Added Prim's Algorithm

greedy_methods/Prim's_algorithm.py

@@ -0,0 +1,64 @@
+// Prim's Algorithm - Minimum Spanning Tree (MST)
+// Language: C++
+// Category: Greedy Algorithms
+
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <utility>
+
+using namespace std;
+
+void primMST(int V, vector<vector<pair<int, int>>> &adj) {
+ vector<int> key(V, INT_MAX);
+ vector<int> parent(V, -1);
+ vector<bool> inMST(V, false);
+
+ priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
+
+ // Start from vertex 0
+ key[0] = 0;
+ pq.push({0, 0});
+
+ while (!pq.empty()) {
+ int u = pq.top().second;
+ pq.pop();
+
+ inMST[u] = true;
+
+ for (auto &[v, weight] : adj[u]) {
+ if (!inMST[v] && weight < key[v]) {
+ key[v] = weight;
+ pq.push({key[v], v});
+ parent[v] = u;
+ }
+ }
+ }
+
+ cout << "Edges in MST:\n";
+ int totalWeight = 0;
+ for (int i = 1; i < V; ++i) {
+ cout << parent[i] << " - " << i << " (" << key[i] << ")\n";
+ totalWeight += key[i];
+ }
+ cout << "Total Weight = " << totalWeight << endl;
+}
+
+int main() {
+ int V, E;
+ cout << "Enter number of vertices and edges: ";
+ cin >> V >> E;
+
+ vector<vector<pair<int, int>>> adj(V);
+ cout << "Enter edges (u v w):\n";
+ for (int i = 0; i < E; ++i) {
+ int u, v, w;
+ cin >> u >> v >> w;
+ adj[u].push_back({v, w});
+ adj[v].push_back({u, w});
+ }
+
+ primMST(V, adj);
+
+ return 0;
+}