<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) {
        map<int, vector<pair<int, int>>> values;
        
        int h = matrix.size();
        int w = matrix[0].size();

        for (auto i = 0; i < h; ++i) {
            auto& line = matrix[i];
            for (auto j = 0; j < w; ++j) {
                values[line[j]].push_back({i, j});
            }
        }

        vector<vector<int>> dp(h, vector<int>(w));
        auto res = 0;

        for (auto& [v, indexes] : values) {
            for (auto [i, j] : indexes) {
                auto& cur = dp[i][j];
                if (--i >= 0 && matrix[i][j] < v) cur = dp[i][j];
                if ((i += 2) < h && matrix[i][j] < v) cur = max(cur, dp[i][j]); 
                --i;
                if (--j >= 0 && matrix[i][j] < v) cur = max(cur, dp[i][j]);
                if ((j += 2) < w && matrix[i][j] < v) cur = max(cur, dp[i][j]);
                ++cur;
                res = max(res, cur);
            }
        }
        return res;
    }
};
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