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 comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
- Task
Sort an integer array with the radix sort algorithm.
The primary purpose is to complete the characterization of sort algorithms task.
11l
F flatten(some_list)
[Int] new_list
L(sub_list) some_list
new_list [+]= sub_list
R new_list
F radix_sort(l, =p = -1, =s = -1)
I s == -1
s = String(max(l)).len
I p == -1
p = s
V i = s - p
I i >= s
R l
V bins = [[Int]()] * 10
L(e) l
bins[Int(String(e).zfill(s)[i])] [+]= e
R flatten(bins.map(b -> radix_sort(b, @p - 1, @s)))
V arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
print(radix_sort(arr))- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
AArch64 Assembly
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program radixSort64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeConstantesARM64.inc"
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .asciz "Value : @ \n"
szCarriageReturn: .asciz "\n"
.align 4
TableNumber: .quad 12485,301,16,25,5006,9,-154389710,26,4400,71,115
#TableNumber: .quad 10,9,8,7,6,-5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 8
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: // entry of program
ldr x0,qAdrTableNumber // address number table
mov x1,0 // first element
mov x2,NBELEMENTS // number of élements
bl radixSort
ldr x0,qAdrTableNumber // address number table
bl displayTable
ldr x0,qAdrTableNumber // address number table
mov x1,NBELEMENTS // number of élements
bl isSorted // control sort
cmp x0,1 // sorted ?
beq 1f
ldr x0,qAdrszMessSortNok // no !! error sort
bl affichageMess
b 100f
1: // yes
ldr x0,qAdrszMessSortOk
bl affichageMess
100: // standard end of the program
mov x0,0 // return code
mov x8,EXIT // request to exit program
svc 0 // perform the system call
qAdrsZoneConv: .quad sZoneConv
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrsMessResult: .quad sMessResult
qAdrTableNumber: .quad TableNumber
qAdrszMessSortOk: .quad szMessSortOk
qAdrszMessSortNok: .quad szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of elements > 0 */
/* x0 return 0 if not sorted 1 if sorted */
isSorted:
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
mov x2,0
ldr x4,[x0,x2,lsl 3]
1:
add x2,x2,1
cmp x2,x1
bge 99f
ldr x3,[x0,x2, lsl 3]
cmp x3,x4
blt 98f
mov x4,x3
b 1b
98:
mov x0,0 // not sorted
b 100f
99:
mov x0,1 // sorted
100:
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* radix sort */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the first element */
/* r2 contains the number of element */
/* no registers save */
radixSort:
str lr,[sp,-16]! // save 1 register
mov x7,0b1111 // mask one digit hexa
mov x10,0 // digit counter
1:
add x3,x1,1 // start index i
2: // start loop
ldr x4,[x0,x3,lsl 3] // load value A[i]
and x8,x4,x7 // and mask
sub x5,x3,1 // index j
3:
ldr x6,[x0,x5,lsl 3] // load value A[j]
and x9,x6,x7 // and mask
cmp x9,x8 // compare one digit hexa
ble 4f
add x5,x5,1 // increment index j
str x6,[x0,x5,lsl 3] // store value A[j+1]
sub x5,x5,2 // j = j - 1
cmp x5,x1
bge 3b // loop if j >= first item
4:
add x5,x5,1 // increment index j
str x4,[x0,x5,lsl 3] // store value A[i] in A[j+1]
add x3,x3,1 // increment index i
cmp x3,x2 // end ?
blt 2b // no -> loop
//bl displayTable
lsl x7,x7,4 // shift mask 4 bits left
add x10,x10,1 // increment counter
cmp x10,16 // 16 digits ?
blt 1b // no loop
100:
ldr lr,[sp],16 // restaur 1 registers
ret // return to address lr x30
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* x0 contains the address of table */
displayTable:
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
mov x2,x0 // table address
mov x3,0
1: // loop display table
ldr x0,[x2,x3,lsl 3]
ldr x1,qAdrsZoneConv
bl conversion10S // décimal conversion
ldr x0,qAdrsMessResult
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc // insert result at // character
bl affichageMess // display message
add x3,x3,1
cmp x3,NBELEMENTS - 1
ble 1b
ldr x0,qAdrszCarriageReturn
bl affichageMess
mov x0,x2
100:
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"Value : -154389710 Value : +9 Value : +16 Value : +25 Value : +26 Value : +71 Value : +115 Value : +301 Value : +4400 Value : +5006 Value : +12485 Table sorted.
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
ARM Assembly
/* ARM assembly Raspberry PI */
/* program radixSort1.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes */
/************************************/
.include "../constantes.inc"
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessSortOk: .asciz "Table sorted.\n"
szMessSortNok: .asciz "Table not sorted !!!!!.\n"
sMessResult: .asciz "Value : @ \n"
szCarriageReturn: .asciz "\n"
.align 4
TableNumber: .int 1,110,30,6,201,5004,29,10,1008,4,7,-25000
#TableNumber: .int 10,9,8,7,6,5,4,3,2,1
.equ NBELEMENTS, (. - TableNumber) / 4
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
ldr r0,iAdrTableNumber @ address number table
mov r1,#0 @ first element
mov r2,#NBELEMENTS @ number of élements
bl radixSort
ldr r0,iAdrTableNumber @ address number table
bl displayTable
ldr r0,iAdrTableNumber @ address number table
mov r1,#NBELEMENTS @ number of élements
bl isSorted @ control sort
cmp r0,#1 @ sorted ?
beq 1f
ldr r0,iAdrszMessSortNok @ no !! error sort
bl affichageMess
b 100f
1: @ yes
ldr r0,iAdrszMessSortOk
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsMessResult: .int sMessResult
iAdrTableNumber: .int TableNumber
iAdrszMessSortOk: .int szMessSortOk
iAdrszMessSortNok: .int szMessSortNok
/******************************************************************/
/* control sorted table */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements > 0 */
/* r0 return 0 if not sorted 1 if sorted */
isSorted:
push {r2-r4,lr} @ save registers
mov r2,#0
ldr r4,[r0,r2,lsl #2]
1:
add r2,#1
cmp r2,r1
movge r0,#1
bge 100f
ldr r3,[r0,r2, lsl #2]
cmp r3,r4
movlt r0,#0
blt 100f
mov r4,r3
b 1b
100:
pop {r2-r4,lr}
bx lr @ return
/******************************************************************/
/* radix sort */
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the first element */
/* r2 contains the number of element */
radixSort:
push {r3-r10,lr} @ save registers
mov r7,#0b1111 @ mask one digit hexa
mov r10,#0 @ digit counter
1:
add r3,r1,#1 @ start index i
2: @ start loop
ldr r4,[r0,r3,lsl #2] @ load value A[i]
and r8,r4,r7 @ and mask
sub r5,r3,#1 @ index j
3:
ldr r6,[r0,r5,lsl #2] @ load value A[j]
and r9,r6,r7 @ and mask
cmp r9,r8 @ compare one digit hexa
ble 4f
add r5,#1 @ increment index j
str r6,[r0,r5,lsl #2] @ store value A[j+1]
sub r5,#2 @ j = j - 1
cmp r5,r1
bge 3b @ loop if j >= first item
4:
add r5,#1 @ increment index j
str r4,[r0,r5,lsl #2] @ store value A[i] in A[j+1]
add r3,#1 @ increment index i
cmp r3,r2 @ end ?
blt 2b @ no -> loop
//bl displayTable
lsl r7,#4 @ shift mask 4 bits left
add r10,r10,#1 @ increment counter
cmp r10,#8 @ 8 digits ?
blt 1b @ no loop
100:
pop {r3-r10,lr}
bx lr @ return
/******************************************************************/
/* Display table elements */
/******************************************************************/
/* r0 contains the address of table */
displayTable:
push {r0-r3,lr} @ save registers
mov r2,r0 @ table address
mov r3,#0
1: @ loop display table
ldr r0,[r2,r3,lsl #2]
ldr r1,iAdrsZoneConv @
bl conversion10S @ décimal conversion
ldr r0,iAdrsMessResult
ldr r1,iAdrsZoneConv @ insert conversion
bl strInsertAtCharInc
bl affichageMess @ display message
add r3,#1
cmp r3,#NBELEMENTS - 1
ble 1b
ldr r0,iAdrszCarriageReturn
bl affichageMess
mov r0,r2
100:
pop {r0-r3,lr}
bx lr
iAdrsZoneConv: .int sZoneConv
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"Value : -25000 Value : +1 Value : +4 Value : +6 Value : +7 Value : +10 Value : +29 Value : +30 Value : +110 Value : +201 Value : +1008 Value : +5004 Table sorted.
