Compare sorting algorithms' performance: Difference between revisions
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[[Image:Tcl_sort_reversed.png]]
[[Image:Tcl_sort_random.png]]
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|Wren-sort}}
{{libheader|Wren-fmt}}
The quick, insertion and shell sorts all use the 'in place' implementations in the Wren-sort module.
The radix sort is lifted from the task of that name and, although more complicated, appears to be much faster than the Kotlin version.
For the bubble sort, I have used the optimized Kotlin implementation.
I've limited the size of the arrays to 50,000 though even then the program takes the best part of half an hour to run, due to the extreme slowness of the bubble and insertion sorts for large amounts of shuffled data.
Results presented in tabular form as Wren doesn't have a plotting library available at the present time.
<lang ecmascript>import "random" for Random
import "/sort" for Sort
import "/fmt" for Fmt
var rand = Random.new()
var onesSeq = Fn.new { |n| List.filled(n, 1) }
var shuffledSeq = Fn.new { |n|
var seq = List.filled(n, 0)
for (i in 0...n) seq[i] = 1 + rand.int(10 * n)
return seq
}
var ascendingSeq = Fn.new { |n|
var seq = shuffledSeq.call(n)
seq.sort()
return seq
}
var bubbleSort = Fn.new { |a|
var n = a.count
while (true) {
var n2 = 0
for (i in 1...n) {
if (a[i - 1] > a[i]) {
a.swap(i, i - 1)
n2 = i
}
}
n = n2
if (n == 0) break
}
}
// 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 measureTime = Fn.new { |sort, seq|
var start = System.clock
sort.call(seq)
return ((System.clock - start) * 1e6).round // microseconds
}
var runs = 10
var lengths = [1, 10, 100, 1000, 10000, 50000]
var sorts = [
bubbleSort,
Fn.new { |a| Sort.insertion(a) },
Fn.new { |a| Sort.quick(a) },
radixSort,
Fn.new { |a| Sort.shell(a) }
]
var sortTitles = ["Bubble", "Insert", "Quick ", "Radix ", "Shell "]
var seqTitles = ["All Ones", "Ascending", "Shuffled"]
var totals = List.filled(seqTitles.count, null)
for (i in 0...totals.count) {
totals[i] = List.filled(sorts.count, null)
for (j in 0...sorts.count) totals[i][j] = List.filled(lengths.count, 0)
}
var k = 0
for (n in lengths) {
var seqs = [onesSeq.call(n), ascendingSeq.call(n), shuffledSeq.call(n)]
for (r in 0...runs) {
for (i in 0...seqs.count) {
for (j in 0...sorts.count) {
var seq = seqs[i].toList
totals[i][j][k] = totals[i][j][k] + measureTime.call(sorts[j], seq)
}
}
}
k = k + 1
}
System.print("All timings in microseconds\n")
System.write("Sequence length")
for (len in lengths) Fmt.write("$8d ", len)
System.print("\n")
for (i in 0...seqTitles.count) {
System.print(" %(seqTitles[i]):")
for (j in 0...sorts.count) {
System.write(" %(sortTitles[j]) ")
for (k in 0...lengths.count) {
var time = (totals[i][j][k] / runs).round
Fmt.write("$8d ", time)
}
System.print()
}
System.print("\n")
}</lang>
{{out}}
<pre>
All timings in microseconds
Sequence length 1 10 100 1000 10000 50000
All Ones:
Bubble 1 2 9 61 643 3225
Insert 1 3 16 118 1256 6338
Quick 1 8 92 983 14746 87660
Radix 6 13 62 460 4823 24379
Shell 1 5 59 770 9542 48873
Ascending:
Bubble 1 2 8 61 637 3221
Insert 1 3 16 118 1251 6371
Quick 1 7 65 643 9149 54199
Radix 7 23 169 1648 21428 130609
Shell 1 5 60 779 9537 49041
Shuffled:
Bubble 1 7 451 37271 4025966 99834073
Insert 0 7 295 24040 2597162 64875212
Quick 1 8 101 1149 16256 95590
Radix 5 24 163 1688 22443 136228
Shell 1 8 111 1514 25180 230897
</pre>
The results are much the same as one might have expected beforehand.
As far as the shuffled data is concerned, quick sort is the fastest though radix and shell sorts are also reasonable performers. Bubble and insertion sorts are very slow indeed for large amounts of data.
Conversely, if the data is already sorted into ascending order, bubble and insertion sorts are much faster than the others and radix sort is the slowest.
If all data is the same, a similar pattern emerges except that radix sort performs better than both shell and quick sorts, the latter being the slowest.
| |||
Revision as of 16:23, 4 May 2021
You are encouraged to solve this task according to the task description, using any language you may know.
Measure a relative performance of sorting algorithms implementations.
Plot execution time vs. input sequence length dependencies for various implementation of sorting algorithm and different input sequence types (example figures).
Consider three type of input sequences:
- ones: sequence of all 1's. Example: {1, 1, 1, 1, 1}
- range: ascending sequence, i.e. already sorted. Example: {1, 2, 3, 10, 15}
- shuffled range: sequence with elements randomly distributed. Example: {5, 3, 9, 6, 8}
Consider at least two different sorting functions (different algorithms or/and different implementation of the same algorithm). For example, consider Bubble Sort, Insertion sort, Quicksort or/and implementations of Quicksort with different pivot selection mechanisms. Where possible, use existing implementations.
Preliminary subtask:
- Bubble Sort, Insertion sort, Quicksort, Radix sort, Shell sort
- Query Performance
- Write float arrays to a text file
- Plot x, y arrays
- Polynomial Fitting
General steps:
- Define sorting routines to be considered.
