added prims algorithm

algorithms/CPlusPlus/Graphs/prims-algorithm.cpp

@@ -0,0 +1,59 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+void prims(vector<pair<int,int>> adj[], vector<int> &key, vector<int> &parent, vector<bool> &mst, int V, int E, int &ans)
+{
+    key[0] = 0;
+    for(int count=0; count<V; count++)
+    {
+        int min = INT_MAX, u;
+        //to find the minimum weight of edge from the key array
+        for(int i=0;i<V;i++){
+            if(!mst[i] && key[i] < min){
+                min = key[i];
+                u = i;
+            }
+        }
+        mst[u] = true;
+        ans += key[u];
+
+        for(auto it: adj[u]){
+            int v = it.first;
+            int w = it.second;
+
+            if(!mst[v] && w < key[v]){
+                key[v] = w;
+                parent[v] = u;
+            }
+        }
+    }
+}
+
+int main(){
+    int V,E;
+    cout<<"no of vertex:"; cin>>V;
+    cout<<"no of edges:"; cin>>E;
+
+    vector<pair<int,int>> adj[V];
+
+    int u,v,wt;
+    for(int i=0; i<E; i++){
+        cin>> u >> v >> wt;
+        adj[u].push_back({v,wt});
+        adj[v].push_back({u,wt});
+    }
+
+    vector<int> key(V,INT_MAX);
+    vector<int> parent(V,-1);
+    vector<bool> mst(V,false);
+    int ans=0;
+
+    prims(adj,key,parent,mst,V,E,ans);
+    
+    cout<<ans<<endl;
+    for(int i=1; i<V; i++){
+        cout<<parent[i] << "-" << i << endl;
+    }
+
+    return 0;
+}