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algorithmsortingradix-sort

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.

Solution

  • 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.

    EDIT: As others mentioned below, sorting on each 'digit' separately like this is is called a radix sort. Sorting on each digit with counting sort takes O(N) time and O(N) space (in this particular case). Since we repeat it exactly twice, this gives a total running time of O(N).