Sorting algorithms/Radix sort

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Task
Sorting algorithms/Radix sort
You are encouraged to solve this task according to the task description, using any language you may know.

Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.

For other sorting algorithms, see Category:Sorting Algorithms, or:
O(n logn) Sorts
Heapsort | Mergesort | Quicksort
O(n log2n) Sorts
Shell Sort
O(n2) Sorts
Bubble sort | Cocktail sort | Comb sort | Gnome sort | Insertion sort | Selection sort | Strand sort
Other Sorts
Bead sort | Bogosort | Counting sort | Pancake sort | Permutation sort | Radix sort | Sleep sort | Stooge sort | Sort three variables


Task

Sort an integer array with the   radix sort algorithm.

The primary purpose is to complete the characterization of sort algorithms task.

Ada

radix_sort.adb:

with Ada.Text_IO;
procedure Radix_Sort is
type Integer_Array is array (Positive range <>) of Integer;
 
procedure Least_Significant_Radix_Sort (Data : in out Integer_Array; Base : Positive := 10) is
type Bucket is record
Count  : Natural := 0;
Content : Integer_Array (Data'Range);
end record;
 
subtype Bucket_Index is Integer range -Base + 1 .. Base - 1;
type Bucket_Array is array (Bucket_Index) of Bucket;
 
procedure Append (To : in out Bucket; Item : Integer) is
begin
To.Count := To.Count + 1;
To.Content (To.Count) := Item;
end Append;
 
function Get_Nth_Digit (Value : Integer; N : Positive) return Integer is
Result : Integer := (Value / (Base ** (N - 1))) mod Base;
begin
if Value < 0 then
Result := -Result;
end if;
return Result;
end Get_Nth_Digit;
 
function Get_Maximum return Natural is
Result : Natural := 0;
begin
for I in Data'Range loop
if abs (Data (I)) > Result then
Result := abs (Data (I));
end if;
end loop;
return Result;
end Get_Maximum;
 
function Split (Pass : Positive) return Bucket_Array is
Buckets : Bucket_Array;
begin
for I in Data'Range loop
Append (To => Buckets (Get_Nth_Digit (Data (I), Pass)),
Item => Data (I));
end loop;
return Buckets;
end Split;
 
function Merge (Buckets : Bucket_Array) return Integer_Array is
Result  : Integer_Array (Data'Range);
Current_Index : Positive := 1;
begin
for Sublist in Buckets'Range loop
for Item in 1 .. Buckets (Sublist).Count loop
Result (Current_Index) := Buckets (Sublist).Content (Item);
Current_Index := Current_Index + 1;
end loop;
end loop;
return Result;
end Merge;
 
Max_Number  : Natural := Get_Maximum;
Digit_Count : Positive := 1;
begin
-- count digits of biggest number
while Max_Number > Base loop
Digit_Count := Digit_Count + 1;
Max_Number := Max_Number / Base;
end loop;
for Pass in 1 .. Digit_Count loop
Data := Merge (Split (Pass));
end loop;
end Least_Significant_Radix_Sort;
 
Test_Array : Integer_Array := (170, 45, 75, -90, -802, 24, 2, 66);
begin
Least_Significant_Radix_Sort (Test_Array, 4);
for I in Test_Array'Range loop
Ada.Text_IO.Put (Integer'Image (Test_Array (I)));
end loop;
Ada.Text_IO.New_Line;
end Radix_Sort;

output:

-802-90 2 24 45 66 75 170


ALGOL 68

PROC radixsort = (REF []INT array) VOID:
(
[UPB array]INT zero;
[UPB array]INT one;
BITS mask := 16r01;
INT zero_index := 0,
one_index := 0,
array_index := 1;
 
WHILE ABS(mask) > 0 DO
WHILE array_index <= UPB array DO
IF (BIN(array[array_index]) AND mask) = 16r0 THEN
zero_index +:= 1;
zero[zero_index] := array[array_index]
ELSE
one_index +:= 1;
one[one_index] := array[array_index]
FI;
array_index +:= 1
OD;
 
array_index := 1;
FOR i FROM 1 TO zero_index DO
array[array_index] := zero[i];
array_index +:= 1
OD;
 
FOR i FROM 1 TO one_index DO
array[array_index] := one[i];
array_index +:=1
OD;
 
array_index := 1;
zero_index := one_index := 0;
mask := mask SHL 1
OD
);
 
main:
(
[10]INT a;
FOR i FROM 1 TO UPB a DO
a[i] := ROUND(random*1000)
OD;
 
print(("Before:", a));
print((newline, newline));
radixsort(a);
print(("After: ", a))
)
Output:
Before:       +459       +941       +623       +386       +263       +766       +129       +554       +160       +328
                                                                                                                     
After:        +129       +160       +263       +328       +386       +459       +554       +623       +766       +941

AutoHotkey

Radix_Sort(data){
loop, parse, data, `,
n := StrLen(A_LoopField)>n?StrLen(A_LoopField):n
loop % n {
bucket := [] , i := A_Index
loop, parse, data, `,
bucket[SubStr(A_LoopField,1-i)] .= (bucket[SubStr(A_LoopField,1-i)]?",":"") A_LoopField
data := ""
for i, v in bucket
data .= (data?",":"") v
}
return data
}
Examples:
d = 170,45,75,90,802,2,24,66
MsgBox, 262144, , % Radix_Sort(d)
Outputs:
2,24,45,66,75,90,170,802

BBC BASIC

The array index is assumed to start at zero. The third parameter of PROCradixsort() is the radix used.

      DIM test%(9)
test%() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
PROCradixsort(test%(), 10, 10)
FOR i% = 0 TO 9
PRINT test%(i%) ;
NEXT
PRINT
END
 
DEF PROCradixsort(a%(), n%, r%)
LOCAL d%, e%, i%, l%, m%, b%(), bucket%()
DIM b%(n%-1), bucket%(r%-1)
FOR i% = 0 TO n%-1
IF a%(i%) < l% l% = a%(i%)
IF a%(i%) > m% m% = a%(i%)
NEXT
a%() -= l%
m% -= l%
e% = 1
WHILE m% DIV e%
bucket%() = 0
FOR i% = 0 TO n%-1
bucket%(a%(i%) DIV e% MOD r%) += 1
NEXT
FOR i% = 1 TO r%-1
bucket%(i%) += bucket%(i% - 1)
NEXT
FOR i% = n%-1 TO 0 STEP -1
d% = a%(i%) DIV e% MOD r%
bucket%(d%) -= 1
b%(bucket%(d%)) = a%(i%)
NEXT
a%() = b%()
e% *= r%
ENDWHILE
a%() += l%
ENDPROC

Output:

       -31         0         1         2         2         4        65        83        99       782

C

Radix sort, "digits" are most significant bits.
#include <stdio.h>
#include <limits.h>
#include <stdlib.h>
#include <time.h>
 
// Get size of statically allocated array
#define ARR_LEN(ARR) (sizeof ARR / sizeof *ARR)
// Generate random number in the interval [M,N]
#define RAND_RNG(M,N) (M + rand() / (RAND_MAX / (N - M + 1) + 1));
 
static void swap(unsigned *a, unsigned *b) {
unsigned tmp = *a;
*a = *b;
*b = tmp;
}
 
/* sort unsigned ints */
static void rad_sort_u(unsigned *from, unsigned *to, unsigned bit)
{
if (!bit || to < from + 1) return;
 
unsigned *ll = from, *rr = to - 1;
for (;;) {
/* find left most with bit, and right most without bit, swap */
while (ll < rr && !(*ll & bit)) ll++;
while (ll < rr && (*rr & bit)) rr--;
if (ll >= rr) break;
swap(ll, rr);
}
 
if (!(bit & *ll) && ll < to) ll++;
bit >>= 1;
 
rad_sort_u(from, ll, bit);
rad_sort_u(ll, to, bit);
}
 
/* sort signed ints: flip highest bit, sort as unsigned, flip back */
static void radix_sort(int *a, const size_t len)
{
size_t i;
unsigned *x = (unsigned*) a;
 
for (i = 0; i < len; i++)
x[i] ^= INT_MIN;
 
rad_sort_u(x, x + len, INT_MIN);
 
for (i = 0; i < len; i++)
x[i] ^= INT_MIN;
}
 
int main(void)
{
 
srand(time(NULL));
int x[16];
 
for (size_t i = 0; i < ARR_LEN(x); i++)
x[i] = RAND_RNG(-128,127)
 
radix_sort(x, ARR_LEN(x));
 
for (size_t i = 0; i < ARR_LEN(x); i++)
printf("%d%c", x[i], i + 1 < ARR_LEN(x) ? ' ' : '\n');
}
output
-182 -175 -151 -141 -70 -51 -20 -5 -1 41 70 103 171 198 227 242

C++

Implements a least significant digit radix sort and a recursive most significant digit radix sort.

