// union/find with weighting and path compaction

#include <iostream.h>

int *parent;
bool *root;

void Initialize(int n)
{// One element per set/class/tree.
   root = new bool[n+1];
   parent = new int[n+1];
   for (int e = 1; e <= n; e++) {
      parent[e] = 1;
      root[e] = true;}
}

int Find(int e)
{// Return root of tree containing e.
 // Compact path from e to root.
   int j = e;
   // find root
   while (!root[j])
      j = parent[j];
   
   // compact
   int f = e;  // start at e
   while (f != j) {// f is not root
      int pf = parent[f];
      parent[f] = j;  // move f to level 2
      f = pf;         // f moves to old parent 
      }

   return j;
}

void Union(int i, int j)
{// Combine trees with roots i and j.
   if (parent[i] < parent[j]) {
      // i becomes subtree of j
      parent[j] += parent[i];
      root[i] = false;
      parent[i] = j; }
   else {// j becomes subtree of i
      parent[i] += parent[j];
      root[j] = false;
      parent[j] = i;}
}

void main(void)
{
   Initialize(10);
   Union(1,2);
   Union(3,4);
   Union(1,3);
   cout << "Find(1) = " << Find(1) << " Find(2) = " << Find(2) << endl;
   cout << "Find(3) = " << Find(3) << " Find(4) = " << Find(4) << endl;
   cout << "Find(5) = " << Find(5) << " Find(6) = " << Find(6) << endl;
}