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
C
Radix sort, "digits" are most significant bits.<lang c>#include <stdio.h>
- include <limits.h>
- include <stdlib.h>
typedef unsigned int uint;
- define swap(a, b) { tmp = a; a = b; b = tmp; }
- define each(i, x) for (i = 0; i < x; i++)
/* sort unsigned ints */ 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 */ void radix_sort(int *a, int len) { int 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; }
inline void radix_sort_unsigned(uint *a, int len) { _rad_sort_u(a, a + len - 1, (uint)INT_MIN); }
int main() { int len = 16, x[len], 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 {
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, " "));
}</lang> Output:
-802 -90 2 24 45 66 75 170
D
<lang d>import std.stdio ; import std.math, std.conv, std.traits, std.range, std.algorithm, std.array ;
auto rdxsort(int 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 = array(r) ; // input is Range => return a new array
E absMax = reduce!max(map!abs(r)) ;
immutable passes = 1 + to!int(log(absMax)/log(N)) ;
foreach(pass;0..passes) { 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 = reduce!"a~b"(bucket) ; }
return res ;
}
void main() {
auto a = [170, 45, 75, -90, 2, 24, -802, 66] ; writeln(rdxsort(a)) ; writeln(rdxsort(map!"1-a"(a))) ;
}</lang> Output :
[-802, -90, 2, 24, 45, 66, 75, 170] [-169, -74, -65, -44, -23, -1, 91, 803]
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]
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>
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
The wikipedia article cited in the introduction includes a python implementation of LSB radix sort.
Ruby
Negative number handling courtesy the Tcl solution. <lang ruby>class Array
def radix_sort(base=10) ary = dup rounds = (Math.log(self.max.abs)/Math.log(base)).ceil rounds.times do |i| buckets = Hash.new {|h,k| h[k] = []} ary.each do |n| digit = (n/base**i) % base digit = digit + base unless n<0 buckets[digit] << n end ary = buckets.values_at(*(0..2*base)).compact.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</lang>
running with $DEBUG on produces:
[0, [0, 0, 1, 1, 3, 6, 7, 8, 8, 9]] [0, 0, 1, 1, 3, 6, 7, 8, 8, 9] [0, [170, 90, 2, 802, 24, 45, 75, 66]] [1, [2, 802, 24, 45, 66, 170, 75, 90]] [2, [2, 24, 45, 66, 75, 90, 170, 802]] [2, 24, 45, 66, 75, 90, 170, 802] [0, [-66, -802, 170, 90, 2, 24, 45, 75]] [1, [-66, -802, 2, 24, 45, 170, 75, 90]] [2, [-802, -66, 2, 24, 45, 75, 90, 170]] [-802, -66, 2, 24, 45, 75, 90, 170]
Tcl
<lang tcl>package require Tcl 8.5 proc splitByRadix {lst base power} {
# create a list of empty lists to hold the split by digit set out [lrepeat [expr {$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