- Define appropriate sequence generators and write timings.
- Plot timings.
- What conclusions about relative performance of the sorting routines could be made based on the plots?
AutoHotkey
<lang ahk>; BUGGY - FIX
- Persistent
- SingleInstance OFF
SetBatchLines, -1 SortMethods := "Bogo,Bubble,Cocktail,Counting,Gnome,Insertion,Merge,Permutation,Quick,Selection,Shell,BuiltIn" Gui, Add, Edit, vInput, numbers,separated,by,commas,without,spaces,afterwards Loop, PARSE, SortMethods, `, Gui, Add, CheckBox, v%A_LoopField%, %A_LoopField% Sort Gui, Add, Button, gTest, Test! Gui, Show,, SortTest! Return Test: SplashTextOn,,, Test Commencing Sleep 2500 SplashTextOff Gui, +OwnDialogs Gui, Submit, NoHide Loop, PARSE, SortMethods, `, { If (%A_LoopField%) { DllCall("QueryPerformanceCounter", "Int64 *", %A_LoopField%Begin) %A_LoopField%Out := %A_LoopField%Sort(Input) DllCall("QueryPerformanceCounter", "Int64 *", %A_LoopField%Time) %A_LoopField%End := %A_LoopField%Begin + %A_LoopField%Time %A_LoopField%Time -= %A_LoopField%Begin } } Time := "" Loop, PARSE, SortMethods, `, If (%A_LoopField%) Time .= A_LoopField . " Sort: " . %A_LoopField%Time . "`t`t" . %A_LoopField%Out . "`r`n" MsgBox,, Results!, %Time% Return
- Sorting funtions (Bogo, Bubble, Cocktail, Counting, Gnome, Insertion, Merge, Permutation, Quick, Selection, Shell, BuiltIn)
BogoSort(var) { sorted := 1 Loop, Parse, var { current := A_LoopField rest := SubStr(var, A_Index) Loop, Parse, rest { If (current > A_LoopField) sorted := 0 } } While !sorted { sorted := 1 Loop, Parse, var, `, { current := A_LoopField rest := SubStr(var, A_Index) Loop, Parse, rest, `, { If (current > A_LoopField) sorted := 0 } }
Sort, var, D`, Random } Return var }
BubbleSort(var) { StringSplit, array, var, `, hasChanged = 1 size := array0 While hasChanged { hasChanged = 0 Loop, % (size - 1) { i := array%A_Index% aj := A_Index + 1 j := array%aj% If (j < i) { temp := array%A_Index% array%A_Index% := array%aj% array%aj% := temp hasChanged = 1 } } } Loop, % size sorted .= "," . array%A_Index% Return substr(sorted,2) }
CocktailSort(var) { StringSplit array, var, `, i0 := 1, i1 := array0 Loop { Changed = Loop % i1-- -i0 { j := i0+A_Index, i := j-1 If (array%j% < array%i%) t := array%i%, array%i% := array%j%, array%j% := t ,Changed = 1 } IfEqual Changed,, Break Loop % i1-i0++ { i := i1-A_Index, j := i+1 If (array%j% < array%i%) t := array%i%, array%i% := array%j%, array%j% := t ,Changed = 1 } IfEqual Changed,, Break } Loop % array0 sorted .= "," . array%A_Index% Return SubStr(sorted,2) }
CountingSort(var) { max := min := substr(var, 1, instr(var, ",")) Loop, parse, var, `, { If (A_LoopField > max) max := A_LoopField
Else If (A_LoopField < min) min := A_LoopField } Loop % max-min+1 i := A_Index-1, a%i% := 0 Loop, Parse, var, `, i := A_LoopField-min, a%i%++ Loop % max-min+1 { i := A_Index-1, v := i+min Loop % a%i% t .= "," v } Return SubStr(t,2) }
GnomeSort(var) { StringSplit, a, var, `, i := 2, j := 3 While i <= a0 { u := i-1 If (a%u% < a%i%) i := j, j := j+1 Else { t := a%u%, a%u% := a%i%, a%i% := t If (--i = 1) i := j, j++ } } Loop % a0 sorted .= "," . a%A_Index% Return SubStr(sorted,2) }
InsertionSort(var) { StringSplit, a, var, `, Loop % a0-1 { i := A_Index+1, v := a%i%, j := i-1 While j>0 and a%j%>v u := j+1, a%u% := a%j%, j-- u := j+1, a%u% := v } Loop % a0 sorted .= "," . a%A_Index% Return SubStr(sorted,2) }
MergeSort(var) {
StringReplace, t, var, `,,, UseErrorLevel
L := ((t = "") ? 0 : ErrorLevel+1)
If (2 > L)
Return var
StringGetPos, p, var, `,, % "L" L//2
list0 := MergeSort(SubStr(var,1,p))
list1 := MergeSort(SubStr(var,p+2))
If (list0 = "")
