<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) {
        int n = matrix.size(), m = matrix[0].size();
        vector<vector<int>> dirs = {{0,1}, {0,-1}, {1,0}, {-1,0}};

        vector<vector<int>> len(n, vector<int>(m)), indeg(n, vector<int>(m));
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < m; j++) {
                for(auto d : dirs) {
                    int x = i+d[0], y = j+d[1];
                    if(x<n && x>=0 && y<m && y>=0 && matrix[i][j] > matrix[x][y]) indeg[i][j]++;
                }
            }
        }
        int level = 1;
        queue<pair<int,int>> q;
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < m; j++) {
                if(indeg[i][j] == 0) q.push({i,j});
            }
        }

        while(!q.empty()) {
            int t = q.size();
            for(int p = 0; p < t; p++) {
                auto cur = q.front(); q.pop();
                int i = cur.first, j = cur.second;
                len[i][j] = level;
                for(auto d : dirs) {
                    int x = i+d[0], y = j+d[1];
                    if(x<n && x>=0 && y<m && y>=0 && matrix[i][j] < matrix[x][y]) {
                        indeg[x][y]--;
                        if(indeg[x][y] == 0) q.push({x,y});
                    }
                }
            }
            level++;
        }
        return level-1;
    }
};
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