Note: the LSD radix sort uses the standard library std::stable_partition algorithm. This algorithm is guaranteed to preserve relative order and has a higher runtime cost. The MSD radix sort uses std::partition and can be significantly faster.

#include <algorithm>
#include <iostream>
#include <iterator>
 
// Radix sort comparator for 32-bit two's complement integers
class radix_test
{
const int bit; // bit position [0..31] to examine
public:
radix_test(int offset) : bit(offset) {} // constructor
 
bool operator()(int value) const // function call operator
{
if (bit == 31) // sign bit
return value < 0; // negative int to left partition
else
return !(value & (1 << bit)); // 0 bit to left partition
}
};
 
// Least significant digit radix sort
void lsd_radix_sort(int *first, int *last)
{
for (int lsb = 0; lsb < 32; ++lsb) // least-significant-bit
{
std::stable_partition(first, last, radix_test(lsb));
}
}
 
// Most significant digit radix sort (recursive)
void msd_radix_sort(int *first, int *last, int msb = 31)
{
if (first != last && msb >= 0)
{
int *mid = std::partition(first, last, radix_test(msb));
msb--; // decrement most-significant-bit
msd_radix_sort(first, mid, msb); // sort left partition
msd_radix_sort(mid, last, msb); // sort right partition
}
}
 
// test radix_sort
int main()
{
int data[] = { 170, 45, 75, -90, -802, 24, 2, 66 };
 
lsd_radix_sort(data, data + 8);
// msd_radix_sort(data, data + 8);
 
std::copy(data, data + 8, std::ostream_iterator<int>(std::cout, " "));
 
return 0;
}

Output:

-802 -90 2 24 45 66 75 170 

C#

Works with: C# version 3.0+
using System;
 
namespace RadixSort
{
class Program
{
static void Sort(int[] old)
{
int i, j;
int[] tmp = new int[old.Length];
for (int shift = 31; shift > -1; --shift)
{
j = 0;
for (i = 0; i < old.Length; ++i)
{
bool move = (old[i] << shift) >= 0;
if (shift == 0 ? !move : move) // shift the 0's to old's head
old[i-j] = old[i];
else // move the 1's to tmp
tmp[j++] = old[i];
}
Array.Copy(tmp, 0, old, old.Length-j, j);
}
}
static void Main(string[] args)
{
int[] old = new int[] { 2, 5, 1, -3, 4 };
Console.WriteLine(string.Join(", ", old));
Sort(old);
Console.WriteLine(string.Join(", ", old));
Console.Read();
}
}
}

D

Shorter Version

import std.stdio, std.math, std.traits, std.range, std.algorithm;
 
ElementType!R[] radixSort(size_t N=10, R)(R r)
if (hasLength!R && isRandomAccessRange!R &&
isIntegral!(ElementType!R)) {
alias ElementType!R E;
 
static if (isDynamicArray!R)
alias r res; // input is array => in place sort
else
E[] res = r.array(); // input is Range => return a new array
 
E absMax = r.map!abs().reduce!max();
immutable nPasses = 1 + cast(int)(log(absMax) / log(N));
 
foreach (pass; 0 .. nPasses) {
auto bucket = new E[][](2 * N - 1, 0);
foreach (v; res) {
int bIdx = abs(v / (N ^^ pass)) % N;
bIdx = (v < 0) ? -bIdx : bIdx;
bucket[N + bIdx - 1] ~= v;
}
res = bucket.join();
}
 
return res;
}
 
void main() {
auto items = [170, 45, 75, -90, 2, 24, -802, 66];
items.radixSort().writeln();
items.map!q{1 - a}().radixSort().writeln();
}
Output:
[-802, -90, 2, 24, 45, 66, 75, 170]
[-1, -23, -44, -65, -74, -169, 91, 803]

More Efficient Version

import std.array, std.traits;
 
// considered pure for this program
extern(C) void* alloca(in size_t length) pure nothrow;
 
void radixSort(size_t MAX_ALLOCA=5_000, U)(U[] data)
pure nothrow if (isUnsigned!U) {
static void radix(in uint byteIndex, in U[] source, U[] dest)
pure nothrow {
immutable size_t sourceSize = source.length;
ubyte* curByte = (cast(ubyte*)source.ptr) + byteIndex;
uint[ubyte.max + 1] byteCounter;
for (size_t i = 0; i < sourceSize; i++, curByte += U.sizeof)
byteCounter[*curByte]++;
 
{
uint indexStart;
foreach (uint i; 0 .. byteCounter.length) {
immutable size_t tempCount = byteCounter[i];
byteCounter[i] = indexStart;
indexStart += tempCount;
}
}
 
curByte = (cast(ubyte*)source.ptr) + byteIndex;
for (size_t i = 0; i < sourceSize; i++, curByte += U.sizeof) {
uint* countPtr = byteCounter.ptr + *curByte;
dest[*countPtr] = source[i];
(*countPtr)++;
}
}
 
U[] tempData;
if (U.sizeof * data.length <= MAX_ALLOCA) {
U* ptr = cast(U*)alloca(data.length * U.sizeof);
if (ptr != null)
tempData = ptr[0 .. data.length];
}
if (tempData.empty)
tempData = uninitializedArray!(U[])(data.length);
 
static if (U.sizeof == 1) {
radix(0, data, tempData);
data[] = tempData[];
} else {
for (uint i = 0; i < U.sizeof; i += 2) {
radix(i + 0, data, tempData);
radix(i + 1, tempData, data);
}
}
}
 
void main() {
import std.stdio;
uint[] items = [170, 45, 75, 4294967206, 2, 24, 4294966494, 66];
items.radixSort();
writeln(items);
}
Output:
[2, 24, 45, 66, 75, 170, 4294966494, 4294967206]

Original C++ code, modified (unknown license), by Andre Reinald, Paul Harris, Ryan Rohrer, Dirk Jagdmann: http://www.cubic.org/docs/download/radix_ar_2011.cpp

Eiffel

Works for positive integers. Splits up into two buckets according to the binary representation of the number.

