Sorting algorithms are incredibly important and used by us on a daily basis. In this course we have investigated and analyzed numerous sorting algorithms. In each of the following questions, you are given an input array A with n elements, where n is a very large positive integer. You will then compare two sorting algorithms and justify which of the two algorithms is faster in sorting this array A. In your responses, you must clearly explain which of the two algorithms runs faster. Make sure you rigorously justify your answer, carefully proving whether each algorithm is O(n), O(n log n), or O(n2). (a) Let A = [5, 5, 5, 5, 5, . . . , 5] be an array where all of the elements are equal to 5. Determine whether Selection Sort or Insertion Sort sorts this array faster. (b) Let A = [n, n -1, n - 2, . . . . 3, 2, 1] be an array where the rst n positive integers are listed in decreasing order. Determine whether Heapsort or Quicksort sorts this array faster. For this question, assume the Quicksort pivot is always the right-most element. (c) Let A be an array, where each of the n elements is a randomly chosen integer between 1 and n. For example, if n = 12, this array could be A = [3, 5, 1, 10, 5, 7, 9, 12, 2, 8, 8, 6]. Determine whether Bubble Sort or Bucket Sort sorts this array faster.
Sorting algorithms are incredibly important and used by us on a daily basis. In this course we have
investigated and analyzed numerous sorting algorithms.
In each of the following questions, you are given an input array A with n elements, where n is a very large
positive integer. You will then compare two sorting algorithms and justify which of the two algorithms
is faster in sorting this array A.
In your responses, you must clearly explain which of the two algorithms runs faster. Make sure you
rigorously justify your answer, carefully proving whether each
(a) Let A = [5, 5, 5, 5, 5, . . . , 5] be an array where all of the elements are equal to 5.
Determine whether Selection Sort or Insertion Sort sorts this array faster.
(b) Let A = [n, n -1, n - 2, . . . . 3, 2, 1] be an array where the rst n positive integers are listed in
decreasing order.
Determine whether Heapsort or Quicksort sorts this array faster.
For this question, assume the Quicksort pivot is always the right-most element.
(c) Let A be an array, where each of the n elements is a randomly chosen integer between 1 and n.
For example, if n = 12, this array could be A = [3, 5, 1, 10, 5, 7, 9, 12, 2, 8, 8, 6].
Determine whether Bubble Sort or Bucket Sort sorts this array faster.
(d) Let A be an array, where each of the n elements is a randomly chosen digit between 0 and 9.
For example, if n = 12, this array could be A = [3, 5, 1, 0, 5, 7, 9, 2, 2, 8, 8, 6].
Determine whether Counting Sort or Merge Sort sorts this array faster.
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