<p>Given an <code>m x n</code> integer matrix <code>heightMap</code> representing the height of each unit cell in a 2D elevation map, return <em>the volume of water it can trap after raining</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/08/trap1-3d.jpg" style="width: 361px; height: 321px;" />
<pre>
<strong>Input:</strong> heightMap = [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> After the rain, water is trapped between the blocks.
We have two small ponds 1 and 3 units trapped.
The total volume of water trapped is 4.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/08/trap2-3d.jpg" style="width: 401px; height: 321px;" />
<pre>
<strong>Input:</strong> heightMap = [[3,3,3,3,3],[3,2,2,2,3],[3,2,1,2,3],[3,2,2,2,3],[3,3,3,3,3]]
<strong>Output:</strong> 10
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == heightMap.length</code></li>
	<li><code>n == heightMap[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= heightMap[i][j] &lt;= 2 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int trapRainWater(vector<vector<int>>& heightMap) {
        size_t m = heightMap.size();
        size_t n = heightMap[0].size();
        vector<vector<int>> fun = heightMap;
        for (size_t i = 1; i < m - 1; ++i) {
            for (size_t j = 1; j < n - 1; ++j) {
                fun[i][j] = std::numeric_limits<int>::max();
            }
        }
        bool changes = true;
        while (changes) {
            changes = false;
            for (size_t i = 1; i < m - 1; ++i) {
                for (size_t j = 1; j < n - 1; ++j) {
                    int my_height = heightMap[i][j];
                    std::array<int, 4> nbr{fun[i][j-1], fun[i][j+1], fun[i-1][j], fun[i+1][j]};
                    int smallest_nbr = std::ranges::min(nbr);
                    int new_bound = std::max(my_height, smallest_nbr);
                    if (new_bound < fun[i][j]) {
                        changes = true;
                        fun[i][j] = new_bound;
                    }
                }
            }
        }
        int total = 0;
        for (size_t i = 1; i < m - 1; ++i) {
            for (size_t j = 1; j < n - 1; ++j) {
                total -= heightMap[i][j];
                total += fun[i][j];
            }
        }
        return total;
    }
};
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