 
class
RADIX_SORT
 
feature
 
radix_sort (ar: ARRAY [INTEGER])
-- Array 'ar' sorted in ascending order.
require
ar_not_void: ar /= Void
not_negative: across ar as a all a.item >= 0 end
local
bucket_1, bucket_0: LINKED_LIST [INTEGER]
j, k, dig: INTEGER
do
create bucket_0.make
create bucket_1.make
dig := digits (ar)
across
0 |..| dig as c
loop
across
ar as r
loop
if r.item.bit_test (c.item) then
bucket_1.extend (r.item)
else
bucket_0.extend (r.item)
end
end
from
j := 1
until
j > bucket_0.count
loop
ar [j] := bucket_0 [j]
j := j + 1
end
from
k := j
j := 1
until
j > bucket_1.count
loop
ar [k] := bucket_1 [j]
k := k + 1
j := j + 1
end
bucket_0.wipe_out
bucket_1.wipe_out
end
ensure
is_sorted: is_sorted (ar)
end
 
feature {NONE}
 
digits (ar: ARRAY [INTEGER]): INTEGER
-- Number of digits of the largest item in 'ar'.
local
max: INTEGER
math: DOUBLE_MATH
do
create math
across
ar as a
loop
if a.item > max then
max := a.item
end
end
Result := math.log_2 (max).ceiling + 1
end
 
is_sorted (ar: ARRAY [INTEGER]): BOOLEAN
--- Is 'ar' sorted in ascending order?
local
i: INTEGER
do
Result := True
from
i := ar.lower
until
i >= ar.upper
loop
if ar [i] > ar [i + 1] then
Result := False
end
i := i + 1
end
end
 
end
 

Test:

 
class
APPLICATION
 
create
make
 
feature
 
make
local
test: ARRAY [INTEGER]
do
create rs
create test.make_empty
test := <<5, 4, 999, 5, 70, 0, 1000, 55, 1, 2, 3>>
io.put_string ("Unsorted:%N")
across
test as t
loop
io.put_string (t.item.out + " ")
end
rs.radix_sort (test)
io.put_string ("%NSorted:%N")
across
test as t
loop
io.put_string (t.item.out + " ")
end
end
 
rs: RADIX_SORT
 
end
 
Output:
Unsorted:
5 4 999 5 70 0 1000 55 1 2 3
Sorted:
0 1 2 3 4 5 5 55 70 999 1000

Elixir

Translation of: Ruby
defmodule Sort do
def radix_sort(list), do: radix_sort(list, 10)
 
def radix_sort([], _), do: []
def radix_sort(list, base) do
max = abs(Enum.max_by(list, &abs(&1)))
sorted = radix_sort(list, base, max, 1)
{minus, plus} = Enum.partition(sorted, &(&1<0))
Enum.reverse(minus, plus)
end
 
defp radix_sort(list, _, max, m) when max<m, do: list
defp radix_sort(list, base, max, m) do
buckets = List.to_tuple(for _ <- 0..base-1, do: [])
bucket2 = Enum.reduce(list, buckets, fn x,acc ->
i = abs(x) |> div(m) |> rem(base)
put_elem(acc, i, [x | elem(acc, i)])
end)
list2 = Enum.reduce(base-1..0, [], fn i,acc -> Enum.reverse(elem(bucket2, i), acc) end)
radix_sort(list2, base, max, m*base)
end
end
 
IO.inspect Sort.radix_sort([-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028])
Output:
[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]

Fortran

 
*=======================================================================
* RSORT - sort a list of integers by the Radix Sort algorithm
* Public domain. This program may be used by any person for any purpose.
* Origin: Herman Hollerith, 1887
*
*___Name____Type______In/Out____Description_____________________________
* IX(N) Integer Both Array to be sorted in increasing order
* IW(N) Integer Neither Workspace
* N Integer In Length of array
*
* ASSUMPTIONS: Bits in an INTEGER is an even number.
* Integers are represented by twos complement.
*
* NOTE THAT: Radix sorting has an advantage when the input is known
* to be less than some value, so that only a few bits need
* to be compared. This routine looks at all the bits,
* and is thus slower than Quicksort.
*=======================================================================
SUBROUTINE RSORT (IX, IW, N)
IMPLICIT NONE
INTEGER IX, IW, N
DIMENSION IX(N), IW(N)
 
INTEGER I, ! count bits
$ ILIM, ! bits in an integer
$ J, ! count array elements
$ P1OLD, P0OLD, P1, P0, ! indices to ones and zeros
$ SWAP
LOGICAL ODD ! even or odd bit position
 
* IF (N < 2) RETURN ! validate
J = 0 ! find bit size of an integer
J = NOT(J)
ILIM = 0
DO I = 1, 32767 ! much bigger than exists
J = ISHFT(J, -1)
IF (.NOT. BTEST(J, 0)) THEN
ILIM = I
GO TO 10
END IF
END DO
10 CONTINUE
 
*=======================================================================
* Alternate between putting data into IW and into IX
*=======================================================================
P1 = N+1
P0 = N ! read from 1, N on first pass thru
ODD = .FALSE.
DO I = 0, ILIM-2
P1OLD = P1
P0OLD = P0 ! save the value from previous bit
P1 = N+1
P0 = 0 ! start a fresh count for next bit
 
IF (ODD) THEN
DO J = 1, P0OLD, +1 ! copy data from the zeros
IF ( BTEST(IW(J), I) ) THEN
P1 = P1 - 1
IX(P1) = IW(J)
ELSE
P0 = P0 + 1
IX(P0) = IW(J)
END IF
END DO
DO J = N, P1OLD, -1 ! copy data from the ones
IF ( BTEST(IW(J), I) ) THEN
P1 = P1 - 1
IX(P1) = IW(J)
ELSE
P0 = P0 + 1
IX(P0) = IW(J)
END IF
END DO
 
ELSE
DO J = 1, P0OLD, +1 ! copy data from the zeros
IF ( BTEST(IX(J), I) ) THEN
P1 = P1 - 1
IW(P1) = IX(J)
ELSE
P0 = P0 + 1
IW(P0) = IX(J)
END IF
END DO
DO J = N, P1OLD, -1 ! copy data from the ones
IF ( BTEST(IX(J), I) ) THEN
P1 = P1 - 1
IW(P1) = IX(J)
ELSE
P0 = P0 + 1
IW(P0) = IX(J)
END IF
END DO
END IF ! even or odd i
 
ODD = .NOT. ODD
END DO ! next i
 
*=======================================================================
* the sign bit
*=======================================================================
P1OLD = P1
P0OLD = P0
P1 = N+1
P0 = 0
 
* if sign bit is set, send to the zero end
DO J = 1, P0OLD, +1
IF ( BTEST(IW(J), ILIM-1) ) THEN
P0 = P0 + 1
IX(P0) = IW(J)
ELSE
P1 = P1 - 1
IX(P1) = IW(J)
END IF
END DO
DO J = N, P1OLD, -1
IF ( BTEST(IW(J), ILIM-1) ) THEN
P0 = P0 + 1
IX(P0) = IW(J)
ELSE
P1 = P1 - 1
IX(P1) = IW(J)
END IF
END DO
 
*=======================================================================
* Reverse the order of the greater value partition
*=======================================================================
P1OLD = P1
DO J = N, (P1OLD+N)/2+1, -1
SWAP = IX(J)
IX(J) = IX(P1)
IX(P1) = SWAP
P1 = P1 + 1
END DO
RETURN
END ! of RSORT
 
 
***********************************************************************
* test program
***********************************************************************
PROGRAM t_sort
IMPLICIT NONE
INTEGER I, N
PARAMETER (N = 11)
INTEGER IX(N), IW(N)
LOGICAL OK
 
DATA IX / 2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666 /
 
PRINT *, 'before: ', IX
CALL RSORT (IX, IW, N)
PRINT *, 'after: ', IX
 
* compare
OK = .TRUE.
DO I = 1, N-1
IF (IX(I) > IX(I+1)) OK = .FALSE.
END DO
IF (OK) THEN
PRINT *, 't_sort: successful test'
ELSE
PRINT *, 't_sort: failure!'
END IF
END ! of test program
 
Output:
 before:  2 24 45 0 66 75 170 -802 -90 1066 666
 after:  -802 -90 0 2 24 45 66 75 170 666 1066
 t_sort: successful test

Go

LSD radix 256, negatives handled by flipping the high bit.

package main
 
import (
"bytes"
"encoding/binary"
"fmt"
)
 
