Question

Algorithm to sort a list L of n positive integer keys which need not to be distinct. Should have complexity of O(n+N) where N = maxL(i) - minL(i)?

I tried to something like merge sort, but that gives me O(nlogn). I am given O(N) extra space so it doesn’t have to be O(n) complexity. However, i don’t know if my mergesort-like algorithm is allowed to take a multiplicity of log n times. please help?

Answer 1

The algorithm you describe seems to be a variant of the “count sort” (I was taught it as “librarian sort”, ordinamento del libraio)

This is the pseudocode from Wikipedia:

''' allocate an array Count[0..k] ; initialize each array cell to zero ; THEN '''
for each input item x:
    Count[key(x)] = Count[key(x)] + 1
total = 0
for i = 0, 1, ... k:
    c = Count[i]
    Count[i] = total
    total = total + c

''' allocate an output array Output[0..n-1] ; THEN '''
for each input item x:
    store x in Output[Count[key(x)]]
    Count[key(x)] = Count[key(x)] + 1
return Output

http://en.wikipedia.org/wiki/Counting_sort