<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) {

        int height = 0;
        if(matrix.empty()) {
            return height;
        }
        
        int numRows = matrix.size();
        int numCols = matrix[0].size();
        std::vector<std::vector<int>> grid(numRows + 2, std::vector<int>(numCols + 2, 0));
        for(int i = 0; i < numRows; ++i) {
            std::copy(matrix[i].begin(), matrix[i].end(), grid[i + 1].begin() + 1);
        }
        
        std::vector<std::vector<int>> outDegree(numRows + 2, std::vector<int>(numCols + 2));
        for(int i = 1; i <= numRows; ++i) {
            for(int j = 1; j <= numCols; ++j) {
                for(auto dir : directions) {
                    if(grid[i][j] < grid[i + dir.first][j + dir.second]) {
                        ++outDegree[i][j];
                    }
                }
            }
        }

        numRows += 2;
        numCols += 2; 
        std::vector<std::pair<int, int>> leaves;
        for(int i = 1; i < numRows - 1; ++i) {
            for(int j = 1; j < numCols - 1; ++j) {
                if(outDegree[i][j] == 0) {
                    leaves.push_back({i, j});
                }
            }
        }

        while(!leaves.empty()) {

            ++height;
            std::vector<std::pair<int, int>> newLeaves;
            for(auto node : leaves) {
                for(auto dir : directions) {
                    int newRow = node.first + dir.first;
                    int newCol = node.second + dir.second;

                    if(grid[node.first][node.second] > grid[newRow][newCol]) {
                        if(--outDegree[newRow][newCol] == 0) {
                            newLeaves.push_back({newRow, newCol});
                        }
                    }
                }
            }
            leaves = newLeaves;
        }
        return height;
    }

private: 
    std::vector<std::pair<int, int>> directions {{0, 1}, {1, 0}, {-1, 0}, {0, -1}};

};
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