Merge pull request ephremdeme#6 from amarks444/amarks444-patch-4

Implemented Kruskals Algorithm.

Author: amarks444

kruskal.cpp

@@ -0,0 +1,104 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define ll long long int
+#define pb push_back
+#define mp make_pair
+#define f first
+#define s second
+#define mod 1000000007
+#define iAmInevitable ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
+//map<ll,ll> freq;
+//map<ll,ll> :: iterator itr;
+//for(itr=freq.begin();itr!=freq.end();itr++)
+//itr->f itr->s
+const ll MAX = 1e6 + 5;
+typedef pair<ll, ll> PII;
+ll id[MAX],rank1[MAX] ,nodes, edges;
+pair <ll, PII > p[MAX];
+// Time Complexity O(ElogV)
+
+void initialize()
+{
+ for(ll i = 0;i < MAX;++i)
+ {
+ id[i] = i;
+ rank1[i]=0; // or memset(rank,0,sizeof(rank))
+ }
+}
+
+// A utility function to find set of an element i 
+// (uses path compression technique) 
+ll findRoot(ll x)
+{
+ // find root and make root as parent of x and evrything else in the path
+ // path compression 
+ if(id[x] != x)
+ {
+ id[x] = findRoot(id[x]);
+ }
+ return id[x];
+}
+// A function that does union of two sets of x and y 
+// (uses union by rank) 
+void union1(ll x, ll y) 
+{ 
+ ll xroot = findRoot(x); 
+ ll yroot = findRoot(y); 
+ 
+ // Attach smaller rank tree under root of high 
+ // rank tree (Union by Rank) 
+ if (rank1[xroot] < rank1[yroot]) 
+ id[xroot]= yroot;
+ else if (rank1[xroot] > rank1[yroot]) 
+ id[yroot] = xroot ; 
+ 
+ // If ranks are same, then make one as root and 
+ // increment its rank by one 
+ else
+ { 
+ id[yroot] = xroot ; 
+ rank1[xroot] ++; 
+ } 
+} 
+
+
+long long kruskal(pair<ll, PII > p[])
+{
+ ll x, y;
+ long long cost, minimumCost = 0;
+ for(ll i = 0;i < edges;++i)
+ {
+ // Selecting edges one by one in increasing order from the beginning
+ x = p[i].second.first;
+ y = p[i].second.second;
+ cost = p[i].first;
+ // Check if the selected edge is creating a cycle or not
+ if(findRoot(x) != findRoot(y))
+ { //if not add the edges to the minimum spanning trees. 
+ minimumCost += cost;
+ union1(x, y);
+ } 
+ }
+ return minimumCost;
+}
+
+int main()
+{
+ iAmInevitable;
+ ll x, y;
+ long long weight, cost, minimumCost;
+ initialize();
+ cin >> nodes >> edges;
+ for(ll i = 0;i < edges;++i)
+ {
+ cin >> x >> y >> weight;
+ p[i] = mp(weight, mp(x, y));
+ }
+ // Sort the edges in the ascending order
+ sort(p, p + edges);
+ minimumCost = kruskal(p);
+ cout << minimumCost << endl;
+ return 0;
+}
+
+//This Code is Contributed by Amar Shankar