Create 407. Trapping Rain Water II

407. Trapping Rain Water II

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+class Solution {
+public:
+    int trapRainWater(vector<vector<int>>& heightMap) {
+        if (heightMap.empty() || heightMap[0].empty()) return 0;
+
+        int rows = heightMap.size(), cols = heightMap[0].size();
+        vector<vector<int>> graph(rows * cols + 1);
+        int virtualStart = rows * cols;
+
+        // Direction vectors for moving in 4 directions
+        vector<int> dx = {0, 0, 1, -1};
+        vector<int> dy = {1, -1, 0, 0};
+
+        // Build the graph
+        for (int i = 0; i < rows; i++) {
+            for (int j = 0; j < cols; j++) {
+                int currentCell = i * cols + j;
+
+                // Connect boundary cells to virtual start node
+                if (i == 0 || i == rows - 1 || j == 0 || j == cols - 1) {
+                    graph[virtualStart].push_back(currentCell);
+                }
+
+                // Connect current cell to its neighbors
+                for (int k = 0; k < 4; k++) {
+                    int x = i + dx[k], y = j + dy[k];
+                    if (x >= 0 && x < rows && y >= 0 && y < cols) {
+                        graph[currentCell].push_back(x * cols + y);
+                    }
+                }
+            }
+        }
+
+        // Dijkstra-like BFS to calculate distances
+        auto calculateDistances = [&](int start) {
+            vector<int> dist(graph.size(), INT_MAX / 2);
+            dist[start] = 0;
+
+            // Min-heap to prioritize cells with smaller heights
+            set<pair<int, int>> pq; // {distance, node}
+            pq.insert({0, start});
+
+            while (!pq.empty()) {
+                auto [currentDist, currentNode] = *pq.begin();
+                pq.erase(pq.begin());
+
+                for (int neighbor : graph[currentNode]) {
+                    int weight = heightMap[neighbor / cols][neighbor % cols];
+                    if (max(currentDist, weight) < dist[neighbor]) {
+                        pq.erase({dist[neighbor], neighbor});
+                        dist[neighbor] = max(currentDist, weight);
+                        pq.insert({dist[neighbor], neighbor});
+                    }
+                }
+            }
+
+            return dist;
+        };
+
+        vector<int> dist = calculateDistances(virtualStart);
+
+        // Calculate trapped water
+        int trappedWater = 0;
+        for (int i = 0; i < rows; i++) {
+            for (int j = 0; j < cols; j++) {
+                int cell = i * cols + j;
+                int boundaryHeight = dist[cell];
+                if (boundaryHeight > heightMap[i][j]) {
+                    trappedWater += boundaryHeight - heightMap[i][j];
+                }
+            }
+        }
+
+        return trappedWater;
+    }
+};