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Suppose we are given two sorted arrays A[1..n] and B[1..n]. Describe an algorithm to find the median element in the union of A and B in O(log n) time. You can assume that the arrays contain no duplicate elements.

Suppose we are given two sorted arrays A[1..n] and B[1..n]. Describe an algorithm to find the median element in the union of A and B in O(log n) time. You can assume that the arrays contain no duplicate elements.

Database System Concepts
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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Please answer questions A-D
21. (a) Suppose we are given two sorted arrays A[1..n] and B[1..n]. Describe an algorithm to find the median element in the union of A and B in O(logn) time. You can assume that the arrays contain no duplicate elements. (b) Suppose we are given two sorted arrays A[1..m] and B[1..n] and an integer k. Describe an algorithm to find the kth smallest element in AUB in O(log(m + n)) time. For example, if k = 1, your algorithm should return the smallest element of AUB.) [Hint: Use your solution to part (a).] "(c) Now suppose we are given three sorted arrays A[1..n], B[1..n], and C[1..n], and an integer k. Describe an algorithm to find the kth smallest element in AUBUC in O(logn) time. 55 RECURSION (d) Finally, suppose we are given a two dimensional array A[1.. m, 1..n] in which every row A[i, ] is sorted, and an integer k. Describe an algorithm to find the kth smallest element in A as quickly as possible. How does the running time of your algorithm depend on m? [Hint: Solve problem 16 first.] W
Transcribed Image Text:21. (a) Suppose we are given two sorted arrays A[1..n] and B[1..n]. Describe an algorithm to find the median element in the union of A and B in O(logn) time. You can assume that the arrays contain no duplicate elements. (b) Suppose we are given two sorted arrays A[1..m] and B[1..n] and an integer k. Describe an algorithm to find the kth smallest element in AUB in O(log(m + n)) time. For example, if k = 1, your algorithm should return the smallest element of AUB.) [Hint: Use your solution to part (a).] "(c) Now suppose we are given three sorted arrays A[1..n], B[1..n], and C[1..n], and an integer k. Describe an algorithm to find the kth smallest element in AUBUC in O(logn) time. 55 RECURSION (d) Finally, suppose we are given a two dimensional array A[1.. m, 1..n] in which every row A[i, ] is sorted, and an integer k. Describe an algorithm to find the kth smallest element in A as quickly as possible. How does the running time of your algorithm depend on m? [Hint: Solve problem 16 first.] W
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