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
In this task, the goal is to sort an integer array with the radix sort algorithm. The primary purpose is to complete the characterization of sort algorithms task.
Ada
radix_sort.adb: <lang Ada>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;</lang>
output:
-802-90 2 24 45 66 75 170
AutoHotkey
<lang 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 }</lang> Examples:<lang AutoHotkey>d = 170,45,75,90,802,2,24,66 MsgBox, 262144, , % Radix_Sort(d)</lang>
Outputs:
2,24,45,66,75,90,170,802
BBC BASIC
The array index is assumed to start at zero. The third parameter of PROCradixsort() is the radix used. <lang bbcbasic> 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</lang>
Output:
-31 0 1 2 2 4 65 83 99 782
C
Radix sort, "digits" are most significant bits.<lang c>#include <stdio.h>
- include <limits.h>
- include <stdlib.h>
typedef unsigned uint;
- define swap(a, b) { tmp = a; a = b; b = tmp; }
- define each(i, x) for (i = 0; i < x; i++)
/* sort unsigned ints */ static void rad_sort_u(uint *from, uint *to, uint bit) { if (!bit || to < from + 1) return;
uint *ll = from, *rr = to - 1, tmp; while (1) { /* 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; uint *x = (uint*) a;
each(i, len) x[i] ^= INT_MIN; rad_sort_u(x, x + len, INT_MIN); each(i, len) x[i] ^= INT_MIN; }
static inline void radix_sort_unsigned(uint *a, const size_t len) { rad_sort_u(a, a + len, (uint)INT_MIN); }
int main(void) { int len = 16, x[16], i; size_t len = 16, i; each(i, len) x[i] = rand() % 512 - 256;
radix_sort(x, len);
each(i, len) printf("%d%c", x[i], i + 1 < len ? ' ' : '\n');
return 0;
}</lang>output
-182 -175 -151 -141 -70 -51 -20 -5 -1 41 70 103 171 198 227 242
C++
Implements a least significant digit radix sort and a recursive most significant digit radix sort.
Note: the LSD radix sort uses the standard library std::stable_partition algorithm. This algorithm is guaranteed to preserve relative order and has a higher runtime cost. The MSD radix sort uses std::partition and can be significantly faster. <lang cpp>#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;
}</lang> Output:
-802 -90 2 24 45 66 75 170
C#
<lang csharp>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();
}
}
}</lang>
D
Shorter Version
<lang d>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();
}</lang>
- Output:
[-802, -90, 2, 24, 45, 66, 75, 170] [-1, -23, -44, -65, -74, -169, 91, 803]
More Efficient Version
<lang d>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);
}</lang>
- 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
Go
LSD radix 256, negatives handled by flipping the high bit. <lang go>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)
}</lang> 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: <lang groovy>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()
}</lang>
Test: <lang groovy>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]))</lang>
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
<lang 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</lang>
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.
<lang unicon>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</lang>
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 }..
<lang j> 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 )</lang>
An alternate implementation is <lang j>radixsort=: (] #~ [: +/ =/) i.@(>./)</lang>
This uses the maximum value of the list for the base, which allows the list to be sorted in one pass.
Example use:
<lang j> radixsort ?.@#~10 4 5 6 6 6 6 6 8 8</lang>
Or, for negative number support:
<lang j>rsort=: (] + radixsort@:-) <./</lang>
Example:
<lang j> rsort _6+?.@#~10 _2 _1 0 0 0 0 0 2 2</lang>
Java
<lang 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;
}</lang>
<lang Java> 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; }
} </lang>
- 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
<lang 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);
</lang> Example <lang jq>
- 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) </lang>
- Output:
true true true
Mathematica
<lang Mathematica>ClearAll[SortByPos, RadixSort] SortByPos[data : {_List ..}, pos_Integer] := Module[{digs, order},
digs = dataAll, pos; order = Ordering[digs]; dataorder ]
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 ]</lang>
Testing out the algorithm: <lang Mathematica>RadixSort[{170,45,75,-90,-802,24,2,66}] RadixSort[{170,45,75,90,802,2,24,66}]</lang>
- Output:
{-802,-90,2,24,45,66,75,170}
{2,24,45,66,75,90,170,802}
NetRexx
Uses a suggestion in the discussion page to handle negative values.
Limitations - Handles decimal digits only.
