Question

This is a counting sort algorithm. I want to change the last for loop of it to for j<---1 to n.
I know that this will be correct, but I want to show this for one of my friends. How can I write my reason for it? Please help me! Thanks.

Counting Sort(A[1,..n]) //C[1,...k] is the temporary memory and k is the range of integers
   for  i<-- 1 to k
      C[i]<-- 0
   for  j<-- 1 to n
      C[A[j]]<--C[A[j]]+1
   for  i<--2 to k
      C[i]<--C[i]+C[i-1]
   for  j<--n downto 1
      B[C[A[j]]]<--A[j]
      C[A[j]]<--C[A[j]]-1

Answer 1

The above code is absolutely correct. If you change the last loop from 1 to n the output will be correct but the relative order of the elements with same values will get reversed. For e.g – If original array contains only 3 elements and all of them are let say 5 then in case of 1 to n, the last five will be the first element, second last 5 will be the second element and the first 5 will be the last element i.e relative order of same elements got reversed.