Create Solution.cpp

Author: JawadSher

23 - Graph Data Structure Problems/14 - Minimum Spanning Tree | Prim's Algorithm/Solution.cpp

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+class Solution
+{
+public:
+    // Function to find the sum of weights of edges of the Minimum Spanning Tree (MST)
+    int spanningTree(int V, vector<vector<int>> adj[])
+    {
+        // Create a vector to track if a node is included in the MST (initialized to false)
+        vector<int> MST(V, false);
+
+        // Create a priority queue (min-heap) to store edges, 
+        // where each element is a pair: (weight, vertex)
+        priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
+        
+        // Variable to store the total weight of the MST
+        int totalWeight = 0;
+        
+        // Push the first node (0th vertex) with weight 0 into the priority queue to start from
+        pq.push({0, 0});
+        
+        // While there are still nodes to be processed
+        while (!pq.empty()) {
+            // Get the edge with the minimum weight (top of the priority queue)
+            pair<int, int> top = pq.top();
+            pq.pop();
+            
+            // Extract the weight and node from the pair
+            int weight = top.first;
+            int node = top.second;
+            
+            // If the node is already included in MST, skip it
+            if (MST[node]) continue;
+            
+            // Mark the current node as included in the MST
+            MST[node] = true;
+            
+            // Add the weight of the current edge to the total MST weight
+            totalWeight += weight;
+            
+            // Explore all adjacent nodes (neighbors) of the current node
+            for (auto &edge : adj[node]) {
+                int vertex = edge[0];  // Get the adjacent vertex
+                int vertexWeight = edge[1];  // Get the weight of the edge to the adjacent vertex
+                
+                // If the adjacent vertex is not already in the MST, add it to the priority queue
+                if (!MST[vertex]) pq.push({vertexWeight, vertex});
+            }
+        }
+        
+        // Return the total weight of the Minimum Spanning Tree
+        return totalWeight;
+    }
+};