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Consider the numbers 94, 53, 96, 87, 43, 75, 23, 75, 35, 34, 20, 94, 28. Sort the numbers in increasing order (smallest number first, largest number last) using Shell sort, with gaps 6, 3, and 1. Show all steps in the evolution of the sort.

A) 94, 53, 96, 87, 43, 75, 23, 75, 35, 34, 20, 94, 28
B) 20, 23, 28, 34, 35, 43, 53, 75, 75, 87, 94, 94, 96
C) 96, 94, 94, 87, 75, 75, 53, 43, 35, 34, 28, 23, 20
D) 20, 23, 28, 34, 35, 43, 53, 75, 75, 87, 94, 94, 96

Answer :

Final answer:

Following the Shell sort algorithm with gaps of 6, 3, and 1, the array is sorted through multiple passes, resulting in a final sorted array of numbers in increasing order.

Explanation:

When sorting the numbers 94, 53, 96, 87, 43, 75, 23, 75, 35, 34, 20, 94, 28 using Shell sort with gaps of 6, 3, and 1, we need to sort segments of the array that are 6, 3, and 1 indices apart, respectively, in multiple passes. First, we sort elements that are 6 indices apart, then 3, and finally we perform a regular insertion sort with a gap of 1.

After sorting with a gap of 6: 20, 53, 43, 87, 94, 75, 23, 75, 35, 34, 96, 94, 28.

Next, sorting with a gap of 3: 20, 34, 43, 23, 94, 75, 35, 75, 96, 53, 94, 87, 28.

Finally, sorting with a gap of 1 (usual insertion sort): 20, 23, 28, 34, 35, 43, 53, 75, 75, 87, 94, 94, 96.

This final list is our sorted array in increasing order.

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