The Algorithm Mergesort, calls the Algorithm Merge. i) Determine the number of comparisons required by Algorithm Merge to merge the arrays A = [12, 15, 26, 29, 36] and B = [2, 5, 14, 25, 35, 47, 49] (ii) Perform a desk trace of the algorithm Merge to show how the arrays A and B are combined. (iii) The computational complexity for Algorithm Merge is O(n) in the worst case. Explain how this was obtained. (iv) Let C(n) be the number of key comparisons required to execute Algorithm Mergesort on a list of n elements. Write a recurrence relation for the number of comparisons made by the algorithm in the worst case. Explain how each term is obtained.
The Algorithm Mergesort, calls the Algorithm Merge. i) Determine the number of comparisons required by Algorithm Merge to merge the arrays A = [12, 15, 26, 29, 36] and B = [2, 5, 14, 25, 35, 47, 49] (ii) Perform a desk trace of the algorithm Merge to show how the arrays A and B are combined. (iii) The computational complexity for Algorithm Merge is O(n) in the worst case. Explain how this was obtained. (iv) Let C(n) be the number of key comparisons required to execute Algorithm Mergesort on a list of n elements. Write a recurrence relation for the number of comparisons made by the algorithm in the worst case. Explain how each term is obtained.
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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The
i) Determine the number of comparisons required by Algorithm Merge to merge the arrays A = [12, 15, 26, 29,
36] and B = [2, 5, 14, 25, 35, 47, 49]
(ii) Perform a desk trace of the algorithm Merge to show how the arrays A and B are
combined.
(iii) The computational complexity for Algorithm Merge is O(n) in the worst case.
Explain how this was obtained.
(iv) Let C(n) be the number of key comparisons required to execute Algorithm Mergesort
on a list of n elements. Write a recurrence relation for the number of comparisons
made by the algorithm in the worst case. Explain how each term is obtained.
![ALGORITHM Merge(B[0..p- 1], C[0..q - 1], A[0..p+q-1])
//Merges two sorted arrays into one sorted array
//Input: Arrays B[0..p - 1] and C[0..q - 1] both sorted
//Output: Sorted array A[0..p+q - 1] of the elements of B and C
i←0; j←0; k ←0
while i < p and j <q do
if B[i] ≤ C[j]
A[k]← B[i]; i←i+1
else A[k]C[j]; j←j+1
k+k+1
if i = p
copy C[j..q - 1] to A[k..p+q - 1]
else copy B[i..p - 1] to A[k..p+q − 1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16a501d0-ad86-4e86-a9d4-08a716d78319%2F49193690-fc1f-45db-a57d-1f7fcdeae36c%2Fp7sfu0w_processed.png&w=3840&q=75)
Transcribed Image Text:ALGORITHM Merge(B[0..p- 1], C[0..q - 1], A[0..p+q-1])
//Merges two sorted arrays into one sorted array
//Input: Arrays B[0..p - 1] and C[0..q - 1] both sorted
//Output: Sorted array A[0..p+q - 1] of the elements of B and C
i←0; j←0; k ←0
while i < p and j <q do
if B[i] ≤ C[j]
A[k]← B[i]; i←i+1
else A[k]C[j]; j←j+1
k+k+1
if i = p
copy C[j..q - 1] to A[k..p+q - 1]
else copy B[i..p - 1] to A[k..p+q − 1]
![Mergesort Algorithm
ALGORITHM Mergesort(A[0..n – 1])
//Sorts array A[0..n - 1] by recursive mergesort
//Input: An array A[0..n - 1] of orderable elements
//Output: Array A[0..n - 1] sorted in nondecreasing order
if n > 1
copy A[0..[n/2] - 1] to B[0..[n/2] - 1]
copy A[[n/2]..n - 1] to C[0.. [n/2] - 1]
Mergesort (B[0..[n/2] - 1])
Mergesort (C[0..[n/21 - 1])
Merge(B, C, A) //see below](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16a501d0-ad86-4e86-a9d4-08a716d78319%2F49193690-fc1f-45db-a57d-1f7fcdeae36c%2Fnk2ydgx6_processed.png&w=3840&q=75)
Transcribed Image Text:Mergesort Algorithm
ALGORITHM Mergesort(A[0..n – 1])
//Sorts array A[0..n - 1] by recursive mergesort
//Input: An array A[0..n - 1] of orderable elements
//Output: Array A[0..n - 1] sorted in nondecreasing order
if n > 1
copy A[0..[n/2] - 1] to B[0..[n/2] - 1]
copy A[[n/2]..n - 1] to C[0.. [n/2] - 1]
Mergesort (B[0..[n/2] - 1])
Mergesort (C[0..[n/21 - 1])
Merge(B, C, A) //see below
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