Part A: The Fixed Point Problem is: Given a sorted array of distinct elements A[1...n), determine whether there exists some i such that A[i] = i. Consider the following recursive algorithm (and assume that the function returns nothing if the array A is empty): function f(A[1...n]): m = []; if A[m] = m return m; if A[m] > m return f(A[1...m-1]); if A[m] m so the algorithm always misses half the list. O Yes. If A[m]>m, then it is impossible to have A[i] = i for any i 2 m (and the same for the other case). O No. It is impossible for A[m]
Part A: The Fixed Point Problem is: Given a sorted array of distinct elements A[1...n), determine whether there exists some i such that A[i] = i. Consider the following recursive algorithm (and assume that the function returns nothing if the array A is empty): function f(A[1...n]): m = []; if A[m] = m return m; if A[m] > m return f(A[1...m-1]); if A[m] m so the algorithm always misses half the list. O Yes. If A[m]>m, then it is impossible to have A[i] = i for any i 2 m (and the same for the other case). O No. It is impossible for A[m]
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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*If you answer the questions correctly and completely, I will give you a thumbs up. Thanks.
![Part A: The Fixed Point Problem is: Given a sorted array of distinct elements A[1 ….. n), determine whether there exists some į such that A[i] = i. Consider the following recursive algorithm (and
assume that the function returns nothing if the array A is empty):
function f(A[1...n]): m = []; if A[m] = m return m; if A[m] > m return f(A[1...m-1]); if A[m] <m return f(A[m +1...n]);
Does this algorithm work? If so, why? If not, why not?
O No. There is no base case.
O No. It is impossible for A[m] > m so the algorithm always misses half the list.
O Yes. If A[m] > m, then it is impossible to have A[i] = for any i > m (and the same for the other case).
O No. It is impossible for A[m] < m so the algorithm always misses half the list.
Part B: Independent of whether it produces the correct answer, what is the running time of the Fixed Point algorithm in terms of n?
○ 0 (√n)
○ O(n)
(n log n)
○ (log n)
* Please answer both parts correctly, and I will provide a thumbs up. Thanks.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1223c4c6-4ebb-4911-bc0d-edb37c26385f%2F2989a252-1c93-4850-ba49-e15e8c912bd2%2Fqngqw0b_processed.png&w=3840&q=75)
Transcribed Image Text:Part A: The Fixed Point Problem is: Given a sorted array of distinct elements A[1 ….. n), determine whether there exists some į such that A[i] = i. Consider the following recursive algorithm (and
assume that the function returns nothing if the array A is empty):
function f(A[1...n]): m = []; if A[m] = m return m; if A[m] > m return f(A[1...m-1]); if A[m] <m return f(A[m +1...n]);
Does this algorithm work? If so, why? If not, why not?
O No. There is no base case.
O No. It is impossible for A[m] > m so the algorithm always misses half the list.
O Yes. If A[m] > m, then it is impossible to have A[i] = for any i > m (and the same for the other case).
O No. It is impossible for A[m] < m so the algorithm always misses half the list.
Part B: Independent of whether it produces the correct answer, what is the running time of the Fixed Point algorithm in terms of n?
○ 0 (√n)
○ O(n)
(n log n)
○ (log n)
* Please answer both parts correctly, and I will provide a thumbs up. Thanks.
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