Sorting algorithms/Radix 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.
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
D
<lang d>import std.stdio, std.math, std.conv, std.traits, std.range, std.algorithm ;
auto rdxsort(int N = 10 , R)(R r)
if(hasLength!R && isRandomAccessRange!R && isIntegral!(ElementType!R)) {
alias ElementType!R E ;
static if(isDynamicArray!R) {
writeln("input is array => in place sort") ;
alias r res ;
E absMax = reduce!max(map!abs(r)) ;
} else {
writeln("input is Range => return a newly sorted array") ;
E[] res ;
E absMax ;
foreach(v;r) {
res ~= v ;
if(absMax < abs(v))
absMax = abs(v) ;
}
}
immutable passes = 1 + to!int(log(absMax)/log(N)) ;
auto pBucket = new E[][](N,0) ; auto nBucket = new E[][](N,0) ;
void split(int pass) {
foreach(v;res) {
auto bIdx = abs(v / (N^^pass)) % N ;
if(v < 0)
nBucket[ bIdx ] ~= v ;
else
pBucket[ bIdx ] ~= v ;
}
}
void merge() {
int idx = 0 ;
foreach_reverse(ref b;nBucket) { // order revrsed for negative
foreach(v;b)
res[idx++] = v ; // reorder from bucket
b.length = 0 ; // reset this bucket
}
foreach(ref b;pBucket) {
foreach(v;b)
res[idx++] = v ; // reorder from bucket
b.length = 0 ; // reset this bucket
}
}
foreach(p;0..passes) {
split(p) ;
merge() ;
}
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 :
input is array => in place sort [-802, -90, 2, 24, 45, 66, 75, 170] input is Range => return a newly sorted array [-169, -74, -65, -44, -23, -1, 91, 803]
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>NB. queue implementation of LSB radix sort. radixSort =: 3 : 0 NB. base radixSort data 16 radixSort y
keys =. x #.^:_1 y NB. compute keys length =. {:#{.keys extra =. (x,-length) {. ,. buckets =. i.x for_pass. 0{i.-length do.
keys =. ,&:>/ (buckets,keys{~"1<pass) <@:}./.extra,keys
extra =. 1 |. extra
end. x#.keys NB. restore the data )</lang>
Sort 10 small numbers in base 3.
(,: 3&radixSort) ?@#~10 1 3 8 9 0 0 8 7 1 6 0 0 1 1 3 6 7 8 8 9
Python
The wikipedia article cited in the introduction includes a python implementation of LSB radix sort.
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 $base {}]
foreach item $lst {
# pulls the selected digit set digit [expr {($item / $base ** $power) % $base}] # 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}]</lang> Output:
0 0 1 1 3 6 7 8 8 9 2 24 45 66 75 90 170 802