using a part of counting sort algorithm for returning the numbers of elements between a and b

Question

Hi I have found this question in the one site which was about counting sort algorithm and this question was an exercise ! I solved this and I want to know that is this correct?

Exercise: Use The idea of Counting Sort algorithm and provide an algorithm with n integer in the range 0 to k, in time O (1) replied that how many of these n elements are in the interval [a, b] ? Of course, your algorithm should process n elements that can help you take the numbers between a and b (0 ≤ a, b ≤ k) . This basic process should be in time Θ (n + k) .

this is my algorithm:

Algorithm Range(A,k,a,b)
{Consider C is the output array of PartOfCountingSort algorithm}
C<--PartOfCountingSort(A,k)
//finding the number of elements between a and b
numberOfElements<-- C[b]-C[a]+1
return numberOfElements
//end of the Range algorithm
------------------------------------
PartOfCountingSort(A,k)  // Theta(n+k)
OutPut: array C is the output of this algorithm
   for  i<-- 1 to k
      C[i]<-- 0
   for  j<-- 1 to A. length
      C[A[j]]<--C[A[j]]+1
   for  i<--2 to k
      C[i]<--C[i]+C[i-1]

Answer 1

It should be

numberOfElements<-- C[b]-C[a - 1]

Recall that C[i] = number of elements lower than or equal to i. You don't want to subtract those equal to a.

You should also handle the cases where a = 0 and maybe when a = 1 too.