<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 {
    int maxLength = 1;

public:
    void addEdge(vector<vector<int>> &e, vector<vector<int>> &m,
                 int x1, int y1, int x2, int y2,
                 vector<int> &in, vector<int> &out) {

        int k = m[0].size();

        if (m[x1][y1] < m[x2][y2]) {
            e[x1 * k + y1].push_back(x2 * k + y2);
            in[x2 * k + y2]++;
            out[x1 * k + y1]++;
        }
        else if (m[x1][y1] > m[x2][y2]) {
            e[x2 * k + y2].push_back(x1 * k + y1);
            in[x1 * k + y1]++;
            out[x2 * k + y2]++;
        }
    }

    void dfs(int cur, vector<vector<int>> &e, int curLength, vector<bool> &isEnd, vector<int> &d) {
        maxLength = max(maxLength, curLength + 1);

        if (d[cur] > curLength + 1)
            return;
        else
            d[cur] = curLength + 1;

        for (int neigh : e[cur])
            dfs(neigh, e, curLength + 1, isEnd, d);
    }

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int n = matrix.size(), m = matrix[0].size();

        vector<int> d_in(n * m), d_out(n * m);
        vector<vector<int>> edges(n * m);

        for (int i = 0; i < n; i++)
            for (int j = 1; j < m; j++)
                addEdge(edges, matrix, i, j-1, i, j, d_in, d_out);

        for (int i = 1; i < n; i++)
            for (int j = 0; j < m; j++)
                addEdge(edges, matrix, i-1, j, i, j, d_in, d_out);

        queue<int> starts;
        vector<bool> isEnd(n * m, false);

        for (int v = 0; v < n * m; v++) {
            if (d_in[v] == 0)
                starts.push(v);
            else if (d_out[v] == 0)
                isEnd[v] = true;
        }

        vector<int> depths(n * m, 1);
        while (!starts.empty()) {
            int s = starts.front();
            starts.pop();

            dfs(s, edges, 0, isEnd, depths);
        }

        return maxLength;
    }
};
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