// declarations for word size of data
type word int32
const wordLen = 4
const highBit = -1 << 31
 
var data = []word{170, 45, 75, -90, -802, 24, 2, 66}
 
func main() {
buf := bytes.NewBuffer(nil)
ds := make([][]byte, len(data))
for i, x := range data {
binary.Write(buf, binary.LittleEndian, x^highBit)
b := make([]byte, wordLen)
buf.Read(b)
ds[i] = b
}
bins := make([][][]byte, 256)
for i := 0; i < wordLen; i++ {
for _, b := range ds {
bins[b[i]] = append(bins[b[i]], b)
}
j := 0
for k, bs := range bins {
copy(ds[j:], bs)
j += len(bs)
bins[k] = bs[:0]
}
}
fmt.Println("original:", data)
var w word
for i, b := range ds {
buf.Write(b)
binary.Read(buf, binary.LittleEndian, &w)
data[i] = w^highBit
}
fmt.Println("sorted: ", data)
}

Output:

original: [170 45 75 -90 -802 24 2 66]
sorted:   [-802 -90 2 24 45 66 75 170]

Groovy

This solution assumes the radix is a power of 2:

def radixSort = { final radixExponent, list ->
def fromBuckets = new TreeMap([0:list])
def toBuckets = new TreeMap()
final radix = 2**radixExponent
final mask = radix - 1
final radixDigitSize = (int)Math.ceil(64/radixExponent)
final digitWidth = radixExponent
(0..<radixDigitSize).each { radixDigit ->
fromBuckets.values().findAll { it != null }.flatten().each {
print '.'
long bucketNumber = (long)((((long)it) >>> digitWidth*radixDigit) & mask)
toBuckets[bucketNumber] = toBuckets[bucketNumber] ?: []
toBuckets[bucketNumber] << it
}
(fromBuckets, toBuckets) = [toBuckets, fromBuckets]
toBuckets.clear()
}
final overflow = 2**(63 % radixExponent)
final pos = {it < overflow}
final neg = {it >= overflow}
final keys = fromBuckets.keySet()
final twosComplIndx = [] + (keys.findAll(neg)) + (keys.findAll(pos))
twosComplIndx.collect { fromBuckets[it] }.findAll { it != null }.flatten()
}

Test:

println (radixSort(3, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))
println (radixSort(3, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))
println (radixSort(3, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))
println ()
println (radixSort(8, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))
println (radixSort(8, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))
println (radixSort(8, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))
println ()
println (radixSort(11, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))
println (radixSort(11, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))
println (radixSort(11, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))
println ()
println (radixSort(16, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))
println (radixSort(16, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))
println (radixSort(16, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))
println ()
println (radixSort(32, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))
println (radixSort(32, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))
println (radixSort(32, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))

Output:

..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

........................................................................................................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
........................................................................................................................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
........................................................................................................................................................................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

..............................................................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
..........................................................................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
..........................................................................................................................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

....................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
............................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
............................................................................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

..........................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
..............................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
..............................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

Haskell

import Data.Bits (Bits(testBit, bitSize))
import Data.List (partition)
 
lsdSort :: (Ord a, Bits a) => [a] -> [a]
lsdSort = fixSort positiveLsdSort
 
msdSort :: (Ord a, Bits a) => [a] -> [a]
msdSort = fixSort positiveMsdSort
 
-- Fix a sort that puts negative numbers at the end, like positiveLsdSort and positiveMsdSort
fixSort sorter list = uncurry (flip (++)) (break (< 0) (sorter list))
 
positiveLsdSort :: (Bits a) => [a] -> [a]
positiveLsdSort list = foldl step list [0..bitSize (head list)] where
step list bit = uncurry (++) (partition (not . flip testBit bit) list)
 
positiveMsdSort :: (Bits a) => [a] -> [a]
positiveMsdSort list = aux (bitSize (head list) - 1) list where
aux _ [] = []
aux (-1) list = list
aux bit list = aux (bit - 1) lower ++ aux (bit - 1) upper where
(lower, upper) = partition (not . flip testBit bit) list

Icon and Unicon

The following is nice and short and works in both languages. However it contains a subtle inefficiency: subscripting a numeric value first coerces it into a string.

procedure main(A)
every writes((!rSort(A)||" ")|"\n")
end
 
procedure rSort(A)
every (min := A[1]) >:= !A
every (mlen := *(A[1]-min)) <:= (!A - min)
every i := !*mlen do {
every put(b := [], |[]\12)
every a := !A do put(b[(a-min)[-i]+2|1], a)
every put(A := [],!!b)
}
return A
end

Sample run:

->radix 31 123 -98 7090 802 2
-98 2 31 123 802 7090
->

J

Generally, this task should be accomplished in J using /:~. Here we take an approach that's more comparable with the other examples on this page.

keys f/. data evaluates the function f on each group of data at the same position as similar keys. Sorting requires ordered keys. This code uses a J idiom: prepend the keys and matching data. The extra data is removed by behead }..

 
radixSortR =: 3 : 0 NB. base radixSort data
16 radixSortR y
:
keys =. x #.^:_1 y NB. compute keys
length =. #{.keys
extra =. (-length) {."0 buckets =. i.x
for_pass. i.-length do.
keys =. ; (buckets,pass{"1 keys) <@:}./.extra,keys
end.
x#.keys NB. restore the data
)

An alternate implementation is

radixsort=: (] #~ [: +/ =/) i.@(>./)

This uses the maximum value of the list for the base, which allows the list to be sorted in one pass.

Example use:

   radixsort ?.@#~10
4 5 6 6 6 6 6 8 8

Or, for negative number support:

rsort=: (] + radixsort@:-) <./

Example:

   rsort _6+?.@#~10
_2 _1 0 0 0 0 0 2 2

Java

public static int[] sort(int[] old) {
// Loop for every bit in the integers
for (int shift = Integer.SIZE - 1; shift > -1; shift--) {
// The array to put the partially sorted array into
int[] tmp = new int[old.length];
// The number of 0s
int j = 0;
 
// Move the 0s to the new array, and the 1s to the old one
for (int i = 0; i < old.length; i++) {
// If there is a 1 in the bit we are testing, the number will be negative
boolean move = old[i] << shift >= 0;
 
// If this is the last bit, negative numbers are actually lower
if (shift == 0 ? !move : move) {
tmp[j] = old[i];
j++;
} else {
// It's a 1, so stick it in the old array for now
old[i - j] = old[i];
}
}
 
// Copy over the 1s from the old array
for (int i = j; i < tmp.length; i++) {
tmp[i] = old[i - j];
}
 
// And now the tmp array gets switched for another round of sorting
old = tmp;
}
 
return old;
}
Translation of: NetRexx
 
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.List;
import java.util.Queue;
 
public class RSortingRadixsort00 {
 
public RSortingRadixsort00() {
 
return;
}
 
public static int[] lsdRadixSort(int[] tlist) {
 
List<Integer> intermediates;
int[] limits = getLimits(tlist);
tlist = rescale(tlist, limits[1]);
 
for (int px = 1; px <= limits[2]; ++px) {
@SuppressWarnings("unchecked")
Queue<Integer> bukits[] = new Queue[10];
for (int ix = 0; ix < tlist.length; ++ix) {
int cval = tlist[ix];
int digit = (int) (cval / Math.pow(10, px - 1) % 10);
if (bukits[digit] == null) {
bukits[digit] = new LinkedList<>();
}
bukits[digit].add(cval);
}
 
intermediates = new ArrayList<>();
for (int bi = 0; bi < 10; ++bi) {
if (bukits[bi] != null) {
while (bukits[bi].size() > 0) {
int nextd;
nextd = bukits[bi].poll();
intermediates.add(nextd);
}
}
}
 
for (int iw = 0; iw < intermediates.size(); ++iw) {
tlist[iw] = intermediates.get(iw);
}
}
 
tlist = rescale(tlist, -limits[1]);
 
return tlist;
}
 
private static int[] rescale(int[] arry, int delta) {
 
for (int ix = 0; ix < arry.length; ++ix) {
arry[ix] -= delta;
}
 
return arry;
}
 
private static int[] getLimits(int[] tlist) {
 
int[] lims = new int[3];
 