Return list1
Else If (list1 = "")
Return list0
list := list0
i0 := (p0 := InStr(list,",",0,i:=p0+1)) ? SubStr(list,i,p0-i) : SubStr(list,i)
list := list1
i1 := (p1 := InStr(list,",",0,i:=p1+1)) ? SubStr(list,i,p1-i) : SubStr(list,i)
Loop {
i := i0>i1
list .= "," i%i%
If (p%i%) {
list := list%i%
i%i% := (p%i% := InStr(list,",",0,i:=p%i%+1)) ? SubStr(list,i,p%i%-i) : SubStr(list,i)
}
Else {
i ^= 1
rtv := SubStr(list "," i%i% (p%i% ? "," SubStr(list%i%,p%i%+1) : ""), 2)
}
}
Return rtv
}
PermutationSort(var) { static a:="a",v:="v" StringSplit, a, var, `, v0 := a0 Loop %v0% v%A_Index% := A_Index unsorted := 0 Loop % %a%0-1 { i := %v%%A_Index%, j := A_Index+1, j := %v%%j% If (%a%%i% > %a%%j%) unSorted := 1 } While unSorted { i := %v%0, i1 := i-1 While %v%%i1% >= %v%%i% { --i, --i1 IfLess i1,1, Return 1 } j := %v%0 While %v%%j% <= %v%%i1% --j t := %v%%i1%, %v%%i1% := %v%%j%, %v%%j% := t, j := %v%0 While i < j t := %v%%i%, %v%%i% := %v%%j%, %v%%j% := t, ++i, --j unsorted := 0 Loop % %a%0-1 { i := %v%%A_Index%, j := A_Index+1, j := %v%%j% If (%a%%i% > %a%%j%) unSorted := 1 } } Loop % a0 i := v%A_Index%, sorted .= "," . a%i% Return SubStr(sorted,2) }
QuickSort(var) { StringSplit, list, var, `, If (list0 <= 1) Return list pivot := list1 Loop, Parse, var, `, { If (A_LoopField < pivot) less .= "," . A_LoopField Else If (A_LoopField > pivot) more .= "," . A_LoopField Else pivotlist .= "," . A_LoopField } less := QuickSort(substr(less,2)) more := QuickSort(substr(more,2)) Return substr(less,2) . pivotList . more }
SelectionSort(var) { StringSplit, a, var, `, Loop % a0-1 { i := A_Index, mn := a%i%, j := m := i Loop % a0-i { j++ If (a%j% < mn) mn := a%j%, m := j } t := a%i%, a%i% := a%m%, a%m% := t } Loop % a0 sorted .= "," . a%A_Index% Return SubStr(sorted,2) }
ShellSort(var) { StringSplit, a, var, `, inc := a0 While inc:=round(inc/2.2) Loop % a0-inc { i := A_Index+inc, t := a%i%, j := i, k := j-inc While j > inc && a%k% > t a%j% := a%k%, j := k, k -= inc a%j% := t } Loop % a0 s .= "," . a%A_Index% Return SubStr(s,2) }
BuiltInSort(var) { Sort, var, N D`, Return var }</lang>
BBC BASIC
<lang bbcbasic> HIMEM = PAGE + 2000000
INSTALL @lib$+"SORTLIB"
INSTALL @lib$+"TIMERLIB"
Sort% = FN_sortinit(0,0)
Timer% = FN_ontimer(1000, PROCtimer, 1)
PRINT "Array size:", 1000, 10000, 100000
@% = &2020A
FOR patt% = 1 TO 4
CASE patt% OF
WHEN 1: PRINT '"Data set to all ones:"
WHEN 2: PRINT '"Data ascending sequence:"
WHEN 3: PRINT '"Data randomly shuffled:"
WHEN 4: PRINT '"Data descending sequence:"
ENDCASE
FOR type% = 1 TO 6
CASE type% OF
WHEN 1: PRINT "Internal (lib)";
WHEN 2: PRINT "Quicksort ";
WHEN 3: PRINT "Radix sort ";
WHEN 4: PRINT "Shellsort ";
WHEN 5: PRINT "Bubblesort ";
WHEN 6: PRINT "Insertion sort";
ENDCASE
FOR power% = 3 TO 5
PROCsorttest(patt%, type%, 10^power%)
NEXT
PRINT
NEXT type%
NEXT patt%
END
DEF PROCsorttest(patt%, type%, size%)
LOCAL a%(), C%, I%
DIM a%(size%-1)
CASE patt% OF
WHEN 1: a%() = 1 : a%() = 1
WHEN 2: FOR I% = 0 TO size%-1 : a%(I%) = I% : NEXT
WHEN 3: FOR I% = 0 TO size%-1 : a%(I%) = I% : NEXT
C% = RND(-123456) : REM Seed
FOR I% = size% TO 2 STEP -1 : SWAP a%(I%-1),a%(RND(I%)-1) : NEXT
WHEN 4: FOR I% = 0 TO size%-1 : a%(I%) = size%-1-I% : NEXT
ENDCASE
Start% = TIME
ON ERROR LOCAL PRINT , " >100.00" ; : ENDPROC
CASE type% OF
WHEN 1: C% = size% : CALL Sort%, a%(0)
WHEN 2: PROCquicksort(a%(), 0, size%)
WHEN 3: PROCradixsort(a%(), size%, 10)
WHEN 4: PROCshellsort(a%(), size%)
WHEN 5: PROCbubblesort(a%(), size%)
WHEN 6: PROCinsertionsort(a%(), size%)
ENDCASE
PRINT , (TIME - Start%)/100;
FOR I% = 0 TO size%-2
IF a%(I%) > a%(I%+1) ERROR 100, "Sort failed!"
