + col[k];
            if (isValid(nrow, ncol, matrix) && matrix[nrow][ncol] > matrix[i][j]) {
                temp = max(solve(nrow, ncol, dis, matrix), temp);
            }
        }

        dis[i][j] += temp;
        return dis[i][j];
    }

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int n = matrix.size();
        int m = matrix[0].size();
        vector<vector<int>> dis(n, vector<int>(m, 1));

        int ans = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans = max(ans, solve(i, j, dis, matrix));
            }
        }

        return ans;
    }
};

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