Question

Assume that there are 16 nodes marked 0 through 16. Initially each element should be in a separate equivalence class. Hand draw the resulting trees for each input pair when you use the weighted quick-union for the sequence 1-2, 3-4, 3-5, 1-7, 3-6, 8-9, 1-8, 3-10, 3-11, 3-12, 3-13, 14-15, 16-0, 14-16, 1-3, 1-14.

Answer 1

Code--->

import java.util.Scanner;
public class QuickUnion
{
private int[] id;//id[i] is equal to parent of i th node
private int[] sz;//sz[i] will tell how many of nodes have ith node as parent
public QuickUnion(int N)//only parameter no of nodes in graph
{
id = new int[N];//intialiy parent of i th node is i only
sz = new int[N];
for (int i = 0; i < N; i++)
{
id[i] = i;//intialiy parent of i th node is i only
sz[i]=1;//initially only one node with the i th node as porent
}
}
public int root(int i)//finding the parent of the node
{
while (i != id[i]) //parent node is the node which is parent of itself
i = id[i];
return i;
}
public boolean find(int p, int q)//if both p and q has same parent then p and q are connected else not
{
return root(p) == root(q);
}
public void unite(int p, int q)
{
int i = root(p);//find root of p
int j = root(q);//find root/parent of q
if(sz[i]<sz[j])//merge smaller tree into larger tree
{
id[i]=j;//Set the id of q's root to the id of p's root
sz[j]=sz[j]+sz[i];//update the sz[] array.
}
else
{
id[j] = i;//Set the id of p's root to the id of q's root
sz[i]=sz[i]+sz[j];//update the sz[] array.
}
}
public void print(int no_of_nodes)
{
boolean [] vis=new boolean[no_of_nodes];//visited array
int i;
for( i = 0; i < no_of_nodes; i++) //initialse visited array to false
vis[i] = false;
int count=0;
int start=0;
while(count<no_of_nodes)//While all nodes are not visited
{
System.out.print("(");
for(i=0;i<no_of_nodes;i++)
{
if(root(start)==root(i)&&vis[i]==false)//node with same root/parent will be connected
{
count++;
vis[i]=true;//mark visited as true
System.out.print(i+" ");
}
}
for(i=0;i<no_of_nodes;i++)
{
if(vis[i]==false)//search for unvisited array
{
start=i;//unconnected node to the previous start node
break;
}
}
System.out.print("),");
}
System.out.println(" ");
}
public static void main(String []args){
Scanner sc = new Scanner(System.in);
int no_of_nodes=17;//0-16
int no_of_edges = sc.nextInt(); //taking input no of edges, you can also use till end of file input
int i,j;
QuickUnion obj=new QuickUnion(no_of_nodes);//intialising class
for(i=0;i<no_of_edges;i++)//connecting graph through edges
{
int u=sc.nextInt();
int v=sc.nextInt();
obj.unite(u,v);//unite or merge the nodes of two edges
System.out.println("After merging "+ u + " and " + v);
obj.print(no_of_nodes);//print the graph
}
}
}

Input--->

16//No of edges(16 in this case)
1 2
3 4
3 5
1 7
3 6
8 9
1 8
3 10
3 11
3 12
3 13
14 15
16 0
14 16
1 3
1 14

Output:

After merging 1 and 2
( 0),( 1 2),( 3),( 4),( 5),( 6),( 7),( 8),( 9),( 10),( 11),( 12),( 13),( 14),( 15),( 16),
After merging 3 and 4
( 0),( 1 2),( 3 4),( 5),( 6),( 7),( 8),( 9),( 10),( 11),( 12),( 13),( 14),( 15),( 16),
After merging 3 and 5
( 0),( 1 2),( 3 4 5),( 6),( 7),( 8),( 9),( 10),( 11),( 12),( 13),( 14),( 15),( 16),
After merging 1 and 7
( 0),( 1 2 7),( 3 4 5),( 6),( 8),( 9),( 10),( 11),( 12),( 13),( 14),( 15),( 16),
After merging 3 and 6
( 0),( 1 2 7),( 3 4 5 6),( 8),( 9),( 10),( 11),( 12),( 13),( 14),( 15),( 16),
After merging 8 and 9
( 0),( 1 2 7),( 3 4 5 6),( 8 9),( 10),( 11),( 12),( 13),( 14),( 15),( 16),
After merging 1 and 8
( 0),( 1 2 7 8 9),( 3 4 5 6),( 10),( 11),( 12),( 13),( 14),( 15),( 16),
After merging 3 and 10
( 0),( 1 2 7 8 9),( 3 4 5 6 10),( 11),( 12),( 13),( 14),( 15),( 16),
After merging 3 and 11
( 0),( 1 2 7 8 9),( 3 4 5 6 10 11),( 12),( 13),( 14),( 15),( 16),
After merging 3 and 12
( 0),( 1 2 7 8 9),( 3 4 5 6 10 11 12),( 13),( 14),( 15),( 16),
After merging 3 and 13
( 0),( 1 2 7 8 9),( 3 4 5 6 10 11 12 13),( 14),( 15),( 16),
After merging 14 and 15
( 0),( 1 2 7 8 9),( 3 4 5 6 10 11 12 13),( 14 15),( 16),
After merging 16 and 0
( 0 16),( 1 2 7 8 9),( 3 4 5 6 10 11 12 13),( 14 15),
After merging 14 and 16
( 0 14 15 16),( 1 2 7 8 9),( 3 4 5 6 10 11 12 13),
After merging 1 and 3
( 0 14 15 16),( 1 2 3 4 5 6 7 8 9 10 11 12 13),
After merging 1 and 14
( 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16),