for (int i_ = 0; i_ < tlist.length; ++i_) {
lims[0] = Math.max(lims[0], tlist[i_]);
lims[1] = Math.min(lims[1], tlist[i_]);
}
lims[2] = (int) Math.ceil(Math.log10(lims[0] - lims[1]));
 
return lims;
}
 
private static void runSample(String[] args) {
 
int[][] lists = {
new int[] { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, },
new int[] { -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, -0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, },
new int[] { 2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666, },
new int[] { 170, 45, 75, 90, 2, 24, 802, 66, },
new int[] { -170, -45, -75, -90, -2, -24, -802, -66, },
};
 
long etime;
lsdRadixSort(Arrays.copyOf(lists[0], lists[0].length)); // do one pass to set up environment to remove it from timings
 
for (int[] tlist : lists) {
System.out.println(array2list(tlist));
etime = System.nanoTime();
tlist = lsdRadixSort(tlist);
etime = System.nanoTime() - etime;
System.out.println(array2list(tlist));
System.out.printf("Elapsed time: %fs%n", ((double) etime / 1_000_000_000.0));
System.out.println();
}
 
return;
}
 
private static List<Integer> array2list(int[] arry) {
 
List<Integer> target = new ArrayList<>(arry.length);
 
for (Integer iv : arry) {
target.add(iv);
}
 
return target;
}
 
public static void main(String[] args) {
 
runSample(args);
 
return;
}
}
 
Output:
[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]
[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Elapsed time: 0.000256s

[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Elapsed time: 0.000198s

[2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666]
[-802, -90, 0, 2, 24, 45, 66, 75, 170, 666, 1066]
Elapsed time: 0.000187s

[170, 45, 75, 90, 2, 24, 802, 66]
[2, 24, 45, 66, 75, 90, 170, 802]
Elapsed time: 0.000088s

[-170, -45, -75, -90, -2, -24, -802, -66]
[-802, -170, -90, -75, -66, -45, -24, -2]
Elapsed time: 0.000113s

jq

# Sort the input array;
# "base" must be an integer greater than 1
def radix_sort(base):
# We only need the ceiling of non-negatives:
def ceil: if . == floor then . else (. + 1 | floor) end;
 
min as $min
| map(. - $min)
| ((( max|log) / (base|log)) | ceil) as $rounds
| reduce range(0; $rounds) as $i
# state: [ base^i, buckets ]
( [1, .];
.[0] as $base_i
| reduce .[1][] as $n
([];
(($n/$base_i) % base) as $digit
| .[$digit] += [$n] )
| [($base_i * base), (map(select(. != null)) | flatten)] )
| .[1]
| map(. + $min) ;
 
def radix_sort:
radix_sort(10);
 

Example

 
# Verify that radix_sort agrees with sort
( [1, 3, 8, 9, 0, 0, 8, 7, 1, 6],
[170, 45, 75, 90, 2, 24, 802, 66],
[170, 45, 75, 90, 2, 24, -802, -66] )
| (radix_sort == sort)
 
Output:
true
true
true

Kotlin

Translation of: Java
// version 1.1.2
 
fun radixSort(original: IntArray): IntArray {
var old = original // Need this to be mutable
// Loop for every bit in the integers
for (shift in 31 downTo 0) {
val tmp = IntArray(old.size) // The array to put the partially sorted array into
var j = 0 // The number of 0s
// Move the 0s to the new array, and the 1s to the old one
for (i in 0 until old.size) {
// If there is a 1 in the bit we are testing, the number will be negative
val move = (old[i] shl shift) >= 0
// If this is the last bit, negative numbers are actually lower
val toBeMoved = if (shift == 0) !move else move
if (toBeMoved)
tmp[j++] = old[i]
else {
// It's a 1, so stick it in the old array for now
old[i - j] = old[i]
}
}
// Copy over the 1s from the old array
for (i in j until tmp.size) tmp[i] = old[i - j]
// And now the tmp array gets switched for another round of sorting
old = tmp
}
return old
}
 
fun main(args: Array<String>) {
val arrays = arrayOf(
intArrayOf(170, 45, 75, -90, -802, 24, 2, 66),
intArrayOf(-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028)
)
for (array in arrays) println(radixSort(array).contentToString())
}
Output:
[-802, -90, 2, 24, 45, 66, 75, 170]
[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]

Mathematica

ClearAll[SortByPos, RadixSort]
SortByPos[data : {_List ..}, pos_Integer] := Module[{digs, order},
digs = data[[All, pos]];
order = Ordering[digs];
data[[order]]
]
RadixSort[x : {_Integer ..}] := Module[{y, digs, maxlen, offset},
offset = Min[x];
y = x - offset;
digs = IntegerDigits /@ y;
maxlen = Max[Length /@ digs];
digs = IntegerDigits[#, 10, maxlen] & /@ y;
digs = Fold[SortByPos, digs, -Range[maxlen]];
digs = FromDigits /@ digs;
digs += offset;
digs
]

Testing out the algorithm:

RadixSort[{170,45,75,-90,-802,24,2,66}]
RadixSort[{170,45,75,90,802,2,24,66}]
Output:
{-802,-90,2,24,45,66,75,170}
{2,24,45,66,75,90,170,802}


NetRexx

Uses a suggestion in the discussion page to handle negative values.
Limitations - Handles decimal digits only.

Using the Rexx class

/* NetRexx */
options replace format comments java crossref symbols nobinary
 
runSample(arg)
return
 
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method radixSort(tlist = Rexx[]) public static returns Rexx[]
 
-- scale the array to start at zero to allow handling of -ve values
parse getLimits(tlist) maxn minn maxl .
tlist = rescale(tlist, minn)
 
loop px = maxl to 1 by -1
bukits = ''
loop ix = 0 to tlist.length - 1
cval = tlist[ix].right(maxl, 0)
parse cval . =(px) digit +1 .
bukits[digit] = bukits[digit] (cval + 0) -- simulates a stack
end ix
intermediates = ''
loop bi = 0 to 9
intermediates = intermediates bukits[bi] -- sumulates unstack
end bi
-- reload array
loop iw = 1 to intermediates.words()
tlist[iw - 1] = intermediates.word(iw)
end iw
end px
 
-- restore the array to original scale
tlist = rescale(tlist, -minn)
return tlist
 
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method rescale(arry = Rexx[], newbase) private static returns Rexx[]
loop ix = 0 to arry.length - 1
arry[ix] = arry[ix] - newbase
end ix
return arry
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method getLimits(arry = Rexx[]) private static returns Rexx
maxn = 0
minn = 0
maxl = 0
loop i_ = 0 to arry.length - 1
maxn = maxn.max(arry[i_])
minn = minn.min(arry[i_])
end i_
maxl = (maxn - minn).length()
return maxn minn maxl
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
lists = [-
[2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666], -
[170, 45, 75, 90, 2, 24, 802, 66], -
[10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0], -
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], -
[-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, -0], -
[-0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10], -
[-10, -19, -18, -17, -18, -15, -14, -13, -12, -11, -100], -
[10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0, -0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10], -
[-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, -0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] -
]
 
loop il = 0 to lists.length - 1
tlist = lists[il]
say ' Input:' Arrays.asList(tlist)
say 'Output:' Arrays.asList(radixSort(tlist))
say
end il
return
 
Output:
 Input: [2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666]
Output: [-802, -90, 0, 2, 24, 45, 66, 75, 170, 666, 1066]

 Input: [170, 45, 75, 90, 2, 24, 802, 66]
Output: [2, 24, 45, 66, 75, 90, 170, 802]

 Input: [10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0]
Output: [0, 1, 2, 3, 4, 5, 7, 8, 8, 9, 10]

 Input: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Output: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

 Input: [-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, 0]
Output: [-10, -9, -8, -8, -7, -5, -4, -3, -2, -1, 0]

 Input: [0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]
Output: [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0]