Using the Rexx class
<lang NetRexx>/* 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
</lang>
- 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
<lang NetRexx>/* 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
</lang>
Perl
Radix sort in base 10. <lang perl>#!/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;
}</lang> To test, add the following lines: <lang perl>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]);
}</lang>
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.) <lang perl6>sub radsort (@ints) {
my $maxlen = [max] @ints».chars;
my @list = @ints».fmt("\%0{$maxlen}d");
for reverse ^$maxlen -> $r {
my @buckets = @list.classify( *.substr($r,1) ).sort: *.key;
if !$r and @buckets[0].key eq '-' { @buckets[0].value .= reverse }
@list = map *.value.values, @buckets;
}
@list».Int;
}
.say for radsort (-2_000 .. 2_000).roll(20);</lang>
- Output:
-1585 -1427 -1228 -1067 -945 -657 -643 -232 -179 -28 37 411 488 509 716 724 1504 1801 1864 1939
PicoLisp
This is a LSD base-2 radix sort using queues: <lang PicoLisp>(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 )</lang>
Output:
: (radixSort (make (do 12 (link (rand -999 999))))) -> (-999 -930 -666 -336 -218 68 79 187 391 405 697 922)
PureBasic
<lang 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</lang> 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.
<lang python>#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))
</lang>
Racket
<lang racket>
- lang racket
(require data/queue)
(define (radix-sort l r)
(define queues (for/vector #:length r ([_ r]) (make-queue)))
(let loop ([l l] [R 1])
(define all-zero? #t)
(for ([x (in-list l)])
(define x/R (quotient x R))
(enqueue! (vector-ref queues (modulo x/R r)) x)
(unless (zero? x/R) (set! all-zero? #f)))
(if all-zero? l
(loop (let q-loop ([i 0])
(define q (vector-ref queues i))
(let dq-loop ()
(if (queue-empty? q)
(if (< i (sub1 r)) (q-loop (add1 i)) '())
(cons (dequeue! q) (dq-loop)))))
(* R r)))))
(for/and ([i 10000]) ; run some tests on random lists with a random radix
(define (make-random-list)
(for/list ([i (+ 10 (random 10))]) (random 100000)))
(define (sorted? l)
(match l [(list) #t] [(list x) #t]
[(list x y more ...) (and (<= x y) (sorted? (cons y more)))]))
(sorted? (radix-sort (make-random-list) (+ 2 (random 98)))))
- => #t, so all passed
</lang>
REXX
This REXX version works with malformed integers. <lang rexx>/*REXX program performs a radix sort on a stemmed integer array. */ aList='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, the abbreviated list is called the integer log function*/ mina=word(aList,1); maxa=mina
do n=1 for words(aList); x=word(aList,n); @.n=x /*list ──► array.*/
mina =min(x,mina); maxa=max(x,maxa)
width=max(length(abs(mina)),length(maxa))
end /*n*/
n=words(aList); w=length(n); call radSort n
do j=1 for n
say 'item' right(j,w) "after the radix sort:" right(@.j,width+1)
end /*j*/
exit /*stick a fork in it, we're done.*/ /*───────────────────────────────────RADSORT subroutine─────────────────*/ radSort: procedure expose @. width; parse arg size; mote=c2d(' '); #=1 !.#._b=1; !.#._i=1 !.#._n=size; do i=1 for size; y=@.i; @.i=right(abs(y),width,0)
if y<0 then @.i='-'@.i
end /*i*/
/*══════════════════════════════════════where the rubber meets the road.*/
do while #\==0; ctr.=0; L='ffff'x; low=!.#._b; n=!.#._n; radi=!.#._i; H=
#=#-1
do j=low for n; parse var @.j =(radi) _ +1; ctr._=ctr._+1
if ctr._==1 then if _\== then do
if _<<L then L=_
if _>>H then H=_
end
end /*j*/
if L>>H then iterate
_=
if L==H then if ctr._==0 then do; #=#+1; !.#._b=low
!.#._n=n
!.#._i=radi+1; iterate
end
L=c2d(L); H=c2d(H); ?=ctr._+low; top._=?; ts=mote; max=L
do k=L to H; _=d2c(k,1); cen=ctr._
if cen>ts then parse value cen k with ts max
?=?+cen; top._=?
end /*k*/
pivot=low
do while pivot<low+n; it=@.pivot
do forever
parse var it =(radi) _ +1; cen=top._-1; if pivot>=cen then leave
top._=cen; ?=@.cen; @.cen=it; it=?
end /*forever*/
top._=pivot; @.pivot=it; pivot=pivot+ctr._
end /*while pivot<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>1 then call .radSortP top._,d; iterate; end
#=#+1; !.#._b=top._
!.#._n=d
!.#._i=radi+1
end /*until i==max*/
end /*while #\==0 */
/*═════════════════════════════════════we're done with the heavy lifting*/
- =0; do i=size by -1 to 1; if @.i>=0 then iterate; #=#+1; @@.#=@.i; end
do j=1 for size; if @.j <0 then iterate; #=#+1; @@.#=@.j; end
do k=1 for size; @.k=@@.k+0; end /*combine neg&pos radix lists*/
return /*───────────────────────────────────.radSortP subroutine───────────────*/ .radSortP: parse arg bbb,nnn
do k=bbb+1 for nnn-1; q=@.k
do j=k-1 by -1 to bbb while q<<@.j; jp=j+1; @.jp=@.j; end
jp=j+1; @.jp=q
end /*k*/
return</lang> output (with the middle section elided.)
