From 34c84edc87826197631afe42c00e38c4b4d20bc8 Mon Sep 17 00:00:00 2001
From: Laiba Ashfaq <abbasilaiba082@gmail.com>
Date: Sun, 12 Oct 2025 23:26:42 +0500
Subject: [PATCH] Implement Prim's algorithm for minimum spanning tree
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Algorithm Name: Prim’s Algorithm

Language: C++

Category: Greedy Algorithms (though you mentioned “Stacks & Queues” in the form, it’s actually a graph/greedy algorithm)

Difficulty: Beginner-friendly / Medium

Description: Builds a Minimum Spanning Tree (MST) by always adding the cheapest edge connecting the tree to an unconnected vertex.
---
 CPP/graph/PrimAlgo.cpp | 49 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100644 CPP/graph/PrimAlgo.cpp

diff --git a/CPP/graph/PrimAlgo.cpp b/CPP/graph/PrimAlgo.cpp
new file mode 100644
index 0000000..bcb3d27
--- /dev/null
+++ b/CPP/graph/PrimAlgo.cpp
@@ -0,0 +1,49 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int INF = 1e9;
+
+void primMST(vector<vector<pair<int,int>>> &adj, int V) {
+    vector<int> key(V, INF);
+    vector<int> parent(V, -1);
+    vector<bool> inMST(V, false);
+
+    key[0] = 0;
+
+    for (int count = 0; count < V-1; count++) {
+        int u = -1;
+        for (int i = 0; i < V; i++)
+            if (!inMST[i] && (u == -1 || key[i] < key[u]))
+                u = i;
+
+        inMST[u] = true;
+
+        for (auto &edge : adj[u]) {
+            int v = edge.first;
+            int w = edge.second;
+            if (!inMST[v] && w < key[v]) {
+                key[v] = w;
+                parent[v] = u;
+            }
+        }
+    }
+
+    cout << "Edge \tWeight\n";
+    for (int i = 1; i < V; i++)
+        cout << parent[i] << " - " << i << " \t" << key[i] << "\n";
+}
+
+int main() {
+    int V, E;
+    cin >> V >> E;
+    vector<vector<pair<int,int>>> adj(V);
+    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(adj, V);
+    return 0;
+}