NEXT
ENDPROC
DEF PROCtimer
Start% += 0
IF (TIME - Start%) > 10000 ERROR 111, ""
ENDPROC
DEF PROCbubblesort(a%(), n%)
LOCAL i%, l%
REPEAT
l% = 0
FOR i% = 1 TO n%-1
IF a%(i%-1) > a%(i%) THEN
SWAP a%(i%-1),a%(i%)
l% = i%
ENDIF
NEXT
n% = l%
UNTIL l% = 0
ENDPROC
DEF PROCinsertionsort(a%(), n%)
LOCAL i%, j%, t%
FOR i% = 1 TO n%-1
t% = a%(i%)
j% = i%
WHILE j%>0 AND t%<a%(ABS(j%-1))
a%(j%) = a%(j%-1)
j% -= 1
ENDWHILE
a%(j%) = t%
NEXT
ENDPROC
DEF PROCquicksort(a%(), s%, n%)
LOCAL l%, p%, r%, t%
IF n% < 2 THEN ENDPROC
t% = s% + n% - 1
l% = s%
r% = t%
p% = a%((l% + r%) DIV 2)
REPEAT
WHILE a%(l%) < p% l% += 1 : ENDWHILE
WHILE a%(r%) > p% r% -= 1 : ENDWHILE
IF l% <= r% THEN
SWAP a%(l%), a%(r%)
l% += 1
r% -= 1
ENDIF
UNTIL l% > r%
IF s% < r% PROCquicksort(a%(), s%, r% - s% + 1)
IF l% < t% PROCquicksort(a%(), l%, t% - l% + 1 )
ENDPROC
DEF PROCshellsort(a%(), n%)
LOCAL h%, i%, j%, k%
h% = n%
WHILE h%
IF h% = 2 h% = 1 ELSE h% DIV= 2.2
FOR i% = h% TO n% - 1
k% = a%(i%)
j% = i%
WHILE j% >= h% AND k% < a%(ABS(j% - h%))
a%(j%) = a%(j% - h%)
j% -= h%
ENDWHILE
a%(j%) = k%
NEXT
ENDWHILE
ENDPROC
DEF PROCradixsort(a%(), n%, r%)
LOCAL d%, e%, i%, l%, m%, b%(), bucket%()
DIM b%(DIM(a%(),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:
Array size: 1000 10000 100000 Data set to all ones: Internal (lib) 0.00 0.01 0.03 Quicksort 0.02 0.27 3.18 Radix sort 0.01 0.05 0.53 Shellsort 0.03 0.36 4.44 Bubblesort 0.00 0.01 0.09 Insertion sort 0.00 0.02 0.26 Data ascending sequence: Internal (lib) 0.00 0.00 0.02 Quicksort 0.02 0.15 1.82 Radix sort 0.02 0.18 2.10 Shellsort 0.03 0.37 4.44 Bubblesort 0.00 0.01 0.09 Insertion sort 0.01 0.03 0.27 Data randomly shuffled: Internal (lib) 0.00 0.02 0.44 Quicksort 0.02 0.26 3.17 Radix sort 0.02 0.17 2.08 Shellsort 0.04 0.73 11.57 Bubblesort 0.69 69.70 >100.00 Insertion sort 0.55 55.54 >100.00 Data descending sequence: Internal (lib) 0.00 0.01 0.10 Quicksort 0.01 0.15 1.90 Radix sort 0.02 0.17 2.06 Shellsort 0.03 0.50 6.39 Bubblesort 0.95 94.77 >100.00 Insertion sort 1.11 >100.00 >100.00
C
(The reference example is Python)
Examples of sorting routines
We can use the codes in the category Sorting Algorithms; since these codes deal with integer arrays, we should change them a little. To accomplish this task I've also renamed them more consistently algorithm_sort; so we have e.g. bubble_sort, quick_sort and so on.
Sequence generators
csequence.h <lang c>#ifndef _CSEQUENCE_H
- define _CSEQUENCE_H
- include <stdlib.h>
void setfillconst(double c); void fillwithconst(double *v, int n); void fillwithrrange(double *v, int n); void shuffledrange(double *v, int n);
- endif</lang>
csequence.c <lang c>#include "csequence.h"
static double fill_constant;
void setfillconst(double c) {
fill_constant = c;
}
void fillwithconst(double *v, int n) {
while( --n >= 0 ) v[n] = fill_constant;
}
void fillwithrrange(double *v, int n) {
int on = n; while( --on >= 0 ) v[on] = n - on;
}
void shuffledrange(double *v, int n) {
int on = n;
fillwithrrange(v, n);
while( --n >= 0 ) {
int r = rand() % on;
double t = v[n];
v[n] = v[r];
v[r] = t;
}
}</lang>
Write timings
We shall use the code from Query Performance. Since the action is a generic function with a single argument, we need wrappers which encapsule each sorting algorithms we want to test.
