Question

Union-Find

Show the contents of the id[ ] array and the number of times array is accessed for each input pair when you that from the of the following sequence of instructions: union(1,2), union(3,4), union(1,7), union(3,6), union(8,9), union(1,8), union(3,10), union(3,11), union(3,12), union(3,13), union(14,15), union(16,0), union(14,16), union(1,3), union(1,14) when the union are

a. Quick-find
b. Quick-union
c. Weighted quick-union

Answer 1

public class Weight

{

private int[] id;

private int[] size;

private int c;

private int array = 0;

public Weight(int N)

{

c = N;

id = new int[N];

for (int a = 0; a < N; a++){

id[a] = a;

}

  

size = new int[N];

for (int a = 0; a < N; a++)

size[a] = 1;

}

public int c()

{

return c;

}

public boolean join(int m, int n)

{

return find(m) == find(n);

}

private int find(int m)

{

while (m != id[m]) m = id[m];

return m;

}

public void un(int m, int n)

{

System.out.println(" union for " + m + "-" + n);

int a = find(m);

int j = find(n);

if (a == j) return;

if (size[a] < size[j])

{

id[a] = j; size[j] += size[a];

}

else

{

id[j] = a; size[a] += size[j];

}

array++;

for (int k = 0; k < 20; k++){

System.out.printf("%d ", id[k]);

}

System.out.println("");  

c--;

}

public static void main(String args[])

{

Weight wqu = new Weight(20);

wqu.un(1, 2);

wqu.un(3, 4);

wqu.un(1, 7);

wqu.un(3, 6);

wqu.un(8, 9);

wqu.un(1, 8);

wqu.un(3, 10);

wqu.un(3, 11);

wqu.un(3, 12);

wqu.un(3, 13);

wqu.un(14, 15);

wqu.un(16, 0);

wqu.un(14, 16);

wqu.un(1, 3);

wqu.un(1, 14);

System.out.println("Number of Array was accessed " + wqu.array + " times.");

System.out.println("Final ID Array is : ");

for (int a = 0; a < 20; a++){

System.out.println("[" + a +"]:"+wqu.id[a]);

}

}

}