Non-Comparison Based Sorts:Counting Sort

• Counting sort
  • Assume you have integer data, 1 ≤ d ≤ k.
  • We can assume that there is auxiliary data, we are just looking at the key.

  • 
    COUNTING_SORT(A)
     For i = 0 to k 
       C[i] = 0
     EndFor
     For i = 1 to A.size-1
       C[A[i]]++
     EndFor
     For i = 1 to k
        C[i] = C[i] + C[i-1]
     EndFor
     For j = A.size-1 downto 0
        C[A[j]] --
        B[C[A[j]]] = A[j]
     EndFor
     

  • Trace this with 7 1 3 1 2 4 5 7 2 4 3
  • Does this work?
  • What is the performance?
  • Claim: Counting sort is stable
  • Counting sort is not in place