<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
{
    bool isInMatrix(int rowCnt, int colCnt, int row, int col)
    {
        return 0 <= row && row < rowCnt 
            && 0 <= col && col < colCnt;
    }

    bool hasEdge(const vector<vector<int>>& matrix, int fromRow, int fromCol, int toRow, int toCol)
    {
        return matrix[fromRow][fromCol] < matrix[toRow][toCol];
    }

    void forEachNeighbor(
        const vector<vector<int>>& matrix,
        std::size_t rowCnt,
        std::size_t colCnt,
        std::size_t row,
        std::size_t col,
        const std::function<void(int, int)>& operation)
    {
        static const std::vector<std::pair<int, int>> directions{
            {+1,  0},
            {-1,  0},
            { 0, +1},
            { 0, -1}
        };

        for(auto [dRow, dCol] : directions)
        {
            int neighborRow = row + dRow;
            int neighborCol = col + dCol;

            if(isInMatrix(rowCnt, colCnt, neighborRow, neighborCol)
                && hasEdge(matrix, row, col, neighborRow, neighborCol))
            {
                operation(neighborRow, neighborCol);
            }
        }
    }

public:
    int longestIncreasingPath(const vector<vector<int>>& matrix)
    {
        std::size_t rowCnt = matrix.size();
        std::size_t colCnt = rowCnt == 0 ? 0 : matrix.front().size();

        std::vector<std::vector<unsigned>> inCnt(
            rowCnt, std::vector<unsigned>(colCnt, 0)
        );

        for(std::size_t row = 0; row < rowCnt; ++row)
            for(std::size_t col = 0; col < colCnt; ++col)
                forEachNeighbor(matrix, rowCnt, colCnt, row, col, [&inCnt](int neighborRow, int neighborCol){
                    inCnt[neighborRow][neighborCol] += 1; 
                });

        std::queue<std::pair<int, int>> q;
        for(std::size_t row = 0; row < rowCnt; ++row)
            for(std::size_t col = 0; col < colCnt; ++col)
                if(inCnt[row][col] == 0)
                    q.emplace(row, col);

        int maxLen = 0;
        unsigned currLvlCnt = q.size();
        while(!q.empty())
        {
            auto [row, col] = q.front();
            q.pop();

            forEachNeighbor(matrix, rowCnt, colCnt, row, col, [&inCnt, &q](int neighborRow, int neighborCol){
                inCnt[neighborRow][neighborCol] -= 1;

                if(inCnt[neighborRow][neighborCol] == 0)
                    q.emplace(neighborRow, neighborCol);
            });

            --currLvlCnt;
            if(currLvlCnt == 0)
            {
                currLvlCnt = q.size();
                ++maxLen;
            }
        }

        return maxLen;
    }
};
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