<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>

const std::vector<std::pair<int, int>> dirs = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};

class Solution {
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        vector<vector<int>> path_size(matrix.size(), vector<int>(matrix[0].size()));
        int result = 0;
        for (int i = 0; i < matrix.size(); i++) {
            for (int j = 0; j < matrix[i].size(); j++) {
                if (path_size[i][j] != 0) continue;
                std::stack<std::pair<int, int>> pending;
                pending.push({i, j});
                while (!pending.empty()) {
                    const auto current = pending.top();
                    bool process_current = true;
                    int max_neighbor_path = 0;
                    for (const auto& dir : dirs) {
                        int x = current.first + dir.first;
                        int y = current.second + dir.second;
                        if (!isInsideMatrix(x, y, matrix.size(), matrix[0].size())) {
                            continue;
                        }
                        if (matrix[x][y] > matrix[current.first][current.second]) {
                            if (path_size[x][y] == 0) {
                                pending.push({x, y});
                                process_current = false;
                            } else if (path_size[x][y] > max_neighbor_path) {
                                max_neighbor_path = path_size[x][y];
                            }
                        }
                    }
                    if (process_current) {
                        pending.pop();
                        if (max_neighbor_path >= path_size[current.first][current.second]) {
                            path_size[current.first][current.second] = max_neighbor_path + 1;
                            if (path_size[current.first][current.second] > result) {
                                result = path_size[current.first][current.second];
                            }
                        }
                    }
                }
            }
        }
        return result;
    }
private:
    bool isInsideMatrix(int x, int y, int n, int m) {
        return x > -1 && y > -1 && x < n && y < m;
    }
};
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