Create Prim's_algorithm.py

### Prim’s Algorithm
- **Language:** C++
- **Description:** Constructs a Minimum Spanning Tree (MST) by starting with one vertex and repeatedly adding the smallest possible edge connecting a vertex inside the MST to one outside it.
- **Complexity:** O(E log V)
- **Use Case:** Network design, cost minimization

Author: ShristiC7

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;
+}