Merge sort has a O(n log₂(n)) complexity.If a computer can sort 1,024 elements in an amount of time x, approximately how long will it take the computer to sort 1,024 times that many, or 1,048,576 elements? A)8,192x B)1,024x C)2,048x D)1,048,576x

Question

Quizplus · Accepted Answer

The time complexity of merge sort is `O(n log n)`, where `n` is the number of elements being sorted. If a computer can sort 1024 elements in time `x`, then the time it would take to sort 1048576 (1024^2) elements is:

`T = n log n * x`
`T = 1048576 log 1048576 * x`
`T ≈ 2097152 * x`

Therefore, it would take approximately 2097152 times as long to sort 1048576 elements as it would to sort 1024 elements. So, the answer is C) 2048x.

Merge Sort Has a O(n Log2(n)) Complexity

Merge Sort Has a O(n Log₂(n)) Complexity