Lecture 03-03-17

Sorting Continued (Radix Sort)

post office sort / bucket sort
Comparison sorting: no gaps
Because there are gaps, have to go through at the end and pick up the “boxes”
Runtime is not only dependent on input but also dependent on the range
n numbers in range O-m
- Time: n + m
- Consideration: is m smaller than nlogn
- If m is bad, then can refine to do better
- Good only up to m < nlogn
Regular bucket sort will do very badly if numbers in the range of 1 to n²
Won’t be good for arbitrary things
Won’t be good if range is something like n^logn

Ex: 1000 numbers in the range up to a 1,000,000
Ex: 10 numbers in range of 0 to 99
Computers can write numbers in any base easily
- Even non 2^k bases
Numbers in the range 0 to n²-1: 2 digit number in base n
Set up 10 buckets
- 0 to 9
- Put in buckets by least significant digit
  - Example
    - 0: 10, 50, etc
- By most significant digits
  - Sort within bucket
- General:
  - Least significant to most significant
  - Bucket sort on that digit until you’re done
Sorts correctly in k passes for k digit numbers
Time complexity:
- Number of digits * number of inputs
Radix not taught because other sorting algorithms have no choice
Choice in radix sort: what base to choose
- Affects how many digits there are in the number
Small base: lot of buckets
Large base: small pass, but then dependent on input size
Poor applications
- Sorting people