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Give a set with 13 elements, show the final result of executing the following instructions with UF WeightedQuickUnion: union(7, 8), union(9, 10), union(11, 12), union(9, 11), union(0, 1), union(0, 2), union(6, 4), union(0, 6). Assuming initially there are 13 components. a) Show the final contents of idl array b) Draw the final forest of trees. union(3,5), union(4, 3).

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Answer #1

In the simple QUICK UNION, we just join the components without any calculation. In the WEIGHTED QUICK UNION, we calculate the number of components in the two parts before joining.

We always place them in an intelligent way as explained in the below figure:

Hence it gives a better performance.

The solution to the given problem is as follows:

SIM stepa: union1,) union,2 118)union(9, o 12 I O 10 1 2 l 2 Slep union CO

===

Hence. we can see that there are 3 trees in the forest after all the unions have been performed.

The id[] array contents are as follows:

component

0

1

2

3

4

5

6

7

8

9

10

11

12

id value

3

3

3

3

3

3

3

7

7

9

9

9

9

===================================================================

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quick-union smaller tree smaller larger tree tree larger tree might put the larger tree lower

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