Arturo
radixSort: function [items][
base: 10
a: new items
rounds: inc floor (ln max a)/ln base
loop rounds 'i [
buckets: array.of: 2*base []
baseI: base ^ i
loop a 'n [
digit: last digits n
if n >= 0 -> digit: digit + base
buckets\[digit]: buckets\[digit] ++ n
]
a: new flatten buckets
]
return a
]
print radixSort [3 1 2 8 5 7 9 4 6]
- Output:
1 2 3 4 5 6 7 8 9
ATS
(*
Stable integer-keyed radix sorts for unsigned and signed integers
of the various typekinds.
The radix is 256.
*)
(*------------------------------------------------------------------*)
#include "share/atspre_staload.hats"
staload UN = "prelude/SATS/unsafe.sats"
(*------------------------------------------------------------------*)
extern fn {a : vt@ype}
{tk : tkind}
g0uint_radix_sort
{n : int}
(arr : &array (a, n) >> _,
n : size_t n)
:<!wrt> void
extern fn {a : vt@ype}
{tk : tkind}
g0uint_radix_sort$key
{n : int}
{i : nat | i < n}
(arr : &RD(array (a, n)),
i : size_t i)
:<> g0uint tk
(*------------------------------------------------------------------*)
extern fn {a : vt@ype}
{tki, tku : tkind}
g0int_radix_sort
{n : int}
(arr : &array (a, n) >> _,
n : size_t n)
:<!wrt> void
extern fn {a : vt@ype}
{tki : tkind}
g0int_radix_sort$key
{n : int}
{i : nat | i < n}
(arr : &RD(array (a, n)),
i : size_t i)
:<> g0int tki
(*------------------------------------------------------------------*)
(* WARNING: Much of the following code does NOT take into account
the linearity of array entries. But this unsafeness is
hidden from the user. *)
fn {}
bin_sizes_to_indices
(bin_indices : &array (size_t, 256) >> _)
:<!wrt> void =
let
fun
loop {i : int | i <= 256}
{accum : int}
.<256 - i>.
(bin_indices : &array (size_t, 256) >> _,
i : size_t i,
accum : size_t accum)
:<!wrt> void =
if i <> i2sz 256 then
let
prval () = lemma_g1uint_param i
val elem = bin_indices[i]
in
if elem = i2sz 0 then
loop (bin_indices, succ i, accum)
else
begin
bin_indices[i] := accum;
loop (bin_indices, succ i, accum + g1ofg0 elem)
end
end
in
loop (bin_indices, i2sz 0, i2sz 0)
end
fn {a : vt@ype}
{tk : tkind}
count_entries
{n : int}
{shift : nat}
(arr : &RD(array (a, n)),
n : size_t n,
bin_indices : &array (size_t?, 256)
>> array (size_t, 256),
all_expended : &bool? >> bool,
shift : int shift)
:<!wrt> void =
let
fun
loop {i : int | i <= n}
.<n - i>.
(arr : &RD(array (a, n)),
bin_indices : &array (size_t, 256) >> _,
all_expended : &bool >> bool,
i : size_t i)
:<!wrt> void =
if i <> n then
let
prval () = lemma_g1uint_param i
val key : g0uint tk = g0uint_radix_sort$key<a><tk> (arr, i)
val key_shifted = key >> shift
val digit = ($UN.cast{uint} key_shifted) land 255U
val [digit : int] digit = g1ofg0 digit
extern praxi set_range :
() -<prf> [0 <= digit; digit <= 255] void
prval () = set_range ()
val count = bin_indices[digit]
val () = bin_indices[digit] := succ count
in
all_expended := all_expended * iseqz key_shifted;
loop (arr, bin_indices, all_expended, succ i)
end
prval () = lemma_array_param arr
in
array_initize_elt<size_t> (bin_indices, i2sz 256, i2sz 0);
all_expended := true;
loop (arr, bin_indices, all_expended, i2sz 0)
end
fn {a : vt@ype}
{tk : tkind}
sort_by_digit
{n : int}
{shift : nat}
(arr1 : &RD(array (a, n)),
arr2 : &array (a, n) >> _,
n : size_t n,
all_expended : &bool? >> bool,
shift : int shift)
:<!wrt> void =
let
var bin_indices : array (size_t, 256)
in
count_entries<a><tk> (arr1, n, bin_indices, all_expended, shift);
if all_expended then
()
else
let
fun
rearrange {i : int | i <= n}
.<n - i>.
(arr1 : &RD(array (a, n)),
arr2 : &array (a, n) >> _,
bin_indices : &array (size_t, 256) >> _,
i : size_t i)
:<!wrt> void =
if i <> n then
let
prval () = lemma_g1uint_param i
val key = g0uint_radix_sort$key<a><tk> (arr1, i)
val key_shifted = key >> shift
val digit = ($UN.cast{uint} key_shifted) land 255U
val [digit : int] digit = g1ofg0 digit
extern praxi set_range :
() -<prf> [0 <= digit; digit <= 255] void
prval () = set_range ()
val [j : int] j = g1ofg0 bin_indices[digit]
(* One might wish to get rid of this assertion somehow,
to eliminate the branch, should it prove a
problem. *)
val () = $effmask_exn assertloc (j < n)
val p_dst = ptr_add<a> (addr@ arr2, j)
and p_src = ptr_add<a> (addr@ arr1, i)
val _ = $extfcall (ptr, "memcpy", p_dst, p_src,
sizeof<a>)
val () = bin_indices[digit] := succ (g0ofg1 j)
in
rearrange (arr1, arr2, bin_indices, succ i)
end
prval () = lemma_array_param arr1
in
bin_sizes_to_indices<> bin_indices;
rearrange (arr1, arr2, bin_indices, i2sz 0)
end
end
fn {a : vt@ype}
{tk : tkind}
g0uint_sort {n : pos}
(arr1 : &array (a, n) >> _,
arr2 : &array (a, n) >> _,
n : size_t n)
:<!wrt> void =
let
fun
loop {idigit_max, idigit : nat | idigit <= idigit_max}
.<idigit_max - idigit>.
