Added Prims Algorithm for MST

Prims_Algorithm.cpp

@@ -0,0 +1,72 @@
+#include<bits/stdc++.h>
+#define ll long long
+#define pii pair<ll,ll>
+#define fi first
+#define sec second
+#define pb push_back
+
+using namespace std;
+
+// Implement Prims Algorithm for MST
+
+ll par[1000001];
+ll ran[1000001];
+
+ll find_set(ll v) {
+    if(v == par[v]) return v;
+    return par[v] = find_set(par[v]);
+}
+
+bool union_set(ll a,ll b) {
+    a = find_set(a);
+    b = find_set(b);
+
+    if(a!=b) {
+        if(ran[a]<ran[b]) swap(a,b);
+        par[b]=a;
+        if(ran[a]==ran[b]) ran[a]++;
+        return true;
+    }
+    return false;
+}
+
+int main() {
+    ll n;      // Number of Nodes
+    cin>>n;
+
+    ll e;      // Number of Edges
+    cin>>e;
+
+    priority_queue<pair<ll,pii>,vector<pair<ll,pii> >, greater<pair<ll,pii> > > edges;
+    for(ll i=0;i<e;i++) {
+        ll s,d,w;
+        cin>>s>>d>>w;
+        edges.push({w,{s,d}});
+    }
+
+    for(ll i=1;i<=n;i++) {
+        par[i]=i;
+        ran[i]=1;
+    }
+
+    ll val=0;
+    vector<pair<ll,pii> > mst;
+    while(!edges.empty()) {
+        pair<ll,pii> top = edges.top();
+        edges.pop();
+
+        ll s = top.sec.fi,d = top.sec.sec,w = top.fi;
+
+        if(union_set(s,d)) {
+            val += w;
+            mst.pb({w,{s,d}});
+        }
+    }
+    cout<<"Value of Minimum Spanning Tree = "<<val<<"\n";
+    cout<<"Edges: \n";
+    for(auto it: mst) {
+        cout<<it.sec.fi<<"->"<<it.sec.sec<<" ("<<it.fi<<")\n";
+    }
+    return 0;
+
+}