Added Kruskal's Algorithm

Algorithms/Graph Algorithms/kruskal_algorithm.cpp

@@ -0,0 +1,81 @@
+#include<bits/stdc++.h>
+using namespace std;
+#define ll long long
+#define MAX 1000005
+ll id[MAX];
+
+// We use disjoint sets to detect whether adding a edge to the growing tree creates a cycle or not.
+
+/**
+    This function set's up the array to implement disjoint sets
+*/
+void setDisjoint(){
+    for(ll i=0; i< MAX; i++)
+        id[i] = i;
+}
+
+/**
+    This function takes the number and returns its root in disjoint set
+*/
+ll root(ll n){
+    while(id[n] != n){
+        id[n] = id[id[n]];
+        n = id[n];
+    }
+    return n;
+}
+
+/**
+        This function takes two number and puts them in same set i.e. performs the union operation
+*/
+void disjointUnion(ll from, ll to){
+    ll p = root(from);
+    ll q = root(to);
+    id[p] = id[q];
+}
+
+/**
+    This function implements the kruskal's algorithm
+*/
+ll kruskal(pair< ll, pair <ll, ll > > p[], ll nodes, ll edges)
+{
+    ll minCost = 0;
+    for(ll i=0; i<edges; i++){
+        ll from = p[i].second.first;
+        ll to = p[i].second.second;
+        ll weight = p[i].first;
+
+        // Checking if adding the edge creates a cycle?
+        if(root(from) != root(to)){
+            minCost += weight;
+            disjointUnion(from,to);
+        }
+    }
+    return minCost;
+}
+
+int main()
+{
+    ll nodes, num_of_edges;
+    ll from, to, weight;
+    setDisjoint();
+    cout << "Enter the number of nodes: ";
+    cin >> nodes;
+
+    cout << "Enter the number of edges: ";
+    cin >> num_of_edges;
+
+    pair< ll, pair <ll, ll > > edges[num_of_edges];
+
+    cout << "Enter the edges in order of : from to weight\n";
+    for(ll i=0; i<num_of_edges; i++){
+        cin >> from >> to >> weight;
+        edges[i] = make_pair(weight, make_pair(from, to));
+    }
+
+    sort(edges, edges + num_of_edges);
+    ll MST = kruskal(edges, nodes, num_of_edges);
+
+    cout << "Minimum cost spanning tree is : " << MST << endl;
+    return 0;
+}