<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>

struct Node {
    int i;
    int j;
    int v;
};
bool comparator(const Node &n1, const Node &n2) {
    return n1.v > n2.v;
}

class Solution {
public:
    vector<vector<int>> neighbor = {
        {0, 1}, {0, -1}, {-1, 0}, {1, 0}
    };
    bool inside(int i, int j, int m, int n) {
        return (i >= 0) && (j >= 0) && (i < m) && (j < n);
    }
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        vector<Node> s;
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                s.push_back({i, j, matrix[i][j]});
            }
        }
        std::sort(s.begin(), s.end(), comparator);
        vector<vector<int>> dist(m, vector<int>(n, 1));
        int ans = 0;
        for (const auto &node : s) {
            int i = node.i;
            int j = node.j;
            int v = node.v;
            for (const auto &b : neighbor) {
                int x = i + b[0];
                int y = j + b[1];
                if (!inside(x, y, m, n))
                    continue;
                int u = matrix[x][y];
                if (u > v) {
                    dist[i][j] = max(dist[i][j], dist[x][y] + 1);
                }
            }
            ans = max(ans, dist[i][j]);
        }
        return ans;
    }
};
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