(arr1 : &array (a, n) >> _,
arr2 : &array (a, n) >> _,
from1to2 : bool,
idigit_max : int idigit_max,
idigit : int idigit)
:<!wrt> void =
if idigit = idigit_max then
begin
if ~from1to2 then
let
val _ =
$extfcall (ptr, "memcpy", addr@ arr1, addr@ arr2,
sizeof<a> * n)
in
end
end
else if from1to2 then
let
var all_expended : bool
in
sort_by_digit<a><tk> (arr1, arr2, n, all_expended,
8 * idigit);
if all_expended then
()
else
loop (arr1, arr2, false, idigit_max, succ idigit)
end
else
let
var all_expended : bool
in
sort_by_digit<a><tk> (arr2, arr1, n, all_expended,
8 * idigit);
if all_expended then
let
val _ =
$extfcall (ptr, "memcpy", addr@ arr1, addr@ arr2,
sizeof<a> * n)
in
end
else
loop (arr1, arr2, true, idigit_max, succ idigit)
end
in
loop (arr1, arr2, true, sz2i sizeof<g1uint tk>, 0)
end
#define SIZE_THRESHOLD 256
extern praxi
unsafe_cast_array
{a : vt@ype}
{b : vt@ype}
{n : int}
(arr : &array (b, n) >> array (a, n))
:<prf> void
implement {a} {tk}
g0uint_radix_sort {n} (arr, n) =
if n <> 0 then
let
prval () = lemma_array_param arr
fn
sort {n : pos}
(arr1 : &array (a, n) >> _,
arr2 : &array (a, n) >> _,
n : size_t n)
:<!wrt> void =
g0uint_sort<a><tk> (arr1, arr2, n)
in
if n <= SIZE_THRESHOLD then
let
var arr2 : array (a, SIZE_THRESHOLD)
prval @(pf_left, pf_right) =
array_v_split {a?} {..} {SIZE_THRESHOLD} {n} (view@ arr2)
prval () = view@ arr2 := pf_left
prval () = unsafe_cast_array{a} arr2
val () = sort (arr, arr2, n)
prval () = unsafe_cast_array{a?} arr2
prval () = view@ arr2 :=
array_v_unsplit (view@ arr2, pf_right)
in
end
else
let
val @(pf_arr2, pfgc_arr2 | p_arr2) = array_ptr_alloc<a> n
macdef arr2 = !p_arr2
prval () = unsafe_cast_array{a} arr2
val () = sort (arr, arr2, n)
prval () = unsafe_cast_array{a?} arr2
val () = array_ptr_free (pf_arr2, pfgc_arr2 | p_arr2)
in
end
end
(*------------------------------------------------------------------*)
fn {a : vt@ype}
{tki, tku : tkind}
g0int_sort {n : int}
(arr : &array (a, n) >> _,
n : size_t n)
:<!wrt> void =
let
macdef get_key = g0int_radix_sort$key<a><tki>
prval () = lemma_array_param arr
in
if n = 0 then
()
else
let
val () = $effmask_exn
assertloc (sizeof<g0int tki> = sizeof<g0uint tku>)
fn
find_least_key (arr : &RD(array (a, n)))
:<> g0int tki =
let
fun
loop {i : int | i <= n}
.<n - i>.
(arr : &RD(array (a, n)),
least_key : g0int tki,
i : size_t i)
:<> g0int tki =
if i <> n then
let
prval () = lemma_g1uint_param i
val key = get_key (arr, i)
in
loop (arr, min (least_key, key), succ i)
end
else
least_key
in
if n = 0 then
get_key (arr, i2sz 0)
else
let
val first_key = get_key (arr, i2sz 0)
in
loop (arr, first_key, i2sz 1)
end
end
val least_key = find_least_key arr
(* The offset is the two's complement of the least key. Thus the
least key is mapped to zero and the order of keys is
preserved. *)
val offset = succ (lnot ($UN.cast{g1uint tku} least_key))
implement
g0uint_radix_sort$key<a><tku> (arr, i) =
let
val keyi = get_key (arr, i)
in
g0i2u keyi + offset
end
in
g0uint_radix_sort<a><tku> (arr, n)
end
end
implement {a} {tki, tku}
g0int_radix_sort (arr, n) =
g0int_sort<a><tki, tku> (arr, n)
(*------------------------------------------------------------------*)
implement
main0 () =
let
implement
g0int_radix_sort$key<int><intknd> (arr, i) =
arr[i]
var arr : array (int, 10)
val () =
array_initize_list<int>
(arr, 10, $list (1, 2, 1, ~2, 330, 5000, 16, ~20000, 1, 2))
val () = g0int_radix_sort<int><intknd, uintknd> (arr, i2sz 10)
val () = println! (list_vt2t (array2list (arr, i2sz 10)))
in
end
(*------------------------------------------------------------------*)- Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC radix_sort_task.dats && ./a.out -20000, -2, 1, 1, 1, 2, 2, 16, 330, 5000
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
B4X
Sub RadixSort (Old() As Int)
Dim i, j As Int
Dim tmp(Old.Length) As Int
For shift = 31 To 0 Step - 1
j = 0
For i = 0 To Old.Length - 1
Dim move As Boolean = Bit.ShiftLeft(Old(i), shift) >= 0
If (shift = 0 And move = False) Or (shift <> 0 And move) Then
Old(i - j) = Old(i)
Else
tmp(j) = Old(i)
j = j + 1
End If
Next
Bit.ArrayCopy(tmp, 0, Old, Old.Length - j, j)
Next
End Sub
Sub Test
Dim arr() As Int = Array As Int(34, 23, 54, -123, 543, 123)
RadixSort(arr)
For Each i As Int In arr
Log(i)
Next
End SubOutput:
-123 23 34 54 123 543
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#
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();
}
}
}
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
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
EasyLang
proc sort . d[] .
# radix = 10
radix = 256
max = 0
for di = 1 to len d[]
if d[di] > max
max = d[di]
.
.
len buck[][] radix
pos = 1
while pos <= max
for i = 1 to radix
len buck[i][] 0
.
for di = 1 to len d[]
h = d[di] div pos mod radix + 1
buck[h][] &= d[di]
.
di = 1
for i = 1 to radix
for j = 1 to len buck[i][]
d[di] = buck[i][j]
di += 1
.
.
pos *= radix
.
.
data[] = [ 29 4 72 44 55 26 27 77 92 5 ]
sort data[]
print data[]
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
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
SUBROUTINE VARRADIX(A , Siz)
!
! No Copyright is exerted due to considerable prior art in the Public Domain.
! This Fortran version by Peter Kelly ~ peter.kelly@acm.org
!
! Permission is hereby granted, free of charge, to any person obtaining
! a copy of this software and associated documentation files (the
! "Software"), to deal in the Software without restriction, including
! without limitation the rights to use, copy, modify, merge, publish,
! distribute, sublicense, and/or sell copies of the Software, and to
! permit persons to whom the Software is furnished to do so, subject to
! the following conditions:
! The above copyright notice and this permission notice shall be
! included in all copies or substantial portions of the Software.
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
! EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
! MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
! IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
! CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
! TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
! SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
!
!
! LSD sort with a configurable RADIX, Using a RADIX of 256 performs well, hence I have defaulted it in. It is snarly fast.
! It could be optimized by merging the two routines but this way gives greater clarity as to what's going on.
IMPLICIT NONE
!
! PARAMETER definitions
!
INTEGER , PARAMETER :: BASE = 256 ! whatever base you need, just change this
!
! Dummy arguments
!
INTEGER :: Siz
INTEGER , DIMENSION(Siz) :: A
!
! Local variables
!
INTEGER , ALLOCATABLE , DIMENSION(:) :: b
INTEGER , ALLOCATABLE , DIMENSION(:) :: c
INTEGER :: exps
INTEGER :: maxs
!
ALLOCATE(b(Siz))
ALLOCATE(c(BASE))
exps = 1
maxs = MAXVAL(A)
DO WHILE ( (maxs/exps)>0 )
CALL XXCOUNTING_SORT(A , Siz , exps , BASE , b , c)
exps = exps*BASE
END DO
deallocate(C)
deallocate(B)
RETURN
CONTAINS
!
!//b is the base you want
!//exp is the value used for the division
SUBROUTINE XXCOUNTING_SORT(A , Siz , Exps , Base , B , C)
IMPLICIT NONE
! I used zero based arrays as it made the calcs infinitely easier :)
!
! Dummy arguments
!
INTEGER :: Base
INTEGER :: Exps
INTEGER :: Siz ! Size
INTEGER , DIMENSION(0:) :: A
INTEGER , DIMENSION(0:) :: B
INTEGER , DIMENSION(0:) :: C
INTENT (IN) Base , Exps , Siz
INTENT (INOUT) A , B , C
!
! Local variables
!
INTEGER :: i
INTEGER :: k
!
C = 0 ! Init the arrays
B = 0
!
DO i = 0 , Siz - 1 , 1
k = MOD((A(i)/Exps) , Base) ! Fill Histo
C(k) = C(k) + 1
END DO
!
DO i = 1 , Base - 1 , 1
C(i) = C(i) + C(i - 1) ! Build cumulative Histo
END DO
!