item 1 after the radix sort: -42 item 2 after the radix sort: 0 item 3 after the radix sort: 2 item 4 after the radix sort: 3 item 5 after the radix sort: 4 item 6 after the radix sort: 5 item 7 after the radix sort: 5 item 8 after the radix sort: 6 item 9 after the radix sort: 6 item 10 after the radix sort: 7 item 11 after the radix sort: 7 item 12 after the radix sort: 7 item 13 after the radix sort: 8 . . . (middle section elided.) . . . item 92 after the radix sort: 40 item 93 after the radix sort: 41 item 94 after the radix sort: 43 item 95 after the radix sort: 43 item 96 after the radix sort: 45 item 97 after the radix sort: 47 item 98 after the radix sort: 49 item 99 after the radix sort: 53 item 100 after the radix sort: 55 item 101 after the radix sort: 59 item 102 after the radix sort: 61 item 103 after the radix sort: 67 item 104 after the radix sort: 71 item 105 after the radix sort: 73 item 106 after the radix sort: 79 item 107 after the radix sort: 83 item 108 after the radix sort: 89 item 109 after the radix sort: 97 item 110 after the radix sort: 101 item 111 after the radix sort: 103 item 112 after the radix sort: 107 item 113 after the radix sort: 109 item 114 after the radix sort: 113
Ruby
Negative number handling courtesy the Tcl solution. <lang ruby>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</lang>
running with $DEBUG on produces:
[0, [0, 0, 1, 1, 3, 6, 7, 8, 8, 9]] [0, 0, 1, 1, 3, 6, 7, 8, 8, 9] [0, [170, 90, 2, 802, 24, 45, 75, 66]] [1, [2, 802, 24, 45, 66, 170, 75, 90]] [2, [2, 24, 45, 66, 75, 90, 170, 802]] [2, 24, 45, 66, 75, 90, 170, 802] [0, [-66, -802, 170, 90, 2, 24, 45, 75]] [1, [-66, -802, 2, 24, 45, 170, 75, 90]] [2, [-802, -66, 2, 24, 45, 75, 90, 170]] [-802, -66, 2, 24, 45, 75, 90, 170] [0, [-10000, 100000, 400, 10000, 23]] [1, [-10000, 100000, 400, 10000, 23]] [2, [-10000, 100000, 10000, 23, 400]] [3, [-10000, 100000, 10000, 23, 400]] [4, [-10000, 100000, 23, 400, 10000]] [5, [-10000, 23, 400, 10000, 100000]] [-10000, 23, 400, 10000, 100000]
another version (After sorting at the absolute value, it makes a negative order reverse.) <lang ruby>class Array
def radix_sort(base=10)
ary = dup
m, max = 1, ary.minmax.map(&:abs).max
while m <= max
buckets = Array.new(base){[]}
ary.each {|n| buckets[(n.abs / m) % base] << n}
ary = buckets.flatten
m *= base
end
ary.partition{|n| n<0}.inject{|minus,plus| minus.reverse + plus}
end
end</lang>
Tcl
<lang tcl>package require Tcl 8.5 proc splitByRadix {lst base power} {
# create a list of empty lists to hold the split by digit
set out [lrepeat [expr {$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
}</lang> Demonstrations: <lang tcl>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}]</lang> Output:
0 0 1 1 3 6 7 8 8 9 2 24 45 66 75 90 170 802 -802 -66 2 24 45 75 90 170
zkl
In place int sort, fairly light on garbage creation. <lang zkl>fcn radixSort(ns){ // ints only, inplace, ns is mutable
b:=(0).pump(20,List,List.create.fpM("-")); // 20 buckets: -10..10
z:=ns.reduce(fcn(a,b){if(a.abs()>b.abs()) a else b},0); // max # digits
m:=1;
while(z){
ns.apply2('wrap(n){b[(n/m)%10 +10].append(n)});
ns.clear(); b.apply2(ns.extend); // flatten ie sorted on mth digit
b.apply("clear"); // reset buckets
m *= 10; z /= 10;
}
ns
}</lang> <lang zkl>radixSort(T(170, 45, 75, 90, 802, 2, 24, 66)).println(); radixSort(T(170, 45, 75, -90, -802, 24, 2, 66)).println();</lang>
- Output:
L(2,24,45,66,75,90,170,802) L(-802,-90,2,24,45,66,75,170)