<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 m = matrix.size();
        int n = matrix[0].size();
        std::vector<std::vector<int>> lp(m, std::vector<int>(n, 1));
        std::deque<std::tuple<int, int, int>> flat {};

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                flat.emplace_back(matrix[i][j], i, j);
            }
        }

        std::sort(flat.begin(), flat.end(), std::greater<>());

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

        while (!flat.empty()) {
            auto [val, i, j] = flat.front();
            flat.pop_front();

            for (auto d : directions) {
                int ia = i + d.first;
                int ja = j + d.second;
                if (ia >= 0 && ia < m && ja >= 0 && ja < n && val < matrix[ia][ja]) {
                    lp[i][j] = std::max(lp[i][j], 1 + lp[ia][ja]);
                }
            }
            res = std::max(res, lp[i][j]);
        }

        return res;
    }
};
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