Q:

An array of length N can contain values 1,2,3 ... N^2. Is it possible to sort in O(n) time?

Given an array of length N. It can contain values from ranging from 1 to N^2 (N squared) both inclusive, values are integral. Is it possible to sort this array in O(N) time? If possible how?
Edit: This is not a homework.

A:

Write each integer in base N, that is each x can be represented as (x1, x2) with x = 1 + x1 + x2*N. Now you can sort it twice with counting sort, once on x1 and once on x2, resulting in the sorted array.

A:

Yes, you can, using radix sort with N buckets and two passes. Basically, you treat the numbers as having 2 digits in base N.

