<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();

        vector<pair<int, int>> allCoords;
        for (uint i = 0; i < m; ++i){
            for (uint j = 0; j < n; ++j){
                allCoords.emplace_back(i, j);
            }
        }
        sort(allCoords.begin(), allCoords.end(), [&matrix](const pair<int, int> &a, const pair<int, int> &b){
            return matrix[a.first][a.second] < matrix[b.first][b.second];
        });

        vector<int> path(n, 0);
        vector<vector<int>> longestPath(m, path);

        int totalMax = 0;

        for (uint i = 0; i < allCoords.size(); ++i){
            int cMax = 0;
            int cVal = matrix[allCoords[i].first][allCoords[i].second];
            if (allCoords[i].first > 0 && cVal > matrix[allCoords[i].first-1][allCoords[i].second]) 
                cMax = max(cMax, longestPath[allCoords[i].first-1][allCoords[i].second]);
            if (allCoords[i].second > 0 && cVal > matrix[allCoords[i].first][allCoords[i].second-1]) 
                cMax = max(cMax, longestPath[allCoords[i].first][allCoords[i].second-1]);
            if (allCoords[i].first < m - 1 && cVal > matrix[allCoords[i].first+1][allCoords[i].second]) 
                cMax = max(cMax, longestPath[allCoords[i].first+1][allCoords[i].second]);
            if (allCoords[i].second < n - 1 && cVal > matrix[allCoords[i].first][allCoords[i].second+1]) 
                cMax = max(cMax, longestPath[allCoords[i].first][allCoords[i].second+1]);
            longestPath[allCoords[i].first][allCoords[i].second] = ++cMax;
            if (cMax > totalMax) totalMax = cMax;
        }

        return totalMax;
    }
};
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