Problem 3. Given an array A[1: n] of n positive integers (possibly with repetitions), your goal is to find whether there is a sub-array All: r] such that Ali) = n. Example. Given A = [13, 1,2, 3, 4, 7, 2, 3,8, 9] for n = 10, the answer is Yes since elements in A2 : 5] add up to n = 10. On the other hand, if the input array is A = [3, 2,6,8, 20, 2, 4] for n = 7, the answer is No since no sub-array of A adds up ton=7. Hint: Observe that if Ali] = n, then Ali] = E A[i] – n; this may come handy!
Problem 3. Given an array A[1: n] of n positive integers (possibly with repetitions), your goal is to find whether there is a sub-array All: r] such that Ali) = n. Example. Given A = [13, 1,2, 3, 4, 7, 2, 3,8, 9] for n = 10, the answer is Yes since elements in A2 : 5] add up to n = 10. On the other hand, if the input array is A = [3, 2,6,8, 20, 2, 4] for n = 7, the answer is No since no sub-array of A adds up ton=7. Hint: Observe that if Ali] = n, then Ali] = E A[i] – n; this may come handy!
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...
Related questions
Question
algorithms are solely theoretical for a and b. please number the steps of the
![Problem 3. Given an array A[1 : n] of n positive integers (possibly with repetitions), your goal is to find
whether there is a sub-array A[l : r] such that
Ali] = n.
10, the answer is Yes since elements in A[2 : 5] add
Example. Given A = [13, 1,2, 3, 4, 7,2, 3, 8, 9] for n
up to n = 10. On the other hand, if the input array is A = [3, 2,6, 8, 20, 2, 4] for n = 7, the answer is No
since no sub-array of A adds up to n = 7.
%3D
%3D
Hìnt: Observe that if Ali] = n, then Ali] = E-1 A[i] – n; this may come handy!
(a) Design an algorithm for this problem with worst-case runtime of O(n).
(b) Now suppose our goal is to instead find whether there is a sub-array A[l, r] such that
Ali] = n².
Design a randomized algorithm for this case with worst-case expected runtime of O(n).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff26fda3f-4323-495f-b28b-f131dcfa5992%2F97288ef6-acdc-4a48-9c3c-0b57eabecc1c%2Fj486idb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 3. Given an array A[1 : n] of n positive integers (possibly with repetitions), your goal is to find
whether there is a sub-array A[l : r] such that
Ali] = n.
10, the answer is Yes since elements in A[2 : 5] add
Example. Given A = [13, 1,2, 3, 4, 7,2, 3, 8, 9] for n
up to n = 10. On the other hand, if the input array is A = [3, 2,6, 8, 20, 2, 4] for n = 7, the answer is No
since no sub-array of A adds up to n = 7.
%3D
%3D
Hìnt: Observe that if Ali] = n, then Ali] = E-1 A[i] – n; this may come handy!
(a) Design an algorithm for this problem with worst-case runtime of O(n).
(b) Now suppose our goal is to instead find whether there is a sub-array A[l, r] such that
Ali] = n².
Design a randomized algorithm for this case with worst-case expected runtime of O(n).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Computer Networking: A Top-Down Approach (7th Edi…](https://www.bartleby.com/isbn_cover_images/9780133594140/9780133594140_smallCoverImage.gif)
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
![Computer Organization and Design MIPS Edition, Fi…](https://www.bartleby.com/isbn_cover_images/9780124077263/9780124077263_smallCoverImage.gif)
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
![Network+ Guide to Networks (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337569330/9781337569330_smallCoverImage.gif)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
![Computer Networking: A Top-Down Approach (7th Edi…](https://www.bartleby.com/isbn_cover_images/9780133594140/9780133594140_smallCoverImage.gif)
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
![Computer Organization and Design MIPS Edition, Fi…](https://www.bartleby.com/isbn_cover_images/9780124077263/9780124077263_smallCoverImage.gif)
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
![Network+ Guide to Networks (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337569330/9781337569330_smallCoverImage.gif)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
![Concepts of Database Management](https://www.bartleby.com/isbn_cover_images/9781337093422/9781337093422_smallCoverImage.gif)
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
![Prelude to Programming](https://www.bartleby.com/isbn_cover_images/9780133750423/9780133750423_smallCoverImage.jpg)
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
![Sc Business Data Communications and Networking, T…](https://www.bartleby.com/isbn_cover_images/9781119368830/9781119368830_smallCoverImage.gif)
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY