1. You are given the following list: [71,65,62,60,58,55,48,42,41,40,38,37,29,25,

Question

1. You are given the following list: [71,65,62,60,58,55,48,42,41,40,38,37,29,25,22] to be used in the BST constructor a. Draw the resulting tree produced by the constructor. b. How balanced is the tree c. Could you represent this particular BST with another data structure? Base your answer in the BST you have drawn in item a d. What is the time complexity of searching 22 in this BST? e. What happens if you create a new tree by traversing the original BST inorder? 2. Consider the following BST root 42 37 60 25 40 65 29 38 41 48 58 62 71 a. How would you rearrange the initial list in question 1, so that the resulting BST looks like the one right above? b. How balanced is this tree c. What is the time complexity of searching 22 in this BST? d. What process done on arrays is similar to item c in, both, dynamics and complexity? e. Traverse the BST with r+l. What can you tell about the list of values printed?

Explanation / Answer

Solution:

a)

42 37 60 25 40 55 65 22 29 38 41 48 58 62 71

b)

The tree is balanced with the balancing factor of 0 at every node.

c)

4 comparison will be done to search for 22. log n basically since the height of the given tree is 4.

d)

first 22 is compared with 42, since 22 is smaller, we go to the left subtree and compare with 37 again the process grows recursively until 22 (the searched element) is compared with 22 (the node in the tree) and the result is returned.

e)

r+l means right node first, then root, then left.

The traversal would be:

71 65 62 60 58 55 48 42 41 40 38 37 29 25 22

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