Radix Sort

1
Radix Sort

• CSC 172
• SPRING 2004
• LECTURE 25

2
Theoretical bound?

• A n logn t
• A 524,288 19 111
• A 1.110-5
• 1.110-5 134,217,728 27 40,380
• 1.110-5 524,288 256 27/19 40,380
• But we got 26,700 111 256

3
What happened?

• The key word in the theoretical proof was
  comparison based
• Some sorts are not comparison based

4
Radix Sort

• Unlike other methods, radix sort considers the
  structure of the keys
• Assume that the keys are represented in base M
  number system (M radix)
• i.e. if M 2 we are in the binary number system
• 910 10012
• Sorting is done by comparing bits in the same
  position
• This will extend to keys that are alphanumeric
  strings

5
Radix Exchange Sort
Sort array with respect to the leftmost bit
6
Radix Exchange Sort
Partition Array
Recursively sort subarrays Ignoring leftmost bit
7
Time

• How many bits in the keys? b
• How much work per bit? N
• O(bN)
• Not bad for 16 bit shorts

8
Exchange

• In place, like Quicksort
• Repeat
• Scan top-down to find a 1
• Scan bottom-up to find a 0
• Exchange keys
• Until scan indices cross

9

• public static void mySorter(shortB)
• int mask 0x8000
• mySorter(B,0,B.length -1, mask)

10

• public static void mySorter(short B,int
  bottom,int top, int mask)
• if (mask lt 0 ) return
• int oldtop top
• int oldbottom bottom
• while (top gt bottom)
• while ((bottom lt (B.length - 1))
• ((((int) Bbottom) mask) 0)) bottom
• while ((top gt0) ((((int) Btop) mask) gt
  0)) top --
• if (top gt bottom)
• short temp Bbottom
• Bbottom Btop
• Btop temp
• mySorter(B,oldbottom,top,maskgtgt1)
• mySorter(B,top1,oldtop,maskgtgt1)
• return