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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 E A[i] = n. i=l Example. Given A = up to n = 10. On the other hand, if the input array is A = since no sub-array of A adds up to n = 7. [13, 1, 2, 3, 4, 7, 2, 3, 8, 9] for n = 10, the answer is Yes since elements in A[2 : 5] add [3, 2, 6, 8, 20, 2, 4] for n = 7, the answer is No Hint: Observe that if -, A[i] = n, then A[i] = E=1 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 A[l : r] such that E A[i] = n. i=l Example. Given A = up to n = 10. On the other hand, if the input array is A = since no sub-array of A adds up to n = 7. [13, 1, 2, 3, 4, 7, 2, 3, 8, 9] for n = 10, the answer is Yes since elements in A[2 : 5] add [3, 2, 6, 8, 20, 2, 4] for n = 7, the answer is No Hint: Observe that if -, A[i] = n, then A[i] = E=1 A[i] - n; this may come handy!

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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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 EAli) = n. i=l Example. Given A = 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. [13, 1, 2, 3, 4, 7, 2, 3, 8,9] for n = 10, the answer is Yes since elements in A[2 : 5] add Hint: Observe that if - A[i] = n, then A[i] = E-1 A[i] - - n; this may come handy!
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 EAli) = n. i=l Example. Given A = 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. [13, 1, 2, 3, 4, 7, 2, 3, 8,9] for n = 10, the answer is Yes since elements in A[2 : 5] add Hint: Observe that if - A[i] = n, then A[i] = E-1 A[i] - - n; this may come handy!
(b) Now suppose our goal is to instead find whether there is a sub-array A[l, r] such that Ali] = n². i=l Design a randomized algorithm for this case with worst-case expected runtime of O(n).
Transcribed Image Text:(b) Now suppose our goal is to instead find whether there is a sub-array A[l, r] such that Ali] = n². i=l Design a randomized algorithm for this case with worst-case expected runtime of O(n).
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