writetimings.h <lang c>#ifndef _WRITETIMINGS_H
- define _WRITETIMINGS_H
- include "sorts.h"
- include "csequence.h"
- include "timeit.h"
/* we repeat the same MEANREPEAT times, and get the mean; this *should*
give "better" results ... */
- define MEANREPEAT 10.0
- define BUFLEN 128
- define MAKEACTION(ALGO) \
int action_ ## ALGO (int size) { \
ALGO ## _sort(tobesorted, size); \
return 0; }
- define MAKEPIECE(N) { #N , action_ ## N }
int action_bubble(int size); int action_shell(int size); int action_quick(int size); int action_insertion(int size); int action_merge(int size); int doublecompare( const void *a, const void *b ); int action_qsort(int size); int get_the_longest(int *a);
struct testpiece {
const char *name; int (*action)(int);
}; typedef struct testpiece testpiece_t;
struct seqdef {
const char *name; void (*seqcreator)(double *, int);
}; typedef struct seqdef seqdef_t;
- endif</lang>
writetimings.c <lang c>#include <stdio.h>
- include <stdlib.h>
- include "writetimings.h"
double *tobesorted = NULL; const char *bname = "data_"; const char *filetempl = "%s%s_%s.dat"; int datlengths[] = {100, 200, 300, 500, 1000, 5000, 10000, 50000, 100000};
testpiece_t testpieces[] = { // MAKEPIECE(bubble),
MAKEPIECE(shell),
MAKEPIECE(merge),
MAKEPIECE(insertion),
MAKEPIECE(quick),
MAKEPIECE(qsort),
{ NULL, NULL }
};
seqdef_t seqdefs[] = {
{ "c1", fillwithconst },
{ "rr", fillwithrrange },
{ "sr", shuffledrange },
{ NULL, NULL }
};
MAKEACTION(bubble)
MAKEACTION(insertion)
MAKEACTION(quick)
MAKEACTION(shell)
int action_merge(int size) {
double *res = merge_sort(tobesorted, size); free(res); /* unluckly this affects performance */ return 0;
}
int doublecompare( const void *a, const void *b ) {
if ( *(const double *)a < *(const double *)b ) return -1; else return *(const double *)a > *(const double *)b;
} int action_qsort(int size) {
qsort(tobesorted, size, sizeof(double), doublecompare); return 0;
}
int get_the_longest(int *a) {
int r = *a;
while( *a > 0 ) {
if ( *a > r ) r = *a;
a++;
}
return r;
}
int main()
{
int i, j, k, z, lenmax; char buf[BUFLEN]; FILE *out; double thetime;
lenmax = get_the_longest(datlengths);
printf("Bigger data set has %d elements\n", lenmax);
tobesorted = malloc(sizeof(double)*lenmax);
if ( tobesorted == NULL ) return 1;
setfillconst(1.0);
for(i=0; testpieces[i].name != NULL; i++) {
for(j=0; seqdefs[j].name != NULL; j++) {
snprintf(buf, BUFLEN, filetempl, bname, testpieces[i].name,
seqdefs[j].name);
out = fopen(buf, "w");
if ( out == NULL ) goto severe;
printf("Producing data for sort '%s', created data type '%s'\n",
testpieces[i].name, seqdefs[j].name);
for(k=0; datlengths[k] > 0; k++) {
printf("\tNumber of elements: %d\n", datlengths[k]); thetime = 0.0; seqdefs[j].seqcreator(tobesorted, datlengths[k]); fprintf(out, "%d ", datlengths[k]); for(z=0; z < MEANREPEAT; z++) { thetime += time_it(testpieces[i].action, datlengths[k]); } thetime /= MEANREPEAT; fprintf(out, "%.8lf\n", thetime);
}
fclose(out);
}
}
severe:
free(tobesorted); return 0;
}</lang> This code produce several files with the following naming convention:
- data_algorithm_sequence.dat
Where algorithm is one of the following: insertion, merge, shell, quick, qsort (the quicksort in the libc library) (bubble sort became too slow for longest sequences). Sequence is c1 (constant value 1), rr (reverse range), sr (shufled range). These data can be easily plotted by Gnuplot, which can also do fitting. Instead we do our fitting using Polynomial Fitting. <lang c>#include <stdio.h>
- include <stdlib.h>
- include <math.h>
- include "polifitgsl.h"
- define MAXNUMOFDATA 100
double x[MAXNUMOFDATA], y[MAXNUMOFDATA]; double cf[2];
int main() {
int i, nod; int r;
for(i=0; i < MAXNUMOFDATA; i++)
{
r = scanf("%lf %lf\n", &x[i], &y[i]);
if ( (r == EOF) || (r < 2) ) break;
x[i] = log10(x[i]);
y[i] = log10(y[i]);
}
nod = i;
polynomialfit(nod, 2, x, y, cf);
printf("C0 = %lf\nC1 = %lf\n", cf[0], cf[1]);
return 0;
}</lang> Here we search for a fit with C0+C1x "in the log scale", since we supposed the data, once plotted on a logscale graph, can be fitted by a line. We can use e.g. a shell one-liner to produce the parameters for the line for each data file previously output. In particular I've used the following
for el in *.dat ; do fitdata <$el >${el%.dat}.fd ; done
Plot timings and Figures
Once we have all the ".dat" files and associated ".fd", we can use Gnuplot to draw our data and think about conclusions (we could also use the idea in Plot x, y arrays, but it needs too much enhancements to be usable for this analysis). Here an example of such a draw for a single file (using Gnuplot)
gnuplot> f(x) = C0 + C1*x gnuplot> set logscale xy gnuplot> load 'data_quick_sr_u.fd' gnuplot> set xrange [100:100000] gnuplot> set key left gnuplot> plot 10**f(log10(x)), 'data_quick_sr_u.dat'
(The _u.dat are produced by a modified version of the code in order to write timings in microseconds instead of seconds) We can easily write another shell script/one-liner to produce a single file driver for Gnuplot in order to produce all the graph we can be interested in. These graphs show that the linear (in log scale) fit do not always fit the data... I haven't repeated the tests; the problems are when the sequence length becomes huge; for some algorithm that uses extra memory (like implementation of the merge sort), this could depend on the allocation of the needed memory. Another extraneous factor could be system load (the CLOCK_MONOTONIC used by the timing function is system wide rather than per process, so counting time spent in other processes too?). The "most stable" algorithms seem to be quick sort (but not qsort, which indeed is just the libc quick sort, here not plotted!) and shell sort (except for reversed range).
Conclusion: we should repeat the tests...
