Question

If we have some m>0 and need to provide an algorithm to sort n integers in the range 0 to n^m-1 in time O(mn). My suggestion is :

Radix-Sort(A,t)  // t is the digit length
for i=0 to t
    do Insertion-Sort A on digit i

My argument is that the above will run in O(mn) because for each digit t – Insertion sort will take O(n) time since the range for each run is small.

Is this the correct suggestion? What should be the space requirement of the above?

Thanks.

Answer 1

The space requirement is O(m + n) because you need the original numbers and m buckets to place the n items. The runtime is O(mn) which can be >> n which is the issue with radix sort. In all cases its O(mn) but the problem is that if m > n you get something larger than O(n^2). Depending on how it’s written the memory can also be O(mn) in the worst case because you create m copies of the set of n numbers to sort on.