Merge pull request #264 from harshendram/Algo/PrimsAlgorithm

Algo/prims algorithm

Author: Pradeepsingh61

CPP/algorithms/greedy_algorithms/prims_algorithm.cpp

@@ -0,0 +1,82 @@
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <utility>
+#include <climits>
+
+using namespace std;
+
+void primMST(int V, vector<vector<pair<int, int>>> &adj)
+{
+    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
+
+    vector<int> key(V, INT_MAX);
+    vector<int> parent(V, -1);
+    vector<bool> inMST(V, false);
+
+    int start_node = 0;
+    pq.push({0, start_node});
+    key[start_node] = 0;
+
+    while (!pq.empty())
+    {
+        int u = pq.top().second;
+        pq.pop();
+
+        if (inMST[u])
+        {
+            continue;
+        }
+
+        inMST[u] = true;
+
+        for (auto &edge : adj[u])
+        {
+            int v = edge.first;
+            int weight = edge.second;
+
+            if (!inMST[v] && key[v] > weight)
+            {
+                key[v] = weight;
+                pq.push({key[v], v});
+                parent[v] = u;
+            }
+        }
+    }
+
+    int total_weight = 0;
+    cout << "Edges in the Minimum Spanning Tree:" << endl;
+    for (int i = 1; i < V; ++i)
+    {
+        if (parent[i] != -1)
+        {
+            cout << parent[i] << " -- " << i << " == " << key[i] << endl;
+            total_weight += key[i];
+        }
+    }
+    cout << "Total weight of MST: " << total_weight << endl;
+}
+
+void addEdge(vector<vector<pair<int, int>>> &adj, int u, int v, int w)
+{
+    adj[u].push_back({v, w});
+    adj[v].push_back({u, w});
+}
+
+int main()
+{
+    int V = 5;
+    vector<vector<pair<int, int>>> adj(V);
+
+    addEdge(adj, 0, 1, 2);
+    addEdge(adj, 0, 3, 6);
+    addEdge(adj, 1, 2, 3);
+    addEdge(adj, 1, 3, 8);
+    addEdge(adj, 1, 4, 5);
+    addEdge(adj, 2, 4, 7);
+    addEdge(adj, 3, 4, 9);
+
+    primMST(V, adj);
+
+    return 0;
+}