Added Kruskal's Algorithm for finding the minimum spanning tree within a graph

C++/find-minimum-spanning-tree.cpp

@@ -0,0 +1,87 @@
+/*
+ * This algorithm is called Kruskall's Algorithm which is used to find the 
+ * minimum spanning tree (MST) within a graph. MST is basically a tree within
+ * a graph with the least weightage in its edges.
+ *
+ * Time Complexity  : O(M log N) or O(M log M) [variables are as coded]
+ * Space Complexity : O(M)
+ */
+
+#include <iostream>
+#include <algorithm>
+using namespace std;
+
+#define MAX 10000000
+
+int N,M,totalCost;
+int rank[MAX],parent[MAX];
+
+struct edge {int x,y,c;};
+edge A[MAX];
+
+// To find the parent of the node x using Union Disjoint Set Data Structure (UDS).
+int f_find(int x)
+{
+  if(parent[x] != x)
+    parent[x] = f_find(parent[x]);
+  return parent[x];
+}
+
+// To unify and edge with the rest of the tree (coded based on UDS).
+void f_union(int x,int y)
+{
+  if(rank[x] > rank[y])swap(x,y);
+
+  if(rank[x] == rank[y])
+    rank[y] ++;
+
+  parent[x] = y;
+}
+
+// A function to help with the sorting algorithm.
+bool func(edge a, edge b)
+{
+  return a.c < b.c;
+}
+
+// Kruskal's algorithm to find the MST within a graph.
+void kruskall()
+{
+  sort(A, A+M, func);
+
+  // Initializing all the varibales.
+  for(int i=0;i<N;i++)
+    rank[i] = 0, parent[i] = i;
+
+  for(int i=0;i<M;i++)
+    {
+      int x = f_find (A[i].x);
+      int y = f_find (A[i].y);
+
+      if(x!=y)
+	{
+	  f_union(x,y);
+	  totalCost += A[i].c;
+	}
+    }
+
+  cout << totalCost << '\n';
+}
+
+
+// Receiving the input from STDIN
+void get_input()
+{
+  cout << "Enter the number of nodes : "; cin >> N;
+  cout << "Enter the number of edges : "; cin >> M;
+  cout << "Enter the edges in the format of 'Node1 Node2 Cost'\n";
+  for(int i=0;i<M;i++)
+    cin >> A[i].x >> A[i].y >> A[i].c;
+}
+
+int main()
+{
+  get_input();
+  kruskall();
+  return 0;
+}