<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>

vector<vector<int>> dirs{{0, 1}, {0, -1}, {1, 0}, {-1, 0}};

class Solution {
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int n = matrix.size(), m = matrix[0].size(), ans = 1;
        vector<vector<int>> freq(n, vector<int>(m, 1)), vis(n, vector<int>(m, 0));
        priority_queue<vector<int>> q;
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < m; j++) {
                bool isTop = true;
                for(auto &dir: dirs) {
                    int x = i + dir[0], y = j + dir[1];
                    if(x < 0 || x == n) continue;
                    if(y < 0 || y == m) continue;
                    if(matrix[x][y] > matrix[i][j]) {
                        isTop = false;
                        break;
                    }
                }
                if(isTop) q.push({matrix[i][j], i, j});
            }
        }
        while(!q.empty()) {
            vector<int> node = q.top();
            q.pop();
            int i = node[1], j = node[2];
            if(vis[i][j]) continue;
            // cout<<i<<' '<<j<<' '<<freq[i][j]<<'\n';
            vis[i][j] = 1;
            ans = max(ans, freq[i][j]);
            for(auto &dir: dirs) {
                int x = i + dir[0], y = j + dir[1];
                if(x < 0 || x == n) continue;
                if(y < 0 || y == m) continue;
                if(matrix[x][y] >= matrix[i][j] || freq[x][y] > freq[i][j] + 1 || vis[x][y]) continue;
                freq[x][y] = freq[i][j] + 1;
                q.push({matrix[x][y], x, y});
            }
        }

        return ans;
    }
};
54878