D
<lang d>import std.stdio, std.algorithm, std.container, std.datetime,
std.random, std.typetuple;
immutable int[] allOnes, sortedData, randomData;
static this() { // Initialize global Arrays.
immutable size_t arraySize = 10_000;
allOnes = new int[arraySize];
//allOnes[] = 1;
foreach (ref d; allOnes)
d = 1;
sortedData = new int[arraySize];
foreach (immutable i, ref d; sortedData)
d = i;
randomData = new int[arraySize];
foreach (ref d; randomData)
d = uniform(0, int.max);
}
// BubbleSort:
void bubbleSort(T)(T[] list) {
for (int i = list.length - 1; i > 0; i--)
for (int j = i -1; j >= 0; j--)
if (list[i] < list[j])
swap(list[i], list[j]);
}
void allOnesBubble() {
auto data = allOnes.dup; data.bubbleSort; assert(data.isSorted);
}
void sortedBubble() {
auto data = sortedData.dup; data.bubbleSort; assert(data.isSorted);
}
void randomBubble() {
auto data = randomData.dup; data.bubbleSort; assert(data.isSorted);
}
// InsertionSort:
void insertionSort(T)(T[] list) {
foreach (immutable i, currElem; list) {
size_t j = i;
for (; j > 0 && currElem < list[j - 1]; j--)
list[j] = list[j - 1];
list[j] = currElem;
}
}
void allOnesInsertion() {
auto data = allOnes.dup; data.insertionSort; assert(data.isSorted);
}
void sortedInsertion() {
auto data = sortedData.dup; data.insertionSort; assert(data.isSorted);
}
void randomInsertion() {
auto data = randomData.dup; data.insertionSort; assert(data.isSorted);
}
// HeapSort:
void heapSort(T)(T[] data) {
auto h = data.heapify;
while (!h.empty)
h.removeFront;
}
void allOnesHeap() {
auto data = allOnes.dup; data.heapSort; assert(data.isSorted);
}
void sortedHeap() {
auto data = sortedData.dup; data.heapSort; assert(data.isSorted);
}
void randomHeap() {
auto data = randomData.dup; data.heapSort; assert(data.isSorted);
}
// Built-in sort:
void allOnesBuiltIn() {
auto data = allOnes.dup;
data.sort!q{a < b};
assert(data.isSorted);
}
void sortedBuiltIn() {
auto data = sortedData.dup;
data.sort!q{a < b};
assert(data.isSorted);
}
void randomBuiltIn() {
auto data = randomData.dup;
data.sort!q{a < b};
assert(data.isSorted);
}
static void show(in TickDuration[4u] r) {
alias args = TypeTuple!("usecs", int);
writefln(" Bubble Sort: %10d", r[0].to!args);
writefln(" Insertion Sort: %10d", r[1].to!args);
writefln(" Heap Sort: %10d", r[3].to!args);
writefln(" Built-in Sort: %10d", r[2].to!args);
}
void main() {
enum nRuns = 100;
writeln("Timings in microseconds:");
writeln(" Testing against all ones:");
nRuns.benchmark!(allOnesBubble, allOnesInsertion,
allOnesHeap, allOnesBuiltIn).show;
writeln("\n Testing against sorted data.");
nRuns.benchmark!(sortedBubble, sortedInsertion,
sortedHeap, sortedBuiltIn).show;
writeln("\n Testing against random data.");
nRuns.benchmark!(randomBubble, randomInsertion,
randomHeap, randomBuiltIn).show;
}</lang>
- Output:
Timings in microseconds:
Testing against all ones:
Bubble Sort: 7377065
Insertion Sort: 5868
Heap Sort: 25173
Built-in Sort: 34538
Testing against sorted data.
Bubble Sort: 7370520
Insertion Sort: 6006
Heap Sort: 18127
Built-in Sort: 176235
Testing against random data.
Bubble Sort: 27293705
Insertion Sort: 3762374
Heap Sort: 85053
Built-in Sort: 218268
(With 10,000 elements in each array. A naive HeapSort seems faster than the built-in sort in all three cases.)
Erlang
The sort routines are borrowed from bubble sort, insertion sort and quick sort. Plots by eplot. Bubble sort does ones and ranges best. Insertion sort does reversed ranges best. Quick sort handles shuffled numbers best. <lang Erlang> -module( compare_sorting_algorithms ).
-export( [task/0] ).
task() -> Ns = [100, 1000, 10000], Lists = [{"ones", fun list_of_ones/1, Ns}, {"ranges", fun list_of_ranges/1, Ns}, {"reversed_ranges", fun list_of_reversed_ranges/1, Ns}, {"shuffleds", fun list_of_shuffleds/1, Ns}], Sorts = [{bubble_sort, fun bubble_sort:list/1}, {insertion_sort, fun sort:insertion/1}, {iquick_sort, fun quicksort:qsort/1}], Results = [time_list(X, Sorts) || X <- Lists], [file:write_file(X++".png", egd_chart:graph(Y, [{x_label, "log N"}, {y_label, "log ms"}])) || {X, Y} <- Results].
list_of_ones( N ) -> [1 || _X <- lists:seq(1, N)].
list_of_ranges( N ) -> [X || X <- lists:seq(1, N)].
list_of_reversed_ranges( N ) -> lists:reverse( list_of_ranges(N) ).
list_of_shuffleds( N ) -> [random:uniform(N) || _X <- lists:seq(1, N)].
time_list( {List, List_fun, Values}, Sorts ) -> Results = [{Sort, time_sort(Sort_fun, List_fun, Values)} || {Sort, Sort_fun} <- Sorts], {List, Results}.
time_sort( Sort_fun, List_fun, Values ) -> [time(Sort_fun, List_fun, X) || X <- Values].
time( Fun, List_fun, N ) -> {Time, _Result} = timer:tc( fun() -> Fun( List_fun(N) ) end ), {math:log10(N), math:log10(Time)}. </lang>
Go
<lang go>package main
import (
"log" "math/rand" "testing" "time"
"github.com/gonum/plot" "github.com/gonum/plot/plotter" "github.com/gonum/plot/plotutil" "github.com/gonum/plot/vg"
)
// Step 1, sort routines. // These functions are copied without changes from the RC tasks Bubble Sort, // Insertion sort, and Quicksort.
