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[O... 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. a. Give another implementation where update takes O(n) time while is Sorted takes 0(1) time. b. Describe how to use a balanced BST to implement both operations in O(log) time. Discuss why your implementation is correct, preferably using diagrams.
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[O... 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. a. Give another implementation where update takes O(n) time while is Sorted takes 0(1) time. b. Describe how to use a balanced BST to implement both operations in O(log) time. Discuss why your implementation is correct, preferably using diagrams.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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