Question

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?

Answer 1

1,048,576 is 1,024 times 1,024, 1,024 * 1,024 or 1,024 squared or 1,024^2. If a computer takes x amount of time to sort 1,024 elements then the relationship is a 1 to 1. Therefore the computer will take x times x or x^2 (x squared) amount of time to sort 1,048,576.