Question

5. (20 pts) Draw the AVL tree after executing each of the following operations on: y 4 62 z 3 44 x 78 2 0/ 17 50 88 48 54 T2 To T3 • insertion of element 55, then insertion of element 60; • removal of element 78, then removal of element 62. 6. (10 pts) You are given an implementation of binary search tree (e.g., AVL tree) that supports find(k) (finding the element with key = k) in O(logn) time, where n is the total number of elements. Design a function findAll(k1, k2) to find all elements with keys in [k1,k2] in O(logn + s) time, where s is the output size. Present your algorithm in pseudocode, prove its correctness and analyze its complex- ity. You can assume that all elements have different integer key values.

          5. (20 pts) Draw the AVL tree after executing each of the following operations on:
y
4
62
z
3
44
x
78
2
0/
17
50
88
48
54
T2
To
T3
• insertion of element 55, then insertion of element 60;
• removal of element 78, then removal of element 62.
6. (10 pts) You are given an implementation of binary search tree (e.g., AVL tree) that
supports find(k) (finding the element with key = k) in O(logn) time, where n is the
total number of elements. Design a function findAll(k1, k2) to find all elements with
keys in [k1,k2] in O(logn + s) time, where s is the output size.
Present your algorithm in pseudocode, prove its correctness and analyze its complex-
ity. You can assume that all elements have different integer key values.

5. (20 pts) Draw the AVL tree after executing each of the following operations on:
y
4
62
z
3
44
x
78
2
0/
17
50
88
48
54
T2
To
T3
• insertion of element 55, then insertion of element 60;
• removal of element 78, then removal of element 62.
6. (10 pts) You are given an implementation of binary search tree (e.g., AVL tree) that
supports find(k) (finding the element with key = k) in O(logn) time, where n is the
total number of elements. Design a function findAll(k1, k2) to find all elements with
keys in [k1,k2] in O(logn + s) time, where s is the output size.
Present your algorithm in pseudocode, prove its correctness and analyze its complex-
ity. You can assume that all elements have different integer key values.

Added by Matthew C.

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