Algorithms | Sorting | Question 12

What is the worst case time complexity of insertion sort where position of the data to be inserted is calculated using binary search?

(A)

N

(B)

N*log(N)

(C)

N²

(D)

N*log(N)²

Answer: (C)

Explanation:

Applying binary search to calculate the position of the data to be inserted doesn’t reduce the time complexity of insertion sort.

This is because the insertion of data at an appropriate position involves two steps:

1. Calculate the position.
2. Shift the data from the position calculated in step #1 one step right to create a gap where the data will be inserted.
3. Using binary search reduces the time complexity in step #1 from O(N) to O(log(N)). But, the time complexity in step #2 still remains O(N).

 So, overall complexity remains O(N²).

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