Question

Problem 5. Superfast Software Inc. was founded last year by three young

programmers. They all dreamed their company would become a really big

one and would distribute a large number of software products all over the

world. Thus, they decided to use 64-bit integers to represent their inventory

codes. Since it is just a one-year-old company, the inventory database now

contains only 2000 distinct product codes, in the range from 1 to 3000. At

this time they need to sort these codes and one of the co-founders sug-

gests using a general comparison-based O(nlogn)-time sorting algorithm

such as heap-sort. But another co-founder disagrees and suggests using

radix-exchange sort because it is a so-called "linear time" (that is, O(n))

algorithm. Do you think radix exchange sort is good for this case? Explain

your answer.

Answer 1

Heap sort have time complexity of n*log(n) whereas in Radix Sort , time complexity is n*k (where k is the max. no. of digits in the number to be stored).

Since the range is from 1 to 3000 and number to be sorted are 2000. Mathematically , in Radix sort , time complexity will be = 2000*4 = 8000.

And in heap sort , time complexity will be = 2000*log(2000) = 6602.05999133.

So, i think Heap sort will be given preference over Radix sort.