DO i = Siz - 1 , 0 , -1
k = MOD(A(i)/Exps , Base) ! Load the Buffer Array in order
B(C(k) - 1) = A(i)
C(k) = C(k) - 1
END DO
!
DO i = 0 , Siz - 1 , 1 ! Copy across
A(i) = B(i)
END DO
RETURN
END SUBROUTINE XXCOUNTING_SORT
END SUBROUTINE Varradix
!***************************************************************************
! End of LSD sort with any Radix
!***************************************************************************
MODULE LEASTSIG
IMPLICIT NONE
!
! No Copyright is exerted due to considerable prior art in the Public Domain.
! This Fortran version by Peter Kelly ~ peter.kelly@acm.org
!
! Permission is hereby granted, free of charge, to any person obtaining
! a copy of this software and associated documentation files (the
! "Software"), to deal in the Software without restriction, including
! without limitation the rights to use, copy, modify, merge, publish,
! distribute, sublicense, and/or sell copies of the Software, and to
! permit persons to whom the Software is furnished to do so, subject to
! the following conditions:
! The above copyright notice and this permission notice shall be
! included in all copies or substantial portions of the Software.
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
! EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
! MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
! IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
! CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
! TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
! SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
!
! Implementation of a classic Radix Sort LSD style :)
! Works well, Integers only but it goes faster than a comparison sort
CONTAINS
! Main Radix Sort sort function
SUBROUTINE LSDRADIXSORT(A , N)
IMPLICIT NONE
!
! Dummy arguments
!
INTEGER :: N
INTEGER , target, DIMENSION(0:N - 1) :: A ! All arrays based off zero, one day I'll fix it
INTENT (IN) N
INTENT (INOUT) A
!
! Local variables
!
INTEGER , DIMENSION(0:9) :: counts
INTEGER :: digitplace
INTEGER :: i
INTEGER :: j
INTEGER :: largestnum
INTEGER, DIMENSION(0:N - 1) :: results
!
digitplace = 1 ! Count of the keys
largestnum = MAXVAL(A)
DO WHILE ( (largestnum/digitplace)>0 )
counts = 0 ! Init the count array
DO i = 0 , N - 1 , 1
J = (A(i)/digitplace)
J = MODULO(j , 10)
counts(j) = counts(j) + 1
END DO
! Change count(i) so that count(i) now contains actual position of this digit in result()
! Working similar to the counting sort algorithm
DO i = 1 , 9 , 1
counts(i) = counts(i) + counts(i - 1) ! Build up the prefix sum
END DO
!
DO i = N - 1 , 0 , -1 ! Move from left to right
j = (A(i)/digitplace)
j = MODULO(j, 10)
results(counts(j) - 1) = A(i) ! Need to subtract one as we are zero based but prefix sum is 1 based
counts(j) = counts(j) - 1
END DO
!
DO i = 0 , N - 1 , 1 ! Copy the semi-sorted data into the input
A(i) = results(i)
END DO
!
digitplace = digitplace*10
END DO ! While loop
RETURN
END SUBROUTINE LSDRADIXSORT
END MODULE LEASTSIG
!***************************************************************************
! End of Classic LSD sort with Radix 10
!***************************************************************************
!Superfast FORTRAN LSD sort
! Dataset is input array, Scratch is working array
!
SUBROUTINE FASTLSDRAD(Dataset , Scratch , Dsize)
!
! No Copyright is exerted due to considerable prior art in the Public Domain.
! This Fortran version by Peter Kelly ~ peter.kelly@acm.org
!
! Permission is hereby granted, free of charge, to any person obtaining
! a copy of this software and associated documentation files (the
! "Software"), to deal in the Software without restriction, including
! without limitation the rights to use, copy, modify, merge, publish,
! distribute, sublicense, and/or sell copies of the Software, and to
! permit persons to whom the Software is furnished to do so, subject to
! the following conditions:
! The above copyright notice and this permission notice shall be
! included in all copies or substantial portions of the Software.
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
! EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
! MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
! IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
! CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
! TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
! SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
!
! This LSD sort is optimized to a base 16,Radix 256 sort which is about as fast as LSD gets. As well as a fast
! algorithm, it has great cache coherency so performs exceptionally on large data sets,
! I have optimized out all the divide and modulus functions and replaced them with bit shifts for speed.
! A further speed optimization is obtained by using pointers to the DATA and TEMP arrays and swapping them each pass of
! the LSB calculation. In FORTRAN this is a bit clunky but much faster than copying data back and forth between arrays.
!
! All arrays are zero based as this makes the indexing calculations straightforward without the need for
! subsequent adds and subtracts to track the correct index
! .
IMPLICIT NONE
!
! Dummy arguments
!
INTEGER :: Dsize
INTEGER , TARGET , DIMENSION(0:Dsize - 1) :: Scratch ! Declared as TARGET as we will manipulate with pointers
INTEGER , TARGET , DIMENSION(0:Dsize - 1) :: Dataset
INTENT (IN) Dsize
INTENT (INOUT) Scratch , Dataset
!
! Local variables
!
INTEGER , POINTER , DIMENSION(:) :: a ! The pointer to the data
INTEGER , POINTER , DIMENSION(:) :: b ! The pointer to the buffer
INTEGER :: i
INTEGER :: j
INTEGER :: m
INTEGER , DIMENSION(0:255,0:3) :: stats_table
INTEGER :: n
LOGICAL :: swap
INTEGER :: u
!
stats_table = 0 ! index matrix
swap = .TRUE. ! For swapping pointers
!
a => Dataset
b => Scratch
!
DO i = 0 , Dsize - 1 , 1 ! generate histograms
u = a(i)
DO j = 0 , 3 , 1
n = IAND(u , z'FF')
u = SHIFTR(u , 8)
stats_table(n,j) = stats_table(n,j) + 1
END DO
END DO
!
DO i = 0 , 3 , 1 ! convert to indices
m = 0
DO j = 0 , 255 , 1
n = stats_table(j , i)
stats_table(j , i) = m
m = m + n
END DO
END DO
!
DO j = 0 , 3 , 1 ! Radix Sort, sort by LSB
DO i = 0 , Dsize - 1 , 1
u = a(i)
m = IAND(SHIFTR(u,SHIFTL(j,3)) , z'FF') ! Eliminate the MOD 16 and div with shifts
b(stats_table(m,j)) = u ! Push the data into the buffer
stats_table(m,j) = stats_table(m,j) + 1
END DO
!
! Instead of copying back from the temp values swap the array pointers
!
IF( swap )THEN
a => Scratch ! A now points to the b buffer
b => Dataset ! B now is the data set
ELSE
a => Dataset
b => Scratch
END IF
swap = .NOT.swap ! Set to swap back and forth every pass
END DO
!
RETURN
END SUBROUTINE FASTLSDRAD
!***************************************************************************
! End of Superfast LSD sort
!***************************************************************************
*=======================================================================
* 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
*
ILIM = Bit_size(i) !Get the fixed number of bits
*=======================================================================
* 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
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;
}
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
Julia
function radixsort(tobesorted::Vector{Int64})
arr = deepcopy(tobesorted)
for shift in 63:-1:0
tmp = Vector{Int64}(undef, length(arr))
j = 0
for i in 1:length(arr)
if (shift == 0) == ((arr[i] << shift) >= 0)
arr[i - j] = arr[i]
else
tmp[j + 1] = arr[i]
j += 1
end
end
tmp[j+1:end] .= arr[1:length(tmp)-j]
arr = tmp
end
arr
end
function testradixsort()
arrays = [[170, 45, 75, -90, -802, 24, 2, 66], [-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028]]
for array in arrays
println(radixsort(array))
end
end
testradixsort()
- Output:
[-802, -90, 2, 24, 45, 66, 75, 170] [-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]
Kotlin
// 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 /Wolfram Language
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}
Nim
func radixSort[T](a: openArray[T]): seq[T] =
result = @a
## Loop for every bit in the integers.
for shift in countdown(63, 0):
var tmp = newSeq[T](result.len) # The array to put the partially sorted array into.
