<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<pair<int, int>> moves = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
    bool check(int x, int y, int n, int m) {
        return (x >= 0 && x < n) && (y >= 0 && y < m);
    }
    int longestIncreasingPath(vector<vector<int>>& a) {
        int n = a.size(), m = a[0].size();
        map<pair<int, int>, vector<pair<int, int>>> g;
        map<pair<int, int>, int> in;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                for (auto c : moves) {
                    if (check(i + c.first, j + c.second, n, m) &&
                        (a[i + c.first][j + c.second] < a[i][j])) {
                        g[{i + c.first, j + c.second}].push_back({i, j});
                        in[{i, j}]++;
                    }
                }
            }
        }
        queue<pair<int, int>> q;
        map<pair<int, int>, int> ans;
        int mx = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (in[{i, j}] == 0)
                    q.push({i, j});
            }
        }

        while (!q.empty()) {
            int x = q.front().first, y = q.front().second;
            q.pop();
            for (auto c : g[{x, y}]) {
                ans[c] = max(ans[c], ans[{x, y}] + 1);
                mx = max(mx, ans[c]);
                in[c]--;
                if (in[c] == 0)
                    q.push(c);
            }
        }

        return mx + 1;
    }
};
72534