Merge pull request #287 from Himanshu-77/master

Author: abranhe

graphs/kruskal.cpp

@@ -1,81 +1,81 @@
+//
+// The following is C++ implementation of Kruskal's algorithm
+// on a graph. 
+
+// Kruskal's Algorithm is used to find minimum spanning tree
+// of a graph .
+// Here 'Disjoint Sets' method is used for cycle detection.
+// Disjoint sets are sets whose intersection is empty set 
+// if they don't have any common element 
+
 // The All ▲lgorithms Project
 //
 // https://allalgorithms.com/graphs/
 // https://github.com/allalgorithms/cpp
 //
-// Contributed by: Leonardo Su
-// Github: @Leonardosu
+// Contributed by: Himanshu Airan
+// Github: @Himanshu-77
+//
 
-#include <bits/stdc++.h>
-#define f first
-#define s second
-#define mp make_pair
-#define pb push_back
 
+#include<bits/stdc++.h>
 using namespace std;
 
-const int N = 100010;
-typedef pair<int,int> ii;
-typedef pair<int,ii> iii;
-vector<iii> edges;
+const int MAX = 1e4 + 5;
+int id[MAX] ;
 
-int p[N],lv[N];
-int total_cost = 0,n,m;
 
-//Union-Find
-//-------
-int find(int x)
+int root(int x)
 {
-if(p[x] == x) return x;
-return p[x] = find(p[x]);
+ while(id[x] != x)
+ {
+ id[x] = id[id[x]];
+ x = id[x];
+ }
+ return x;
 }
 
-void join(int x,int y)
+int main()
 {
-x = find(x);
-y = find(y);
-
-if(x == y) return;
-if(lv[x] < lv[y]) p[x] = y;
-else if(lv[x] > lv[y]) p[y] = x;
-else
-{
-p[x] = y;
-lv[y]++;
-}
-}
-//-------
+ int nodes, edges, x, y, weight;
+ int cost, minimumCost=0 ;
+ pair <int, pair<int, int> > Graph[MAX];
 
+ // initially all elements are in different sets
+ for(int i = 0;i < MAX;++i)
+ id[i] = i;
+
+
+ // input number of nodes and edges in graph
+ cin >> nodes >> edges;
+ for(int i = 0;i < edges;++i)
+ {
+ cin >> x >> y >> weight;
+ Graph[i] = make_pair(weight, make_pair(x, y));
+ }
+
+ // Sort the edges in the ascending order of weights
+ sort(Graph, Graph + edges);
+
+ // find weight of minimum spanning tree
+ for(int i = 0;i < edges;++i)
+ {
+ // Selecting edges one by one in increasing order from the beginning
+ x = Graph[i].second.first;
+ y = Graph[i].second.second;
+ cost = Graph[i].first;
+ // Check if the selected edge is creating a cycle or not
+ if(root(x) != root(y))
+ {
+ minimumCost += cost;
+
+ // join sets of both elements
+ id[root(x)] = id[root(y)];
+ } 
+ }
 
-int main()
-{
 
-cin>>n>>m; // "n" is the number of vertex and "m" = number of edges
-
-for(int i=1;i<=n;++i)
-p[i] = i,lv[i] = 0;
-
-int a,b,c;
-for(int i=1;i<=m;++i) // Read the input, there is an edge between "a" and "b" with cost c
-{
-cin>>a>>b>>c;
-edges.pb(mp(c,mp(a,b) ));
-}
-
-// Kruskal 
-// --------
-sort(edges.begin(),edges.end());
-
-for(int i=0;i<edges.size();++i)
-{
-int a = edges[i].s.f;
-int b = edges[i].s.s;
-if(find(a) != find(b))
-{
-join(a,b);
-total_cost+=edges[i].f;
-}
-}
-// --------
-cout<<total_cost<<"\n";
+ cout << "Cost of minimum spanning tree is : "
+ << minimumCost << endl;
+ return 0;
 }