var j = 0 # The number of 0s.
for i in 0..result.high:
# If there is a 1 in the bit we are testing, the number will be negative.
let move = result[i] shl shift >= 0
# If this is the last bit, negative numbers are actually lower.
let toBeMoved = if shift == 0: not move else: move
if toBeMoved:
tmp[j] = result[i]
inc j
else:
# It's a 1, so stick it in the result array for now.
result[i - j] = result[i]
# Copy over the 1s from the old array.
for i in j..tmp.high:
tmp[i] = result[i - j]
# And now the tmp array gets switched for another round of sorting.
result =move(tmp)
when isMainModule:
const arrays = [@[170, 45, 75, -90, -802, 24, 2, 66],
@[-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028]]
for a in arrays:
echo radixSort(a)
- Output:
@[-802, -90, 2, 24, 45, 66, 75, 170] @[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]
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]);
}
Phix
with javascript_semantics function radixSortn(sequence s, integer n) sequence buckets = repeat({},10), 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), passes = max(max(s),abs(mins)) passes = floor(log10(passes))+1 if mins<0 then sequence buckets = split_by_sign(s) s = reverse(sq_uminus(radixSortn(buckets[1],passes))) & radixSortn(buckets[2],passes) 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
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))
An alternate implementation using which works on Python 3:
#python3.7 <
def flatten(some_list):
"""
Flatten a list of lists.
Usage: flatten([[list a], [list b], ...])
Output: [elements of list a, elements of list b]
"""
new_list = []
for sub_list in some_list:
new_list += sub_list
return new_list
def radix(some_list, idex=None, size=None):
"""
Recursive radix sort
Usage: radix([unsorted list])
Output: [sorted list]
"""
# Initialize variables not set in the initial call
if size == None:
largest_num = max(some_list)
largest_num_str = str(largest_num)
largest_num_len = len(largest_num_str)
size = largest_num_len
if idex == None:
idex = size
# Translate the index we're looking at into an array index.
# e.g., looking at the 10's place for 100:
# size: 3
# idex: 2
# i: (3-2) == 1
# str(123)[i] -> 2
i = size - idex
# The recursive base case.
# Hint: out of range indexing errors
if i >= size:
return some_list
# Initialize the bins we will place numbers into
bins = [[] for _ in range(10)]
# Iterate over the list of numbers we are given
for e in some_list:
# The destination bin; e.g.,:
# size: 5
# e: 29
# num_s: '00029'
# i: 3
# dest_c: '2'
# dest_i: 2
num_s = str(e).zfill(size)
dest_c = num_s[i]
dest_i = int(dest_c)
bins[dest_i] += [e]
result = []
for b in bins:
#If the bin is empty it skips the recursive call
if b == []:
continue
# Make the recursive call
# Sort each of the sub-lists in our bins
result.append(radix(b, idex-1, size))
# Flatten our list
# This is also called in our recursive call,
# so we don't need flatten to be recursive.
flattened_result = flatten(result)
return flattened_result
That same example but more compact:
#python3.7 <
def flatten(l):
return [y for x in l for y in x]
def radix(l, p=None, s=None):
if s == None:
s = len(str(max(l)))
if p == None:
p = s
i = s - p
if i >= s:
return l
bins = [[] for _ in range(10)]
for e in l:
bins[int(str(e).zfill(s)[i])] += [e]
return flatten([radix(b, p-1, s) for b in bins])
QB64
#lang QB64
'* don't be an a$$. Keep this credit notice with the source:
'* written/refactored by CodeGuy, 2018.
'* also works with negative numbers.
TESTN& = 63
A$ = ""
REDIM b(0 TO TESTN&) AS DOUBLE
FOR s& = -1 TO 1 STEP 2
A$ = A$ + CHR$(13) + CHR$(10) + "Random order:"
FOR i = 0 TO TESTN&
b(i) = (1000 * RND) AND 1023
IF i MOD 2 THEN b(i) = -b(i)
IF i < TESTN& THEN
A$ = A$ + LTRIM$(STR$(b(i))) + ","
ELSE
A$ = A$ + LTRIM$(STR$(b(i))) + CHR$(13) + CHR$(10)
END IF
NEXT
RadixSort b(), 0, TESTN&, s&
IF s& = -1 THEN
A$ = A$ + "descending order" + CHR$(13) + CHR$(10)
ELSE
A$ = A$ + "ascending order" + CHR$(13) + CHR$(10)
END IF
FOR i = 0 TO TESTN&
PRINT b(i);
IF i < TESTN& THEN
A$ = A$ + LTRIM$(STR$(b(i))) + ","
ELSE
A$ = A$ + LTRIM$(STR$(b(i))) + CHR$(13) + CHR$(10)
END IF
NEXT
NEXT
PRINT A$
TYPE MinMaxRec
min AS LONG
max AS LONG
END TYPE
SUB RadixSort (CGSortLibArr() AS DOUBLE, start&, finish&, order&)
ArrayIsInteger CGSortLibArr(), start&, finish&, errindex&, errcon&
IF errcon& THEN
'* use another stable sort and sort anyway
MergeSort CGSortLibArr(), start&, finish&, order&
ELSE
DIM RSMMrec AS MinMaxRec
GetMinMaxArray CGSortLibArr(), start&, finish&, RSMMrec
IF CGSortLibArr(RSMMrec.min) = CGSortLibArr(RSMMrec.max) THEN EXIT SUB '* no div0 bombs
delta# = CGSortLibArr(RSMMrec.max) - CGSortLibArr(RSMMrec.min)
DIM pow2 AS _UNSIGNED _INTEGER64
DIM NtmpN AS _UNSIGNED _INTEGER64
DIM Int64MaxShift AS _INTEGER64: Int64MaxShift = 2 ^ 64
REDIM ct&(-1 TO 1)
REDIM RadixCGSortLibArr(0 TO 1, finish& - start&) AS DOUBLE
SELECT CASE order&
CASE 1
pow2 = Int64MaxShift
bits& = LEN(Int64MaxShift) * 8
DO UNTIL bits& < 0
FOR i& = start& TO finish&
NtmpN = Int64MaxShift * (CGSortLibArr(i&) - CGSortLibArr(RSMMrec.min)) / (delta#)
IF NtmpN AND pow2 THEN
tmpradix% = 1
ELSE
tmpradix% = 0
END IF
RadixCGSortLibArr(tmpradix%, ct&(tmpradix%)) = CGSortLibArr(i&)
ct&(tmpradix%) = ct&(tmpradix%) + 1
NEXT
c& = start&
FOR i& = 0 TO 1
FOR j& = 0 TO ct&(i&) - 1
CGSortLibArr(c&) = RadixCGSortLibArr(i&, j&)
c& = c& + 1
NEXT
ct&(i&) = 0
NEXT
pow2 = pow2 / 2
bits& = bits& - 1
LOOP
CASE ELSE
pow2 = 1
FOR bits& = 0 TO 63
FOR i& = start& TO finish&
NtmpN = Int64MaxShift * (CGSortLibArr(i&) - CGSortLibArr(RSMMrec.min)) / (delta#)
IF NtmpN AND pow2 THEN
tmpradix% = 1
ELSE
tmpradix% = 0
END IF
RadixCGSortLibArr(tmpradix%, ct&(tmpradix%)) = CGSortLibArr(i&)
ct&(tmpradix%) = ct&(tmpradix%) + 1
NEXT
c& = start&
FOR i& = 0 TO 1
FOR j& = 0 TO ct&(i&) - 1
CGSortLibArr(c&) = RadixCGSortLibArr(i&, j&)
c& = c& + 1
NEXT
ct&(i&) = 0
NEXT
pow2 = pow2 * 2
NEXT
END SELECT
ERASE RadixCGSortLibArr, ct&
END IF
END SUB
SUB ArrayIsInteger (CGSortLibArr() AS DOUBLE, start&, finish&, errorindex&, IsInt&)
IsInt& = 1
errorindex& = start&
FOR IsIntegerS& = start& TO finish&
IF CGSortLibArr(IsIntegerS&) MOD 1 THEN
errorindex& = IsIntegerS&
IsInt& = 0
EXIT FUNCTION
END IF
NEXT
END FUNCTION
SUB MergeSort (CGSortLibArr() AS DOUBLE, start&, finish&, order&)
SELECT CASE finish& - start&
CASE IS > 31
middle& = start& + (finish& - start&) \ 2
MergeSort CGSortLibArr(), start&, middle&, order&
MergeSort CGSortLibArr(), middle& + 1, finish&, order&
'IF order& = 1 THEN
EfficientMerge CGSortLibArr(), start&, finish&, order&
'ELSE
' MergeRoutine CGSortLibArr(), start&, finish&, order&
'END IF
CASE IS > 0
InsertionSort CGSortLibArr(), start&, finish&, order&
END SELECT