 Input: [-10, -19, -18, -17, -18, -15, -14, -13, -12, -11, -100]
Output: [-100, -19, -18, -18, -17, -15, -14, -13, -12, -11, -10]

 Input: [10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]
Output: [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 7, 8, 8, 9, 10]

 Input: [-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Output: [-10, -9, -8, -8, -7, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Using Collection classes

/* NetRexx */
options replace format comments java crossref symbols nobinary
 
import java.util.Queue
 
runSample(arg)
return
 
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method radixSort(tlist = Rexx[]) public static returns Rexx[]
 
-- scale the array to start at zero to allow handling of -ve values
limits = ''
parse '!MAXN !MINN !MAXL' maxn_ minn_ maxl_ .
parse getLimits(tlist) maxn minn maxl .
limits[maxn_] = maxn
limits[minn_] = minn
limits[maxl_] = maxl
tlist = rescale(tlist, limits[minn_])
 
loop px = limits[maxl_] to 1 by -1
bukits = Queue[10] -- stacks for digits 0 .. 9
loop ix = 0 while ix < tlist.length
cval = tlist[ix].right(limits[maxl_], 0)
parse cval . =(px) digit +1 . -- extract next digit (fun with parse)
-- alternatively: digit = (cval % (10 ** (px - 1))) // 10
if bukits[digit] == null then bukits[digit] = LinkedList()
bukits[digit].add((cval + 0))
end ix
 
intermediates = ArrayList()
loop bi = 0 to 9
if bukits[bi] \= null then loop while bukits[bi].size() > 0
nextd = bukits[bi].poll()
intermediates.add(nextd)
end
end bi
 
-- reload result array
loop iw = 0 while iw < intermediates.size()
tlist[iw] = Rexx intermediates.get(iw)
end iw
end px
 
-- restore the array to original scale
tlist = rescale(tlist, -limits[minn_])
return tlist
 
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method rescale(arry = Rexx[], newbase) private static returns Rexx[]
loop ix = 0 to arry.length - 1
arry[ix] = arry[ix] - newbase
end ix
return arry
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method getLimits(arry = Rexx[]) private static returns Rexx
maxn = 0
minn = 0
maxl = 0
loop i_ = 0 to arry.length - 1
maxn = maxn.max(arry[i_])
minn = minn.min(arry[i_])
end i_
maxl = (maxn - minn).length()
return maxn minn maxl
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
lists = [-
[2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666], -
[170, 45, 75, 90, 2, 24, 802, 66], -
[10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0], -
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], -
[-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, -0], -
[-0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10], -
[-10, -19, -18, -17, -18, -15, -14, -13, -12, -11, -100], -
[10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0, -0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10], -
[-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, -0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] -
]
 
loop il = 0 to lists.length - 1
tlist = lists[il]
say ' Input:' Arrays.asList(tlist)
say 'Output:' Arrays.asList(radixSort(tlist))
say
end il
return
 

Perl

Radix sort in base 10.

#!/usr/bin/perl
use warnings;
use strict;
 
sub radix {
my @tab = ([@_]);
 
my $max_length = 0;
length > $max_length and $max_length = length for @_;
$_ = sprintf "%0${max_length}d", $_ for @{ $tab[0] }; # Add zeros.
 
for my $pos (reverse -$max_length .. -1) {
my @newtab;
for my $bucket (@tab) {
for my $n (@$bucket) {
my $char = substr $n, $pos, 1;
$char = -1 if '-' eq $char;
$char++;
push @{ $newtab[$char] }, $n;
}
}
@tab = @newtab;
}
 
my @return;
my $negative = shift @tab; # Negative bucket must be reversed.
push @return, reverse @$negative;
for my $bucket (@tab) {
push @return, @{ $bucket // [] };
}
$_ = 0 + $_ for @return; # Remove zeros.
return @return;
}

To test, add the following lines:

use Test::More tests => 1000;
 
for (1 .. 1000) {
my @l = map int rand(2000) - 1000, 0 .. 20;
is_deeply([radix(@l)], [sort { $a <=> $b } @l]);
}

Perl 6

A base-10 radix sort, done on the string representation of the integers. Signs are handled by in-place reversal of the '-' bucket on the last iteration. (The sort in there is not cheating; it only makes sure we process the buckets in the right order, since classify might return the buckets in random order. It might be more efficient to create our own ordered buckets, but this is succinct.)

sub radsort (@ints) {
my $maxlen = [max] @ints».chars;
my @list = @ints».fmt("\%0{$maxlen}d");
 
for reverse ^$maxlen -> $r {
my @buckets = @list.classify( *.substr($r,1) ).sort: *.key;
if !$r and @buckets[0].key eq '-' { @buckets[0].value .= reverse }
@list = flat map *.value.values, @buckets;
}
@list».Int;
}
 
.say for radsort (-2_000 .. 2_000).roll(20);
Output:
-1585
-1427
-1228
-1067
-945
-657
-643
-232
-179
-28
37
411
488
509
716
724
1504
1801
1864
1939

Phix

function radixSortn(sequence s, integer n)
sequence buckets = repeat({},10)
sequence res = {}
for i=1 to length(s) do
integer digit = remainder(floor(s[i]/power(10,n-1)),10)+1
buckets[digit] = append(buckets[digit],s[i])
end for
for i=1 to length(buckets) do
integer len = length(buckets[i])
if len!=0 then
if len=1 or n=1 then
res &= buckets[i]
else
res &= radixSortn(buckets[i],n-1)
end if
end if
end for
return res
end function
 
function split_by_sign(sequence s)
sequence buckets = {{},{}}
for i=1 to length(s) do
integer si = s[i]
if si<0 then
buckets[1] = append(buckets[1],-si)
else
buckets[2] = append(buckets[2],si)
end if
end for
return buckets
end function
 
function radixSort(sequence s)
integer mins = min(s)
integer passes = max(max(s),abs(mins))
passes = floor(log10(passes))+1
if mins<0 then
sequence buckets = split_by_sign(s)
buckets[1] = reverse(sq_uminus(radixSortn(buckets[1],passes)))
buckets[2] = radixSortn(buckets[2],passes)
s = buckets[1]&buckets[2]
else
s = radixSortn(s,passes)
end if
return s
end function
 
?radixSort({1, 3, 8, 9, 0, 0, 8, 7, 1, 6})
?radixSort({170, 45, 75, 90, 2, 24, 802, 66})
?radixSort({170, 45, 75, 90, 2, 24, -802, -66})
?radixSort({100000, -10000, 400, 23, 10000})
Output:
{0,0,1,1,3,6,7,8,8,9}
{2,24,45,66,75,90,170,802}
{-802,-66,2,24,45,75,90,170}
{-10000,23,400,10000,100000}

PicoLisp

This is a LSD base-2 radix sort using queues:

(de radixSort (Lst)
(let Mask 1
(while
(let (Pos (list NIL NIL) Neg (list NIL NIL) Flg)
(for N Lst
(queue
(if2 (ge0 N) (bit? Mask N)
(cdr Pos) Pos Neg (cdr Neg) )
N )
(and (>= (abs N) Mask) (on Flg)) )
(setq
Lst (conc (apply conc Neg) (apply conc Pos))
Mask (* 2 Mask) )
Flg ) ) )
Lst )

Output:

: (radixSort (make (do 12 (link (rand -999 999)))))
-> (-999 -930 -666 -336 -218 68 79 187 391 405 697 922)

PureBasic

Structure bucket
List i.i()
EndStructure
 
DataSection
;sets specify the size (1 based) followed by each integer
set1:
Data.i 10 ;size
Data.i 1, 3, 8, 9, 0, 0, 8, 7, 1, 6 ;data
set2:
Data.i 8
Data.i 170, 45, 75, 90, 2, 24, 802, 66
set3:
Data.i 8
Data.i 170, 45, 75, 90, 2, 24, -802, -66
EndDataSection
 
