Trapping Rain Water II

Description:

Given n x m non-negative integers representing an elevation map 2d where the area of each cell is 1 x 1, compute how much water it is able to trap after raining.

Example

Given 5*4 matrix

[12,13,0,12]
[13,4,13,12]
[13,8,10,12]
[12,13,12,12]
[13,13,13,13]

return 14.

Solution:

class Node {
public:
	int x, y, h;
	Node(int x, int y, int h): x(x), y(y), h(h) {}
};
bool operator>(const Node& n1, const Node& n2) {
	return n1.h > n2.h;
}
class Solution {
public:
	/**
	 * @param heights: a matrix of integers
	 * @return: an integer
	 */
	int trapRainWater(vector<vector<int> > &heights) {
		auto m = (int)heights.size();
		if (m < 3) return 0;
		auto n = (int)heights[0].size();
		if (n < 3) return 0;
		vector<vector<bool>> visited(m, vector<bool>(n, false));
		priority_queue<Node, vector<Node>, ::greater<Node>> heap;
		for (int i = 0; i < m; ++i) {
			heap.push(Node(i, 0, heights[i][0]));
			visited[i][0] = true;
			heap.push(Node(i, n-1, heights[i][n-1]));
			visited[i][n-1] = true;
		}
		for (int i = 1; i < n-1; ++i) {
			heap.push(Node(0, i, heights[0][i]));
			visited[0][i] = true;
			heap.push(Node(m-1, i, heights[m-1][i]));
			visited[m-1][i] = true;
		}
		int rc = 0;
		while (!heap.empty()) {
			auto node = heap.top();
			heap.pop();
			int x = node.x, y = node.y, h = node.h;
			if (x >= 1 && !visited[x-1][y]) {
				if (heights[x-1][y] < h)
					rc += h - heights[x-1][y];
				heap.push(Node(x-1, y, max(h, heights[x-1][y])));
				visited[x-1][y] = true;
			}
			if (x <= m-2 && !visited[x+1][y]) {
				if (heights[x+1][y] < h)
					rc += h - heights[x+1][y];
				heap.push(Node(x+1, y, max(h, heights[x+1][y])));
				visited[x+1][y] = true;
			}
			if (y >= 1 && !visited[x][y-1]) {
				if (heights[x][y-1] < h)
					rc += h - heights[x][y-1];
				heap.push(Node(x, y-1, max(h, heights[x][y-1])));
				visited[x][y-1] = true;
			}
			if (y <= n-2 && !visited[x][y+1]) {
				if (heights[x][y+1] < h)
					rc += h - heights[x][y+1];
				heap.push(Node(x, y+1, max(h, heights[x][y+1])));
				visited[x][y+1] = true;
			}
		}
		return rc;
	}
};