END SUB
SUB EfficientMerge (right() AS DOUBLE, start&, finish&, order&)
half& = start& + (finish& - start&) \ 2
REDIM left(start& TO half&) AS DOUBLE '* hold the first half of the array in left() -- must be the same type as right()
FOR LoadLeft& = start& TO half&
left(LoadLeft&) = right(LoadLeft&)
NEXT
SELECT CASE order&
CASE 1
i& = start&
j& = half& + 1
insert& = start&
DO
IF i& > half& THEN '* left() exhausted
IF j& > finish& THEN '* right() exhausted
EXIT DO
ELSE
'* stuff remains in right to be inserted, so flush right()
WHILE j& <= finish&
right(insert&) = right(j&)
j& = j& + 1
insert& = insert& + 1
WEND
EXIT DO
'* and exit
END IF
ELSE
IF j& > finish& THEN
WHILE i& < LoadLeft&
right(insert&) = left(i&)
i& = i& + 1
insert& = insert& + 1
WEND
EXIT DO
ELSE
IF right(j&) < left(i&) THEN
right(insert&) = right(j&)
j& = j& + 1
ELSE
right(insert&) = left(i&)
i& = i& + 1
END IF
insert& = insert& + 1
END IF
END IF
LOOP
CASE ELSE
i& = start&
j& = half& + 1
insert& = start&
DO
IF i& > half& THEN '* left() exhausted
IF j& > finish& THEN '* right() exhausted
EXIT DO
ELSE
'* stuff remains in right to be inserted, so flush right()
WHILE j& <= finish&
right(insert&) = right(j&)
j& = j& + 1
insert& = insert& + 1
WEND
EXIT DO
'* and exit
END IF
ELSE
IF j& > finish& THEN
WHILE i& < LoadLeft&
right(insert&) = left(i&)
i& = i& + 1
insert& = insert& + 1
WEND
EXIT DO
ELSE
IF right(j&) > left(i&) THEN
right(insert&) = right(j&)
j& = j& + 1
ELSE
right(insert&) = left(i&)
i& = i& + 1
END IF
insert& = insert& + 1
END IF
END IF
LOOP
END SELECT
ERASE left
END SUB
SUB GetMinMaxArray (CGSortLibArr() AS DOUBLE, Start&, Finish&, GetMinMaxArray_minmax AS MinMaxRec)
DIM GetGetMinMaxArray_minmaxArray_i AS LONG
DIM GetMinMaxArray_n AS LONG
DIM GetMinMaxArray_TT AS LONG
DIM GetMinMaxArray_NMod2 AS INTEGER
'* this is a workaround for the irritating malfunction
'* of MOD using larger numbers and small divisors
GetMinMaxArray_n = Finish& - Start&
GetMinMaxArray_TT = GetMinMaxArray_n MOD 10000
GetMinMaxArray_NMod2 = GetMinMaxArray_n - 10000 * ((GetMinMaxArray_n - GetMinMaxArray_TT) / 10000)
IF (GetMinMaxArray_NMod2 MOD 2) THEN
GetMinMaxArray_minmax.min = Start&
GetMinMaxArray_minmax.max = Start&
GetGetMinMaxArray_minmaxArray_i = Start& + 1
ELSE
IF CGSortLibArr(Start&) > CGSortLibArr(Finish&) THEN
GetMinMaxArray_minmax.max = Start&
GetMinMaxArray_minmax.min = Finish&
ELSE
GetMinMaxArray_minmax.min = Finish&
GetMinMaxArray_minmax.max = Start&
END IF
GetGetMinMaxArray_minmaxArray_i = Start& + 2
END IF
WHILE GetGetMinMaxArray_minmaxArray_i < Finish&
IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i) > CGSortLibArr(GetGetMinMaxArray_minmaxArray_i + 1) THEN
IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i) > CGSortLibArr(GetMinMaxArray_minmax.max) THEN
GetMinMaxArray_minmax.max = GetGetMinMaxArray_minmaxArray_i
END IF
IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i + 1) < CGSortLibArr(GetMinMaxArray_minmax.min) THEN
GetMinMaxArray_minmax.min = GetGetMinMaxArray_minmaxArray_i + 1
END IF
ELSE
IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i + 1) > CGSortLibArr(GetMinMaxArray_minmax.max) THEN
GetMinMaxArray_minmax.max = GetGetMinMaxArray_minmaxArray_i + 1
END IF
IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i) < CGSortLibArr(GetMinMaxArray_minmax.min) THEN
GetMinMaxArray_minmax.min = GetGetMinMaxArray_minmaxArray_i
END IF
END IF
GetGetMinMaxArray_minmaxArray_i = GetGetMinMaxArray_minmaxArray_i + 2
WEND
END SUB
SUB InsertionSort (CGSortLibArr() AS DOUBLE, start AS LONG, finish AS LONG, order&)
DIM InSort_Local_ArrayTemp AS DOUBLE
DIM InSort_Local_i AS LONG
DIM InSort_Local_j AS LONG
SELECT CASE order&
CASE 1
FOR InSort_Local_i = start + 1 TO finish
InSort_Local_ArrayTemp = CGSortLibArr(InSort_Local_i)
InSort_Local_j = InSort_Local_i - 1
DO UNTIL InSort_Local_j < start
IF (InSort_Local_ArrayTemp < CGSortLibArr(InSort_Local_j)) THEN
CGSortLibArr(InSort_Local_j + 1) = CGSortLibArr(InSort_Local_j)
InSort_Local_j = InSort_Local_j - 1
ELSE
EXIT DO
END IF
LOOP
CGSortLibArr(InSort_Local_j + 1) = InSort_Local_ArrayTemp
NEXT
CASE ELSE
FOR InSort_Local_i = start + 1 TO finish
InSort_Local_ArrayTemp = CGSortLibArr(InSort_Local_i)
InSort_Local_j = InSort_Local_i - 1
DO UNTIL InSort_Local_j < start
IF (InSort_Local_ArrayTemp > CGSortLibArr(InSort_Local_j)) THEN
CGSortLibArr(InSort_Local_j + 1) = CGSortLibArr(InSort_Local_j)
InSort_Local_j = InSort_Local_j - 1
ELSE
EXIT DO
END IF
LOOP
CGSortLibArr(InSort_Local_j + 1) = InSort_Local_ArrayTemp
NEXT
END SELECT
END SUBQuackery
[ stack ] is digit ( --> s )
[ behead swap witheach min ] is smallest ( [ --> n )
[ [] over smallest
rot witheach
[ over -
rot swap join swap ]
swap
0 digit put
dup size temp put
[ ' [ [ ] ] 16 of
constant
swap witheach
[ dup dip
[ digit share
>> 15 &
2dup peek ]
join
unrot poke ]
dup 0 peek size
temp share != while
behead swap
witheach join
4 digit tally again ]
behead nip
temp release
digit release
[] unrot
witheach
[ over +
rot swap join swap ]
drop ] is radixsort ( [ --> [ )
[] 256 times
[ 1999 random 999 - join ]
radixsort
16 times
[ 16 times
[ behead
dup 0 > if sp
dup abs dup
10 < if sp
100 < if sp
echo sp ] cr ]
drop- Output:
-992 -984 -982 -962 -957 -952 -921 -907 -906 -906 -903 -874 -870 -864 -861 -858 -852 -852 -844 -836 -835 -823 -804 -804 -802 -800 -794 -791 -789 -786 -778 -770 -766 -759 -754 -752 -744 -743 -743 -718 -716 -695 -685 -683 -680 -677 -672 -670 -669 -644 -643 -640 -639 -639 -623 -603 -601 -589 -588 -575 -572 -567 -565 -557 -554 -542 -535 -531 -527 -518 -515 -501 -475 -474 -457 -420 -411 -386 -377 -376 -371 -367 -350 -348 -347 -346 -332 -314 -301 -301 -299 -293 -285 -272 -242 -239 -237 -234 -230 -225 -225 -196 -188 -163 -147 -146 -145 -143 -125 -121 -119 -116 -110 -108 -105 -104 -97 -85 -71 -69 -66 -58 -52 -40 -25 -9 -8 14 23 44 45 49 67 69 83 87 87 127 138 143 145 159 160 166 168 169 178 187 204 218 220 231 231 232 235 237 244 251 255 258 264 265 272 285 287 300 314 337 341 348 351 353 359 367 370 372 376 398 402 410 415 420 443 464 465 474 479 483 516 519 520 541 543 546 552 558 559 561 565 579 596 607 616 637 668 668 679 682 698 698 714 720 728 734 736 744 768 768 789 789 797 797 799 802 802 814 815 815 819 833 841 844 848 862 868 885 887 890 894 906 912 927 930 933 936 946 947 950 955 963 967 968 969 969 989 999
Racket
#lang Racket
(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
Raku
(formerly 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;
@buckets[0].value = @buckets[0].value.reverse.List
if !$r and @buckets[0].key eq '-';
@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
REXX
This REXX version also works with malformed integers. 7, 007, +7, .7e1, 7.0 are all treated as equal.