Procedure setIntegerArray(Array x(1), *setPtr)
Protected i, count
count = PeekI(*setPtr) - 1 ;convert to zero based count
*setPtr + SizeOf(Integer) ;move pointer forward to data
Dim x(count)
For i = 0 To count
x(i) = PeekI(*setPtr + i * SizeOf(Integer))
Next
EndProcedure
 
Procedure displayArray(Array x(1))
Protected i, Size = ArraySize(x())
For i = 0 To Size
Print(Str(x(i)))
If i < Size: Print(", "): EndIf
Next
PrintN("")
EndProcedure
 
Procedure radixSort(Array x(1), Base = 10)
Protected count = ArraySize(x())
If Base < 1 Or count < 1: ProcedureReturn: EndIf ;exit due to invalid values
 
Protected i, pv, digit, digitCount, maxAbs, pass, index
;find element with largest number of digits
For i = 0 To count
If Abs(x(i)) > maxAbs
maxAbs = Abs(x(i))
EndIf
Next
 
digitCount = Int(Log(maxAbs)/Log(Base)) + 1
 
For pass = 1 To digitCount
Dim sortBuckets.bucket(Base * 2 - 1)
pv = Pow(Base, pass - 1)
 
;place elements in buckets according to the current place-value's digit
For index = 0 To count
digit = Int(x(index)/pv) % Base + Base
AddElement(sortBuckets(digit)\i())
sortBuckets(digit)\i() = x(index)
Next
 
;transfer contents of buckets back into array
index = 0
For digit = 1 To (Base * 2) - 1
ForEach sortBuckets(digit)\i()
x(index) = sortBuckets(digit)\i()
index + 1
Next
Next
Next
EndProcedure
 
If OpenConsole()
Dim x(0)
setIntegerArray(x(), ?set1)
radixSort(x()): displayArray(x())
 
setIntegerArray(x(), ?set2)
radixSort(x()): displayArray(x())
 
setIntegerArray(x(), ?set3)
radixSort(x(), 2): displayArray(x())
 
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf

Sample output:

0, 0, 1, 1, 3, 6, 7, 8, 8, 9
2, 24, 45, 66, 75, 90, 170, 802
-802, -66, 2, 24, 45, 75, 90, 170

Python

Works with: Python version 2.6

This is the Wikipedia example code extended with an extra pass to sort negative values correctly.

#python2.6 <
from math import log
 
def getDigit(num, base, digit_num):
# pulls the selected digit
return (num // base ** digit_num) % base
 
def makeBlanks(size):
# create a list of empty lists to hold the split by digit
return [ [] for i in range(size) ]
 
def split(a_list, base, digit_num):
buckets = makeBlanks(base)
for num in a_list:
# append the number to the list selected by the digit
buckets[getDigit(num, base, digit_num)].append(num)
return buckets
 
# concatenate the lists back in order for the next step
def merge(a_list):
new_list = []
for sublist in a_list:
new_list.extend(sublist)
return new_list
 
def maxAbs(a_list):
# largest abs value element of a list
return max(abs(num) for num in a_list)
 
def split_by_sign(a_list):
# splits values by sign - negative values go to the first bucket,
# non-negative ones into the second
buckets = [[], []]
for num in a_list:
if num < 0:
buckets[0].append(num)
else:
buckets[1].append(num)
return buckets
 
def radixSort(a_list, base):
# there are as many passes as there are digits in the longest number
passes = int(round(log(maxAbs(a_list), base)) + 1)
new_list = list(a_list)
for digit_num in range(passes):
new_list = merge(split(new_list, base, digit_num))
return merge(split_by_sign(new_list))
 

Racket

 
#lang racket
 
(require data/queue)
 
(define (radix-sort l r)
(define queues (for/vector #:length r ([_ r]) (make-queue)))
(let loop ([l l] [R 1])
(define all-zero? #t)
(for ([x (in-list l)])
(define x/R (quotient x R))
(enqueue! (vector-ref queues (modulo x/R r)) x)
(unless (zero? x/R) (set! all-zero? #f)))
(if all-zero? l
(loop (let q-loop ([i 0])
(define q (vector-ref queues i))
(let dq-loop ()
(if (queue-empty? q)
(if (< i (sub1 r)) (q-loop (add1 i)) '())
(cons (dequeue! q) (dq-loop)))))
(* R r)))))
 
(for/and ([i 10000]) ; run some tests on random lists with a random radix
(define (make-random-list)
(for/list ([i (+ 10 (random 10))]) (random 100000)))
(define (sorted? l)
(match l [(list) #t] [(list x) #t]
[(list x y more ...) (and (<= x y) (sorted? (cons y more)))]))
(sorted? (radix-sort (make-random-list) (+ 2 (random 98)))))
;; => #t, so all passed
 

REXX

This REXX version also works with malformed integers.       7,   007,   +7,   .7e1,   7.0   are all treated equally.

/*REXX program performs a radix sort on an integer array (can be negative/zero/positive)*/
call gen /*call subroutine to generate numbers. */
call radSort n /*invoke the radix sort subroutine. */
/* [↓] display sorted items ───► term.*/
do j=1 for n; say 'item' right(j,w) "after the radix sort:" right(@.j,w); end
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gen: w=0 /*the max width of an number in the ILF*/
ILF=' 0 2 3 4 5 5 7. 6 6 7 11 7 13 9 8 8 17 8 19 9 10 13 23 9 10 15' ,
' 9 11 29 10 31 10 14 19 12 10 37 21 16 11 41 12 43 15 11 25 47 11 14 12 20 17' ,
'53 11 16 13 22 31 59 12 61 33 13 12 18 16 67 21 26 14 71 12 73 39 13 23 18 18' ,
'79 13 12 43 83 14 22 45 32 17 89 13 20 27 34 49 24 13 97 16 17 14 101' ,
'22 103 19 15 55 107 13 109 18 40 15 113 -42'
/*excluding -42, abbreviated above list is called the integer log function*/
n=words(ILF) /* I────── L── F───────*/
do m=1 for n; _=word(ILF,m)+0; @.m=_; w=max(w,length(_)); end
return /* [↑] W: max width of numbers. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
radSort: procedure expose @. w; parse arg size; mote=c2d(' '); #=1;  !.#._n=size
!.#._b=1;
!.#._i=1; do i=1 for size; y=@.i; @.i=right(abs(y), w, 0); if y<0 then @.i='-'@.i
end /*i*/ /* [↑] negative case*/
 
do while #\==0; ctr.=0; L='ffff'x; low=!.#._b; n=!.#._n; $=!.#._i; H=
#=#-1 /* [↑] is the radix. */
do j=low for n; parse var @.j =($) _ +1; ctr._=ctr._ + 1
if ctr._==1 & _\=='' then do; if _<<L then L=_; if _>>H then H=_
end /* ↑↑ */
end /*j*/ /* └┴─────◄─── << is a strict comparison.*/
_= /* ┌──◄─── >> " " " " */
if L>>H then iterate /*◄─────┘ */
if L==H & ctr._==0 then do; #=#+1;  !.#._b=low;  !.#._n=n;  !.#._i=$ + 1; iterate
end
L=c2d(L); H=c2d(H);  ?=ctr._ + low; top._=?; ts=mote
max=L
do k=L to H; _=d2c(k,1); c=ctr._ /* [↓] swap two item radices.*/
if c>ts then parse value c k with ts max;  ?=?+c; top._=?
end /*k*/
piv=low /*set PIVot to the low part of the sort*/
do while piv < low+n
it=@.piv
do forever; parse var it =($) _ +1; c=top._ -1
if piv>=c then leave; top._=c;  ?=@.c; @.c=it; it=?
end /*forever*/
top._=piv; @.piv=it; piv=piv + ctr._
end /*while piv<low+n */
i=max
do until i==max; _=d2c(i,1); i=i+1; if i>H then i=L; d=ctr._
if d<=mote then do; if d<2 then iterate; b=top._
do k=b+1 for d-1; q=@.k
do j=k-1 by -1 to b while q<<@.j; jp=j+1; @.jp=@.j; end
jp=j+1; @.jp=q
end /*k*/
iterate
end
#=#+1;  !.#._b=top._;  !.#._n=d;  !.#._i=$+1
end /*until i==max*/
end /*while #\==0 */
#=0 /* [↓↓↓] handle neg. and pos. arrays. */
do i=size by -1 to 1; if @.i>=0 then iterate; #=#+1; @@.#=@.i; end
do j=1 for size; if @.j>=0 then do; #=#+1; @@.#=@.j; end; @.j=@@.j+0; end
return /* [↑↑↑] combine 2 lists into 1 list. */

output   (with the middle section elided.)

