Question

We are given an array A holding n integers, for some large n. The array is sorted, and the
values in A range from -2147483648 to 2147483647, evenly distributed. Give Θ expressions
for the following tasks:
A. Running the insertion sort algorithm on the array A:
B. Running the selection sort algorithm on the array A:
C. Performing binary search for integer k which is not in A:
D. Performing interpolation search for integer k not in A:

Answer 1

A. Running the insertion sort algorithm on the array A:

(N), Insertion Sort takes (N) in best case as the Input is Sorted

B. Running the selection sort algorithm on the array A:

(N²), Selection Sort takes (N²) in worst case nd does not care much about the input. Even with Sorted Input it takes

(N²) time

C. Performing binary search for integer k which is not in A:

(Log N), Binary search space reduces by half hence it takes (Log N) time

D. Performing interpolation search for integer k not in A:

In worst case it can take upto O(n), hence (N)

Thanks, PLEASE COMMENT if there is any concern.