/*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, w /*invoke the radix sort subroutine. */
call show /*display the elements in the @ array*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gen: 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───────*/
w= 0; do m=1 for n; _= word(ILF,m) +0; @.m= _; w= max(w, length(_) )
end /*m*/; return /*W: is the maximum width ↑ of numbers*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
radSort: procedure expose @.; parse arg size,w; mote= c2d(' '); #= 1; !.#._n= size
!.#._b= 1; if w=='' then w= 8
!.#._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= $+1; iterate
end
L= c2d(L); H= c2d(H); ?= ctr._ + low; top._= ?; ts= mote
max= L
do k=L to H; _= d2c(k, 1); c= ctr._ /* [↓] swap 2 item radices.*/
if c>ts then parse value c k with ts max; ?= ?+c; top._= ?
end /*k*/
piv= low /*set PIVot to the low part of the sort*/
do while piv<low+n
it= @.piv
do forever; parse var it =($) _ +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 /*j*/
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 for size; if @.i>=0 then iterate; #= #+1; @@.#= @.i
end /*i*/
do j=1 for size; if @.j>=0 then do; #= #+1; @@.#= @.j; end; @.j= @@.j+0
end /*j*/ /* [↑↑↑] combine 2 lists into 1 list. */
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: do j=1 for n; say 'item' right(j, w) "after the radix sort:" right(@.j, w)
end /*j*/; return /* [↑] display sorted items ───► term.*/
- output (with the middle section elided.)
(Output is shown at 3/4 size.)
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
Rust
fn merge(in1: &[i32], in2: &[i32], out: &mut [i32]) {
let (left, right) = out.split_at_mut(in1.len());
left.clone_from_slice(in1);
right.clone_from_slice(in2);
}
// least significant digit radix sort
fn radix_sort(data: &mut [i32]) {
for bit in 0..31 {
// types of small and big is Vec<i32>.
// It will be infered from the next call of merge function.
let (small, big): (Vec<_>, Vec<_>) = data.iter().partition(|&&x| (x >> bit) & 1 == 0);
merge(&small, &big, data);
}
// last bit is sign
let (negative, positive): (Vec<_>, Vec<_>) = data.iter().partition(|&&x| x < 0);
merge(&negative, &positive, data);
}
fn main() {
let mut data = [170, 45, 75, -90, -802, 24, 2, 66, -17, 2];
println!("Before: {:?}", data);
radix_sort(&mut data);
println!("After: {:?}", data);
}
- Output:
Before: [170, 45, 75, -90, -802, 24, 2, 66, -17, 2] After: [-802, -90, -17, 2, 2, 24, 45, 66, 75, 170]
Scala
object RadixSort extends App {
def sort(toBeSort: Array[Int]): Array[Int] = { // Loop for every bit in the integers
var arr = toBeSort
for (shift <- Integer.SIZE - 1 until -1 by -1) { // The array to put the partially sorted array into
val tmp = new Array[Int](arr.length)
// The number of 0s
var j = 0
// Move the 0s to the new array, and the 1s to the old one
for (i <- arr.indices) // If there is a 1 in the bit we are testing, the number will be negative
// If this is the last bit, negative numbers are actually lower
if ((shift == 0) == (arr(i) << shift >= 0)) arr(i - j) = arr(i)
else {
tmp(j) = arr(i)
j += 1
}
// Copy over the 1s from the old array
arr.copyToArray(tmp, j, arr.length - j)
// And now the tmp array gets switched for another round of sorting
arr = tmp
}
arr
}
println(sort(Array(170, 45, 75, -90, -802, 24, 2, 66)).mkString(", "))
}
Scheme
An implementation for non-negative integers only
;;; An illustrative implementation of the radix-10 example at
;;; https://en.wikipedia.org/w/index.php?title=Radix_sort&oldid=1070890278#Least_significant_digit
(cond-expand
(r7rs)
(chicken (import (r7rs))))
(import (scheme base))
(import (scheme write))
(define (sort-by-decimal-digit data power-of-10)
(define bins (make-vector 10 '()))
(do ((i (- (vector-length data) 1) (- i 1)))
((= i -1))
(let* ((element (vector-ref data i))
(digit (truncate-remainder
(truncate-quotient element power-of-10)
10)))
(vector-set! bins digit
(cons element (vector-ref bins digit)))))
(let ((non-zero-found
(let loop ((i 1))
(cond ((= i (vector-length bins)) #f)
((pair? (vector-ref bins i)) #t)
(else (loop (+ i 1)))))))
(when non-zero-found
(let ((i 0))
(do ((j 0 (+ j 1)))
((= j (vector-length bins)))
(do ((p (vector-ref bins j) (cdr p)))
((null? p))
(vector-set! data i (car p))
(set! i (+ i 1))))))
(not non-zero-found)))
(define (radix-sort data)
(let loop ((power-of-10 1))
(let ((done (sort-by-decimal-digit data power-of-10)))
(unless done
(loop (* 10 power-of-10))))))
(define data (vector-copy #(170 45 75 90 2 802 2 66)))
(write data)
(newline)
(radix-sort data)
(write data)
(newline)
- Output:
$ gosh radix_sort_task.scm #(170 45 75 90 2 802 2 66) #(2 2 45 66 75 90 170 802)
An implementation using lexicographic order to support negative integers
The following implementation converts signed integers to a lexicographically ordered representation (specifically, unsigned numbers in the correct order). It then sorts the lexicographically ordered representation, and finally converts back to the original representation.