func bubblesort(a []int) {
for itemCount := len(a) - 1; ; itemCount-- {
hasChanged := false
for index := 0; index < itemCount; index++ {
if a[index] > a[index+1] {
a[index], a[index+1] = a[index+1], a[index]
hasChanged = true
}
}
if hasChanged == false {
break
}
}
}
func insertionsort(a []int) {
for i := 1; i < len(a); i++ {
value := a[i]
j := i - 1
for j >= 0 && a[j] > value {
a[j+1] = a[j]
j = j - 1
}
a[j+1] = value
}
}
func quicksort(a []int) {
var pex func(int, int)
pex = func(lower, upper int) {
for {
switch upper - lower {
case -1, 0:
return
case 1:
if a[upper] < a[lower] {
a[upper], a[lower] = a[lower], a[upper]
}
return
}
bx := (upper + lower) / 2
b := a[bx]
lp := lower
up := upper
outer:
for {
for lp < upper && !(b < a[lp]) {
lp++
}
for {
if lp > up {
break outer
}
if a[up] < b {
break
}
up--
}
a[lp], a[up] = a[up], a[lp]
lp++
up--
}
if bx < lp {
if bx < lp-1 {
a[bx], a[lp-1] = a[lp-1], b
}
up = lp - 2
} else {
if bx > lp {
a[bx], a[lp] = a[lp], b
}
up = lp - 1
lp++
}
if up-lower < upper-lp {
pex(lower, up)
lower = lp
} else {
pex(lp, upper)
upper = up
}
}
}
pex(0, len(a)-1)
}
// Step 2.0 sequence routines. 2.0 is the easy part. 2.5, timings, follows.
func ones(n int) []int {
s := make([]int, n)
for i := range s {
s[i] = 1
}
return s
}
func ascending(n int) []int {
s := make([]int, n)
v := 1
for i := 0; i < n; {
if rand.Intn(3) == 0 {
s[i] = v
i++
}
v++
}
return s
}
func shuffled(n int) []int {
return rand.Perm(n)
}
// Steps 2.5 write timings, and 3 plot timings are coded together. // If write means format and output human readable numbers, step 2.5 // is satisfied with the log output as the program runs. The timings // are plotted immediately however for step 3, not read and parsed from // any formated output. const (
nPts = 7 // number of points per test inc = 1000 // data set size increment per point
)
var (
p *plot.Plot
sortName = []string{"Bubble sort", "Insertion sort", "Quicksort"}
sortFunc = []func([]int){bubblesort, insertionsort, quicksort}
dataName = []string{"Ones", "Ascending", "Shuffled"}
dataFunc = []func(int) []int{ones, ascending, shuffled}
)
func main() {
rand.Seed(time.Now().Unix())
var err error
p, err = plot.New()
if err != nil {
log.Fatal(err)
}
p.X.Label.Text = "Data size"
p.Y.Label.Text = "microseconds"
p.Y.Scale = plot.LogScale{}
p.Y.Tick.Marker = plot.LogTicks{}
p.Y.Min = .5 // hard coded to make enough room for legend
for dx, name := range dataName {
s, err := plotter.NewScatter(plotter.XYs{})
if err != nil {
log.Fatal(err)
}
s.Shape = plotutil.DefaultGlyphShapes[dx]
p.Legend.Add(name, s)
}
for sx, name := range sortName {
l, err := plotter.NewLine(plotter.XYs{})
if err != nil {
log.Fatal(err)
}
l.Color = plotutil.DarkColors[sx]
p.Legend.Add(name, l)
}
for sx := range sortFunc {
bench(sx, 0, 1) // for ones, a single timing is sufficient.
bench(sx, 1, 5) // ascending and shuffled have some randomness though,
bench(sx, 2, 5) // so average timings on 5 different random sets.
}
if err := p.Save(5*vg.Inch, 5*vg.Inch, "comp.png"); err != nil {
log.Fatal(err)
}
}
func bench(sx, dx, rep int) {
log.Println("bench", sortName[sx], dataName[dx], "x", rep)
pts := make(plotter.XYs, nPts)
sf := sortFunc[sx]
for i := range pts {
x := (i + 1) * inc
// to avoid timing sequence creation, create sequence before timing
// then just copy the data inside the timing loop. copy time should
// be the same regardless of sequence data.
s0 := dataFunc[dx](x) // reference sequence
s := make([]int, x) // working copy
var tSort int64
for j := 0; j < rep; j++ {
tSort += testing.Benchmark(func(b *testing.B) {
for i := 0; i < b.N; i++ {
copy(s, s0)
sf(s)
}
}).NsPerOp()
}
tSort /= int64(rep)
log.Println(x, "items", tSort, "ns") // step 2.5, write timings
pts[i] = struct{ X, Y float64 }{float64(x), float64(tSort) * .001}
}
pl, ps, err := plotter.NewLinePoints(pts) // step 3, plot timings
if err != nil {
log.Fatal(err)
}
pl.Color = plotutil.DarkColors[sx]
ps.Color = plotutil.DarkColors[sx]
ps.Shape = plotutil.DefaultGlyphShapes[dx]
p.Add(pl, ps)
}</lang>
- Output:
Step 4, conclusions about relative performance of the sorting routines made based on the plots.
The plots show differences in best and worse case performance for the various data sets. Bubble and insertion sorts show very good best case performance with all one and ascending sequences, beating quicksort. Quicksort shows best case performance with the ascending sequence but worst case performance with the all one sequence.
On random data (triangles) insertion and bubble sort show worse performance than quicksort.
