Algorithmsi Exercises:unionfind

Question1

Give the id[] array that results from the following sequence of 6 unionoperations on a set of ten items using the quick -find algorithm. 6-3 2-3 5-3 5-1 9-3 3-0 Your answer should be a sequence of ten integers, separated by whitespace. Recall:our Quick-find Convention for the Union operation P-q are to change Id[p] (and perhaps some other entries) but not I D[Q].

answer:0 0 0 0 4 0 0 7 8 0

Question explanation
The correct answer is:0 0 0 0 4 0 0 7 8 0

Here's the id[] array after each union operation:

0 1 2 3 4 5 6 7 8 9
6-3:0 1 2 3 4 5 3 7 8 9
2-3:0 1 3 3 4 5 3 7 8 9
5-3:0 1 3 3 4 3 3 7 8 9
5-1:0 1 1 1 4 1 1 7 8 9
9-3:0 1 1 1 4 1 1 7 8 1
3-0:0 0 0 0 4 0 0 7 8 0

Question 2

Give the id[] array that results from the following sequence of 9 Union
Operations on a set of ten items using the weighted quick-union algorithm from lecture.

7-9 9-4 7-0 8-1 3-7 5-6 5-1 3-8 2-6

Your answer should be a sequence of ten integers, separated by whitesp Ace.

Recall:when Joining, trees of equal size, our weighted Quick Union Convention are to
make the root of the SE Cond tree point to the root of the first tree. Also, our weighted
Quick Union algorithm performs union by size (number of nodes)-not union by height-
and does n OT do path compression.

Answer:7 8 7 7 7 7 5 7 5 7
Question explanation
the correct Answer is:7 8 7 7 7 7 5 7 5 7

Here's the id[] array after each union operation:

0 1 2 3 4 5 6 7 8 9
7-9:0 1 2 3 4 5 6 7 8 7
9-4:0 1 2 3 7 5 6 7 8 7
7-0:7 1 2 3 7 5 6 7 8 7
8-1:7 8 2 3 7 5 6 7 8 7
3-7:7 8 2 7 7 5 6 7 8 7
5-6:7 8 2 7 7 5 5 7 8 7
5-1:7 8 2 7 7 5 5 7 5 7
3-8:7 8 2 7 7 7 5 7 5 7
2-6:7 8 7 7 7 7 5 7 5 7

Question 3

Which of the following id[] Array (s) could be the result of running the weighted Quick Union
Algorithm on a set of ten items? Check all the Apply.

Recall that we weighted Quick Union algorithm uses Union by size (number of nodes)
And not union by height.

Answer:choose the last of the last.

Your Answer		score	explanation
5 5 5 5 2 6 4 5 2 3	Correct	0.20	The id[] array contains a cycle:6->4->2->5->6
5 3 6 6 6 5 5 8 6 6	correct	0.20	size of the tree rooted at the parent of 6 < twice the Size of the tree rooted at 6
8 8 1 1 2 4 1 1 8 9	correct	0.20	height of forest = 4 > LG N = LG (TEN)
6 6 1 6 6 1 6 6 2 6	< Span class= "Accessible-text-for-reader" >correct	0.20	6-7 0-7 1-5 2-8 5-8 4-7 6-2 7-3 2-9
	Correct	0.20	2-1 0-3 2-6

Algorithmsi Exercises:unionfind