item   1 after the radix sort: -42
item   2 after the radix sort:   0
item   3 after the radix sort:   2
item   4 after the radix sort:   3
item   5 after the radix sort:   4
item   6 after the radix sort:   5
item   7 after the radix sort:   5
item   8 after the radix sort:   6
item   9 after the radix sort:   6
item  10 after the radix sort:   7
item  11 after the radix sort:   7
item  12 after the radix sort:   7
item  13 after the radix sort:   8
  .
  .
  .
(middle section elided.)
  .
  .
  .
item  92 after the radix sort:  40
item  93 after the radix sort:  41
item  94 after the radix sort:  43
item  95 after the radix sort:  43
item  96 after the radix sort:  45
item  97 after the radix sort:  47
item  98 after the radix sort:  49
item  99 after the radix sort:  53
item 100 after the radix sort:  55
item 101 after the radix sort:  59
item 102 after the radix sort:  61
item 103 after the radix sort:  67
item 104 after the radix sort:  71
item 105 after the radix sort:  73
item 106 after the radix sort:  79
item 107 after the radix sort:  83
item 108 after the radix sort:  89
item 109 after the radix sort:  97
item 110 after the radix sort: 101
item 111 after the radix sort: 103
item 112 after the radix sort: 107
item 113 after the radix sort: 109
item 114 after the radix sort: 113

Ruby

Negative number handling courtesy the Tcl solution.

class Array
def radix_sort(base=10)
ary = dup
rounds = (Math.log(ary.minmax.map(&:abs).max)/Math.log(base)).floor + 1
rounds.times do |i|
buckets = Array.new(2*base){[]}
base_i = base**i
ary.each do |n|
digit = (n/base_i) % base
digit += base if 0<=n
buckets[digit] << n
end
ary = buckets.flatten
p [i, ary] if $DEBUG
end
ary
end
def radix_sort!(base=10)
replace radix_sort(base)
end
end
 
p [1, 3, 8, 9, 0, 0, 8, 7, 1, 6].radix_sort
p [170, 45, 75, 90, 2, 24, 802, 66].radix_sort
p [170, 45, 75, 90, 2, 24, -802, -66].radix_sort
p [100000, -10000, 400, 23, 10000].radix_sort

running with $DEBUG on produces:

[0, [0, 0, 1, 1, 3, 6, 7, 8, 8, 9]]
[0, 0, 1, 1, 3, 6, 7, 8, 8, 9]
[0, [170, 90, 2, 802, 24, 45, 75, 66]]
[1, [2, 802, 24, 45, 66, 170, 75, 90]]
[2, [2, 24, 45, 66, 75, 90, 170, 802]]
[2, 24, 45, 66, 75, 90, 170, 802]
[0, [-66, -802, 170, 90, 2, 24, 45, 75]]
[1, [-66, -802, 2, 24, 45, 170, 75, 90]]
[2, [-802, -66, 2, 24, 45, 75, 90, 170]]
[-802, -66, 2, 24, 45, 75, 90, 170]
[0, [-10000, 100000, 400, 10000, 23]]
[1, [-10000, 100000, 400, 10000, 23]]
[2, [-10000, 100000, 10000, 23, 400]]
[3, [-10000, 100000, 10000, 23, 400]]
[4, [-10000, 100000, 23, 400, 10000]]
[5, [-10000, 23, 400, 10000, 100000]]
[-10000, 23, 400, 10000, 100000]

another version (After sorting at the absolute value, it makes a negative order reverse.)

class Array
def radix_sort(base=10)
ary = dup
m, max = 1, ary.minmax.map(&:abs).max
while m <= max
buckets = Array.new(base){[]}
ary.each {|n| buckets[(n.abs / m) % base] << n}
ary = buckets.flatten
m *= base
end
ary.partition{|n| n<0}.inject{|minus,plus| minus.reverse + plus}
end
end

Sidef

Translation of: Ruby
class Array {
method radix_sort(base=10) {
var arr = self.clone
var rounds = ([arr.minmax].map{.abs}.max.ilog(base) + 1)
for i in (0..rounds) {
var buckets = (2*base -> of {[]})
var base_i = base**i
for n in arr {
var digit = (n/base_i % base)
digit += base if (0 <= n)
buckets[digit].append(n)
}
arr = buckets.flat
}
return arr
}
}
 
for arr in [
[1, 3, 8, 9, 0, 0, 8, 7, 1, 6],
[170, 45, 75, 90, 2, 24, 802, 66],
[170, 45, 75, 90, 2, 24, -802, -66],
[100000, -10000, 400, 23, 10000],
] {
say arr.radix_sort
}
Output:
[0, 0, 1, 1, 3, 6, 7, 8, 8, 9]
[2, 24, 45, 66, 75, 90, 170, 802]
[-802, -66, 2, 24, 45, 75, 90, 170]
[-10000, 23, 400, 10000, 100000]

Tcl

Translation of: Python
package require Tcl 8.5
proc splitByRadix {lst base power} {
# create a list of empty lists to hold the split by digit
set out [lrepeat [expr {$base*2}] {}]
foreach item $lst {
# pulls the selected digit
set digit [expr {($item / $base ** $power) % $base + $base * ($item >= 0)}]
# append the number to the list selected by the digit
lset out $digit [list {*}[lindex $out $digit] $item]
}
return $out
}
 
# largest abs value element of a list
proc tcl::mathfunc::maxabs {lst} {
set max [abs [lindex $lst 0]]
for {set i 1} {$i < [llength $lst]} {incr i} {
set v [abs [lindex $lst $i]]
if {$max < $v} {set max $v}
}
return $max
}
 
proc radixSort {lst {base 10}} {
# there are as many passes as there are digits in the longest number
set passes [expr {int(log(maxabs($lst))/log($base) + 1)}]
# For each pass...
for {set pass 0} {$pass < $passes} {incr pass} {
# Split by radix, then merge back into the list
set lst [concat {*}[splitByRadix $lst $base $pass]]
}
return $lst
}

Demonstrations:

puts [radixSort {1 3 8 9 0 0 8 7 1 6}]
puts [radixSort {170 45 75 90 2 24 802 66}]
puts [radixSort {170 45 75 90 2 24 -802 -66}]

Output:

0 0 1 1 3 6 7 8 8 9
2 24 45 66 75 90 170 802
-802 -66 2 24 45 75 90 170

zkl

In place int sort, fairly light on garbage creation.

fcn radixSort(ns){ // ints only, inplace, ns is mutable
b:=(0).pump(20,List,List().copy); // 20 [empty] buckets: -10..10
z:=ns.reduce(fcn(a,b){ a.abs().max(b.abs()) },0); // |max or min of input|
m:=1;
while(z){
ns.apply2('wrap(n){ b[(n/m)%10 +10].append(n) }); // sort on right digit
ns.clear(); b.pump(ns.extend); // slam buckets over src
b.apply("clear"); // reset buckets
m*=10; z/=10; // move sort digit left
}
ns
}
radixSort(T(170, 45, 75, 90, 802, 2, 24, 66)).println();
radixSort(T(170, 45, 75, -90, -802, 24, 2, 66)).println();
Output:
L(2,24,45,66,75,90,170,802)
L(-802,-90,2,24,45,66,75,170)