;;; An illustrative implementation of the radix-10 example at
;;; https://en.wikipedia.org/w/index.php?title=Radix_sort&oldid=1070890278#Least_significant_digit
(cond-expand
(r7rs)
(chicken (import (r7rs))))
(import (scheme base))
(import (scheme write))
(define (sort-by-decimal-digit data power-of-10)
(define bins (make-vector 10 '()))
(do ((i (- (vector-length data) 1) (- i 1)))
((= i -1))
(let* ((element (vector-ref data i))
(digit (truncate-remainder
(truncate-quotient element power-of-10)
10)))
(vector-set! bins digit
(cons element (vector-ref bins digit)))))
(let ((non-zero-found
(let loop ((i 1))
(cond ((= i (vector-length bins)) #f)
((pair? (vector-ref bins i)) #t)
(else (loop (+ i 1)))))))
(when non-zero-found
(let ((i 0))
(do ((j 0 (+ j 1)))
((= j (vector-length bins)))
(do ((p (vector-ref bins j) (cdr p)))
((null? p))
(vector-set! data i (car p))
(set! i (+ i 1))))))
(not non-zero-found)))
(define (radix-sort data)
(define offset 0)
(do ((i 0 (+ i 1)))
((<= (vector-length data) i))
(let ((x (vector-ref data i)))
(when (negative? x)
(set! offset (max offset (- x))))))
(do ((i 0 (+ i 1)))
((= i (vector-length data)))
(vector-set! data i (+ (vector-ref data i) offset)))
(let loop ((power-of-10 1))
(let ((done (sort-by-decimal-digit data power-of-10)))
(unless done
(loop (* 10 power-of-10)))))
(do ((i 0 (+ i 1)))
((= i (vector-length data)))
(let ((x (vector-ref data i)))
(vector-set! data i (- (vector-ref data i) offset)))))
(define data (vector-copy #(170 45 75 90 2 802 2 66)))
(write data)
(newline)
(radix-sort data)
(write data)
(newline)
(newline)
(set! data (vector-copy #(170 -45 75 -90 2 -802 2 -66)))
(write data)
(newline)
(radix-sort data)
(write data)
(newline)
- Output:
$ chibi radix_sort_task-2.scm #(170 45 75 90 2 802 2 66) #(2 2 45 66 75 90 170 802) #(170 -45 75 -90 2 -802 2 -66) #(-802 -90 -66 -45 2 2 75 170)
Sidef
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]
Tailspin
templates radixsort&{base:}
sink bucketize
def value: $;
$::raw ~/ $@radixsort.digit::raw -> #
when <=0 ?($value::raw <0..>)> do
..|@radixsort.positives: $value;
when <=0> do
..|@radixsort.negatives(last): $value;
otherwise
def bucket: $ mod $base -> \(<?($value<0..>)> $ + 1 ! <=0> $base ! <> $ !\);
..|@radixsort.buckets($bucket): $value;
@radixsort.done: 0;
end bucketize
// Negatives get completed in wrong length-order, we need to collect by length and correct at the end
@: { done: 1, digit: 1, positives: [], negatives: [[]], buckets: [1..$base -> []]};
$... -> !bucketize
$@.done -> #
when <=done´1> do
[$@.negatives(last..1:-1)... ..., $@.positives...] !
otherwise
def previous: $@.buckets;
..|@: {done: 1, digit: $@.digit::raw * $base, buckets:[1..$base -> []]};
..|@.negatives: [];
$previous... ... -> !bucketize
$@.done -> #
end radixsort
[170, 45, 75, 91, 90, 92, 802, 24, 2, 66] -> radixsort&{base:10} -> !OUT::write
'
' -> !OUT::write
[-170, -45, -91, -90, -92, -802, -24, -2, -76] -> radixsort&{base:10} -> !OUT::write
'
' -> !OUT::write
[170, 45, 75, -91, -90, -92, -802, 24, 2, 66] -> radixsort&{base:10} -> !OUT::write
'
' -> !OUT::write
[170, 45, 75, -91, -90, -92, -802, 24, 2, 66] -> radixsort&{base:3} -> !OUT::write- Output:
[2, 24, 45, 66, 75, 90, 91, 92, 170, 802] [-802, -170, -92, -91, -90, -76, -45, -24, -2] [-802, -92, -91, -90, 2, 24, 45, 66, 75, 170] [-802, -92, -91, -90, 2, 24, 45, 66, 75, 170]
Tcl
package require Tcl 8.5
proc splitByRadix {lst base power} {
# create a list of empty lists to hold the split by digit
set out [lrepeat [expr {$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
uBasic/4tH
In uBasic/4tH you can't pass an array as a parameter. All arrays are global.
Dim @t(10)
Push 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
For i = 0 Step 1 While Used()
@t(i) = Pop()
Next
Proc _Radixsort(10, 10)
For i = 0 TO 9
Print @t(i),
Next
Print
End
_Radixsort
Param (2)
Local (5)
Dim @b(a@)
Dim @u(b@)
For e@ = 0 TO a@-1
If @t(e@) < f@ Then f@ = @t(e@)
If @t(e@) > g@ Then g@ = @t(e@)
Next
For e@ = 0 To a@-1 : @t(e@) = @t(e@) - f@ : Next
g@ = g@ - f@
d@ = 1
Do While g@ / d@
For e@ = 0 to a@-1 : @u(e@) = 0 : Next
For e@ = 0 TO a@-1
@u(@t(e@) / d@ % b@) = @u(@t(e@) / d@ % b@) + 1
Next
For e@ = 1 TO b@-1
@u(e@) = @u(e@) + @u(e@ - 1)
Next
For e@ = a@-1 TO 0 Step -1
c@ = @t(e@) / d@ % b@
@u(c@) = @u(c@)-1
@b(@u(c@)) = @t(e@)
Next
For e@ = 0 To a@-1 : @t(e@) = @b(e@) : Next
d@ = d@ * b@
Loop
For e@ = 0 To a@-1 : @t(e@) = @t(e@) + f@ : Next
Return
- Output:
-31 0 1 2 2 4 65 83 99 782 0 OK, 0:177
Wren
This is based on the approach used here which I've adjusted to deal with negative elements.
// counting sort of 'a' according to the digit represented by 'exp'
var countSort = Fn.new { |a, exp|
var n = a.count
var output = [0] * n
var count = [0] * 10
for (i in 0...n) {
var t = (a[i]/exp).truncate % 10
count[t] = count[t] + 1
}
for (i in 1..9) count[i] = count[i] + count[i-1]
for (i in n-1..0) {
var t = (a[i]/exp).truncate % 10
output[count[t] - 1] = a[i]
count[t] = count[t] - 1
}
for (i in 0...n) a[i] = output[i]
}
// sorts 'a' in place
var radixSort = Fn.new { |a|
// check for negative elements
var min = a.reduce { |m, i| (i < m) ? i : m }
// if there are any, increase all elements by -min
if (min < 0) (0...a.count).each { |i| a[i] = a[i] - min }
// now get the maximum to know number of digits
var max = a.reduce { |m, i| (i > m) ? i : m }
// do counting sort for each digit
var exp = 1
while ((max/exp).truncate > 0) {
countSort.call(a, exp)
exp = exp * 10
}
// if there were negative elements, reduce all elements by -min
if (min < 0) (0...a.count).each { |i| a[i] = a[i] + min }
}
var aa = [[4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [170, 45, 75, 90, 2, 24, -802, -66]]
for (a in aa) {
System.print("Unsorted: %(a)")
radixSort.call(a)
System.print("Sorted : %(a)\n")
}
- Output:
Unsorted: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1] Sorted : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782] Unsorted: [170, 45, 75, 90, 2, 24, -802, -66] Sorted : [-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)
Categories:
- Programming Tasks
- Sorting Algorithms
- Sorting
- 11l
- AArch64 Assembly
- Ada
- ALGOL 68
- ARM Assembly
- Arturo
- ATS
- AutoHotkey
- B4X
- BBC BASIC
- C
- C sharp
- C++
- D
- EasyLang
- Eiffel
- Elixir
- Fortran
- Go
- Groovy
- Haskell
- Icon
- Unicon
- J
- Java
- Jq
- Julia
- Kotlin
- Mathematica
- Wolfram Language
- Nim
- NetRexx
- Perl
- Phix
- PicoLisp
- PureBasic
- Python
- QB64
- Quackery
- Racket
- Raku
- REXX
- Ruby
- Rust
- Scala
- Scheme
- Sidef
- Tailspin
- Tcl
- UBasic/4tH
- Wren
- Zkl
- GUISS/Omit