<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) {
        const int n_rows = matrix.size();
        const int n_cols = matrix[0].size();
        
        const int dr[] = {-1, 1, 0, 0};
        const int dc[] = {0, 0, -1, 1};

        // create graph
        std::vector<std::vector<int>> adj(n_rows * n_cols);
        for(int row = 0; row < n_rows; ++row) {
            for(int col = 0; col < n_cols; ++col) {
                for(int k = 0; k < 4; ++k) {
                    int n_row = row + dr[k];
                    int n_col = col + dc[k];
                    if (0 <= n_row && n_row < n_rows && 0 <= n_col && n_col < n_cols && matrix[row][col] < matrix[n_row][n_col]) {
                        int u = row * n_cols + col;
                        int v = n_row * n_cols + n_col;
                        adj[u].push_back(v);
                    }
                }
            }
        }

        stack<int> st;
        std::vector<int> visited(n_rows * n_cols);
        std::function<void(int)> dfs = [&](int u) {
            visited[u] = 1;
            for(int v: adj[u]) {
                if (!visited[v])
                    dfs(v);
            }
            st.push(u);
        };

        for(int u = 0; u < n_rows * n_cols; ++u)
            if (!visited[u])
                dfs(u);

        std::vector<int> dp(n_rows * n_cols, 1);
        while(!st.empty()) {
            int u = st.top();
            st.pop();

            for(int v: adj[u])
                dp[v] = max(dp[v], dp[u] + 1);
        }
        return *max_element(dp.begin(), dp.end());
    }
};
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