Distribution sorting algorithms

Bucket sort

Note: this differs from CLR.

Assumes that, for all i, K_i in {1...m}.

BUCKET SORT
    for j := 1 to m do
       Lj := Λ
    for i := 1 to n do
       append Ki to end of LKi
    L := Λ
    for j := 1 to m do
       concatenate Lj to end of L

T is Θ(m + n)
S is Θ(m) for listheads

Lexicographic (Radix) sort

Do a bucket sort on the least significant digit of the keys, keeping those with equal digits in the same relative order.
Iterate on the next significant digit, etc.

LEXICOGRAPHIC SORT
    Q := Λ
    for j := 0 to M-1 do
       Qj := Λ
    Q ← K1, ..., Km
    for t := r downto 1 do
       while Q ≠ Λ do
          Ki ← Q
          Qdi,t ← Ki
       for j := 0 to M-1 do
          Q := Q | Qj

T is Θ((M+n)r)
S is Θ(M+n)

Example:

Initial	after pass 1	after pass 2	after pass 3
010 112 001 012 100 002 020	010 100 020 001 112 012 002	100 001 002 010 112 012 020	001 002 010 012 020 100 112