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
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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Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8695284e-764c-4713-84c8-81d0f8c23817%2Fc4ba1b03-0365-437e-8774-b2d0127abf6c%2F76e6s4_processed.jpeg&w=3840&q=75)
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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