(b) Consider using the following algorithm on an array A = [5, 3, 6, 4, 1]. %3D Input: Array A[1...n] Output: ?? 1 for i 2 ton do K+ A[i] j+i-1 while j > 0 and Alj] > K do A[j + 1] + A[j] j+j-1 A[j] + K 8 return A 2 4 6 i. Write the array A after each iteration of the outer For-loop, and state what you think the algorithm does. Show all your working.
(b) Consider using the following algorithm on an array A = [5, 3, 6, 4, 1]. %3D Input: Array A[1...n] Output: ?? 1 for i 2 ton do K+ A[i] j+i-1 while j > 0 and Alj] > K do A[j + 1] + A[j] j+j-1 A[j] + K 8 return A 2 4 6 i. Write the array A after each iteration of the outer For-loop, and state what you think the algorithm does. Show all your working.
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part b i
![2.
(a) Write an algorithm in pseudo-code that
• takes as input an array A[1...n], and an item M which occurs at least once
in A.
• returns the index (position) of the last occurrence of the item M in array A.
The following table shows some examples with the expected output of the
algorithm (the last occurrences of M is underlined):
input: A
output
[1,8, 1, 7, 1, 9
[4, 3, 2, 2, 2, 3] 2
[9, 9]
[3, 3, 3, 3]
[4, 3, 3, 3]
1
9.
4
4
Your algorithm should perform as few comparisons as possible.
(b) Consider using the following algorithm on an array A = [5,:
Input: Array A[1...n]
Output: ??
1 for i + 2 to n do
K+ A[i]
j+i-1
while j > 0 and A[j] > K do
A[j + 1] + A[j]
j+j-1
A[j] +
3
4
7
8 return A
i. Write the array A after each iteration of the outer For-loop, and state what
you think the algorithm does. Show all your working.
ii. How many times will line 5 be executed for the array A? How many times
for an array of length n?
ii. How many times will line 4 be executed in the worst case for the array A?
How many times for an array of length n?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20e4511a-d662-4cd1-a8fd-e4373aa191f8%2F96f08365-a88e-47a6-b916-86d03a446a08%2Ff27vw2r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
(a) Write an algorithm in pseudo-code that
• takes as input an array A[1...n], and an item M which occurs at least once
in A.
• returns the index (position) of the last occurrence of the item M in array A.
The following table shows some examples with the expected output of the
algorithm (the last occurrences of M is underlined):
input: A
output
[1,8, 1, 7, 1, 9
[4, 3, 2, 2, 2, 3] 2
[9, 9]
[3, 3, 3, 3]
[4, 3, 3, 3]
1
9.
4
4
Your algorithm should perform as few comparisons as possible.
(b) Consider using the following algorithm on an array A = [5,:
Input: Array A[1...n]
Output: ??
1 for i + 2 to n do
K+ A[i]
j+i-1
while j > 0 and A[j] > K do
A[j + 1] + A[j]
j+j-1
A[j] +
3
4
7
8 return A
i. Write the array A after each iteration of the outer For-loop, and state what
you think the algorithm does. Show all your working.
ii. How many times will line 5 be executed for the array A? How many times
for an array of length n?
ii. How many times will line 4 be executed in the worst case for the array A?
How many times for an array of length n?
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