Algorithm quick-union

Initialize

union ( a, b )
i = Root(a)
j = Root(b)
V[ i ] = j

Index	1	2	3	4	5	6	7	8
Parent	1	2	3	4	5	6	7	8

union ( 3, 7 )

union ( a=3, b=7 )
i = Root(a=3) => i = 3
j = Root(b=7) => j = 7
V[ i ] = Root ( j )
V[ 3 ] = Root ( 7 )
V[ 3 ] = 7

Index	1	2	3	4	5	6	7	8
Parent	1	2	7	4	5	6	7	8
	v[1]	v[2]	v[3]	V[4]	v[5]	v[6]	v[7]	v[8]

union( 2 , 5 )

union ( a=2, b=5 )
i = Root(2) = 2
j = Root(5) = 5
V[ 2 ] = 5

Index	1	2	3	4	5	6	7	8
Parent	1	5	7	4	5	6	7	8
	v[1]	v[2]	v[3]	V[4]	v[5]	v[6]	v[7]	v[8]

union( 2 , 3 )

union ( a=2, b=3 )
i = Root(2) = 5
j = Root(3) = 7
V[ 5 ] = 7

Index	1	2	3	4	5	6	7	8
Parent	1	5	7	4	7	6	7	8
	v[1]	v[2]	v[3]	V[4]	v[5]	v[6]	v[7]	v[8]

union( 3 , 6 )

union ( a=3, b=6 )
i = Root(3) =7
j = Root(6) = 6
V[ 7 ] = 6

Index	1	2	3	4	5	6	7	8
Parent	1	5	7	4	7	6	6	8
	v[1]	v[2]	v[3]	V[4]	v[5]	v[6]	v[7]	v[8]

union( 1 , 4 )

union ( a=1, b=4 )
i = Root(1) = 1
j = Root(4) = 4
V[ 1 ] = 4

Index	1	2	3	4	5	6	7	8
Parent	4	5	7	4	7	6	6	8
	v[1]	v[2]	v[3]	V[4]	v[5]	v[6]	v[7]	v[8]

union( 8, 1 )

union ( a=8, b=1 )
i = Root(8) = 8
j = Root(1) = 4
V[ 8 ] = 4

Index	1	2	3	4	5	6	7	8
Parent	4	5	7	4	7	6	6	4
	v[1]	v[2]	v[3]	V[4]	v[5]	v[6]	v[7]	v[8]

union(4, 7)

union ( a=4, b=7 )
i = Root(4) = 4
j = Root(7) = 6
V[ 4 ] = 6

Index	1	2	3	4	5	6	7	8
Parent	4	5	7	6	7	6	6	4
	v[1]	v[2]	v[3]	V[4]	v[5]	v[6]	v[7]	v[8]