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b. Describe how to use a balanced BST to implement both operations in O(log n) time. Discuss why your implementation is correct, preferably using diagrams.

b. Describe how to use a balanced BST to implement both operations in O(log n) time. Discuss why your implementation is correct, preferably using diagrams.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 2. Let A be a sorted array of integers. You want to implement two functions: . update(i, x) - which takes as input an index i in A and sets A[i] = x. For example, calling update (3,10) will set A[3] = 10. Note that array A might not be completely sorted after an update. is Sorted(i) returns true if the subarray A[0... i] is sorted, otherwise it returns false. A straightforward implementation of the two operations using only the given array can be done as follows: update operation can directly change the value of A[i] to x. is Sorted will scan A[0] up to A[i] while checking if elements are non-decreasing. With the above implementations, update takes O(1) time but is Sorted takes O(n) time. b. Describe how to use a balanced BST to implement both operations in O(log n) time. Discuss why your implementation is correct, preferably using diagrams.
Transcribed Image Text:II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 2. Let A be a sorted array of integers. You want to implement two functions: . update(i, x) - which takes as input an index i in A and sets A[i] = x. For example, calling update (3,10) will set A[3] = 10. Note that array A might not be completely sorted after an update. is Sorted(i) returns true if the subarray A[0... i] is sorted, otherwise it returns false. A straightforward implementation of the two operations using only the given array can be done as follows: update operation can directly change the value of A[i] to x. is Sorted will scan A[0] up to A[i] while checking if elements are non-decreasing. With the above implementations, update takes O(1) time but is Sorted takes O(n) time. b. Describe how to use a balanced BST to implement both operations in O(log n) time. Discuss why your implementation is correct, preferably using diagrams.
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