<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:
    vector<vector<int>> directions = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        if (m == 0) return 0;
        int n = matrix[0].size();
        
        // In-degree matrix to keep track of in-degrees of each cell
        vector<vector<int>> inDegree(m, vector<int>(n, 0));
        
        // Calculate in-degrees
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                for (auto dir : directions) {
                    int x = i + dir[0];
                    int y = j + dir[1];
                    if (x >= 0 && y >= 0 && x < m && y < n && matrix[x][y] > matrix[i][j]) {
                        inDegree[x][y]++;
                    }
                }
            }
        }
        
        // Queue to perform topological sort
        queue<pair<int, int>> q;
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (inDegree[i][j] == 0) {
                    q.push({i, j});
                }
            }
        }
        
        int longestPath = 0;
        while (!q.empty()) {
            int size = q.size();
            longestPath++;
            for (int i = 0; i < size; ++i) {
                auto [x, y] = q.front();
                q.pop();
                for (auto dir : directions) {
                    int nx = x + dir[0];
                    int ny = y + dir[1];
                    if (nx >= 0 && ny >= 0 && nx < m && ny < n && matrix[nx][ny] > matrix[x][y]) {
                        inDegree[nx][ny]--;
                        if (inDegree[nx][ny] == 0) {
                            q.push({nx, ny});
                        }
                    }
                }
            }
        }
        
        return longestPath;
    }
};

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