Given an unsorted array. The array has this property that every element in the array is at most k distance from its position in sorted array where k is a positive integer smaller than the size of the array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity? (A) Insertion Sort with time complexity O(kn) (B) Heap Sort with time complexity O(nLogk) (C) Quick Sort with time complexity O(kLogk) (D) Merge Sort with time complexity O(kLogk)

Considering the following algorithm, analyze its best case, worst case and average case time complexity in terms of a polynomial of n and the asymptotic notation of ɵ. You need to show the steps of your analysis.

Assume that you are given an array containing n integer numbers from the set {0, 1, . . . , k} for some k ≤ n. Design an algorithm to produce a sorted array containing those n numbers in non-decreasing order in time O(n). Present the pseudocode for the algorithm and provide a justification for its running time.

Please justify your answer: Some sorting algorithms require extra space, apart from the space needed for the original  array that needs to be sorted. Which one of the following statements on the space usage of  sorting algorithms is correct?  a.)  A Heapsort for sorting an array of size N requires an amount of extra space proportional  to N.   b.)  Insertion Sort for sorting an array of size N requires an amount of extra space  proportional to N.   c.)  Merge sort for sorting an array of size N requires an amount of extra space proportional  to N.   d.) Quicksort for sorting an array of size N requires an amount of extra space proportional  to N.   e.) None of the above