Non Comparison Based Sorts

• A little more from CLRS
• (I don't like his comparison-counting sort in the book)
• Counting Sort
  • Assumes the key is an integer in the range 0 ... k
  • Assumes the array is from 1 to n (but no problem to shift)

  • COUNTING_SORT(A,k)
    
     fori ← 0 to k do
         C[i] ← 0
     fori ← 0 to n-1 do
         C[A[i]] ← C[A[i]] + 1
     fori ← 1 to k do
         C[i] ← C[i] + C[i-1]
     fori ← 0 to n-1 do
         B[C[A[i]]] ←  A[i]
         C[A[i]] ← C[A[i]] -1
    
    	 

  • Standard questions.
  • What about space?
• Radix Sort
  • Assumes a stable sort exists.
    • A stable sort does not exchange the position of values with equal keys.
    • Bubble and insertion sort can be stable.

  • RADIX_SORT(A,d)
    
     for i ← 1 to d do
         use a stable sort to sort A on digit i
    
    	 

  • Sort 329 457 657 839 436 720 355
  • This is d*O(sort algorithm)
• Bucket Sort
  • Assume the data is uniform on [0, 1)
  • (Or can be mapped to that)

  • BUCKET_SORT(A)
    
     n ← length(A)
     for i < 1 to n do
         insert A[i] into bin B[⌊n*A[i]⌋]
     for i < 1 to n do
         sort B[i] with insertion sort
     for i < 1 to n do
         A ← A + B[i]  // concatenation
    
    	

  • we claim line five is O(1), why?
  • Then the entire thing is O(n), why?