J
<lang j> NB. extracts from other rosetta code projects ts=: 6!:2, 7!:2@] radix =: 3 : 0 256 radix y
a=. #{. z =. x #.^:_1 y e=. (-a) {."0 b =. i.x x#.1{::(<:@[;([: ; (b, {"1) <@}./. e,]))&>/^:a [ z;~a-1 NB. , ([: ; (b, {:"1) <@(}:"1@:}.)/. e,])^:(#{.z) y,.z ) bubble=: (([ (<. , >.) {.@]) , }.@])/^:_ insertion=:((>: # ]) , [ , < #])/ sel=: 1 : 'x # [' quick=: 3 : 0
if. 1 >: #y do. y
else.
e=. y{~?#y
(quick y <sel e),(y =sel e),quick y >sel e
end.
) gaps =: [: }: 1 (1+3*])^:(> {:)^:a:~ # insert =: (I.~ {. ]) , [ , ] }.~ I.~ gapinss =: #@] {. ,@|:@(] insert//.~ #@] $ i.@[) shell =: [: ; gapinss &.>/@(< ,~ ]&.>@gaps) builtin =: /:~
NB. characterization of the sorting algorithms.
sorts =: bubble`insertion`shell`quick`radix`builtin generators =: #&1`(i.@-)`(?.~) NB. data generators
round =: [: <. 1r2&+
ll =: (<_1 0)&{ NB. verb to extract lower left which holds ln data length lc =: (<_1 1)&{ NB. verb to fetch lower center which holds most recent time
NB. maximum_time characterize ln_start_size NB. characterize returns a rank 4 matrix with successive indexes for NB. algorithm, input arrangement, max number of tests in group, length time space characterize =: 4 : 0
max_time =. x
start =. 1 3{.<:y
for_sort. sorts do.
for_generator. generators do. NB. limit time and paging prevention
t =: }. (, (, [: ts 'sort@.0 (generator@.0)' , ":@round@^)@>:@ll) ^: ((lc < max_time"_) *. ll < 17"_) ^:_ start
if. generator -: {.generators do.
g =. ,:t
else.
g =. g,t
end.
end.
if. sort -: {.sorts do.
s =. ,:g
else.
s =. s,g
end.
end.
)
NB. character cell graphics
NB. From j phrases 10E. Approximation d3=: 1&,.@[ %.~ ] NB. a and b such that y is approx. a + b*x
NB. domain and range 0 to 14. D=:14
plot =: 1 : '(=/ round@(u&.(*&(D%<:y))))i.y' NB. function plot size points =: 4 : '1(<"1|:|.round y*D%~<:x)}0$~2#x' NB. size points x,:y
show =: [: |. [: '0'&~:@{:} ' ' ,: ":
plt =: 3 : 0 30 plt y NB. default size 30
n =. >:i.-# experiments =. <@(#~"1 (0&<)@{.)"2 y pts =. n +./ .*x&points@>experiments coef =. d3/@>experiments (_*pts) + n +./ .*1 0 2|:coef&(p."1) plot x ) </lang>
a =: 1 characterize 5 $a NB. a has rank 4 6 3 13 3 'l t s' =: |:a NB. transpose moves length time space to leading dimension l =: |: <: l NB. transpose restores order t =: |: 12 +^. t NB. choose arbitrary time units so that ^. time is positive s =: |: ^. s NB. ln space NB. 6 groups of sort methods with 3 arrangements of data ---> exponentially increasing data lengths, 6j2":t NB. ln time negative infinity indicates avoided experiment 3.83 4.80 5.89 7.15 8.65 10.18 11.90 13.75 __ __ __ __ __ 8.77 10.90 13.13 __ __ __ __ __ __ __ __ __ __ 8.70 10.87 13.11 __ __ __ __ __ __ __ __ __ __ 3.91 5.43 7.13 8.90 10.76 12.73 __ __ __ __ __ __ __ 3.99 5.63 7.42 9.21 11.13 13.06 __ __ __ __ __ __ __ 4.14 5.72 7.58 9.37 11.30 13.26 __ __ __ __ __ __ __ 5.56 6.75 7.90 9.05 10.27 11.60 13.13 __ __ __ __ __ __ 5.61 6.88 8.05 9.40 10.84 12.48 __ __ __ __ __ __ __ 5.67 6.93 8.09 9.43 10.89 12.48 __ __ __ __ __ __ __ 1.95 1.99 2.19 2.46 2.98 3.66 4.63 5.54 6.60 7.61 8.70 9.81 10.99 6.06 7.13 8.09 9.09 10.10 11.10 12.12 __ __ __ __ __ __ 6.09 7.17 8.10 9.11 10.11 11.12 12.14 __ __ __ __ __ __ 3.25 3.33 3.55 4.06 4.77 5.60 6.72 7.75 8.75 10.11 11.21 12.22 __ 3.37 3.87 4.19 4.72 5.53 6.49 7.84 9.29 10.71 11.78 12.88 __ __ 3.42 4.00 4.43 5.07 5.93 7.07 8.06 9.76 10.96 12.10 __ __ __ 0.38 0.38 0.58 1.02 1.68 2.68 3.45 4.42 5.42 6.51 7.64 8.86 9.87 0.49 0.58 0.96 1.55 2.34 3.11 4.31 5.82 7.43 8.70 9.75 10.75 11.75 1.40 2.01 2.88 3.87 4.92 5.92 7.05 8.18 9.45 10.91 12.01 __ __
This display is no less than a bar chart and, frankly, suffices but for the curve fit requirement.
NB. algorithms: bubble 6, insertion 5, shell 4, quick 3, radix 2, builtin 1
NB. rows: log time
NB. cols: log size
NB. data is all 1
show 30 plt l ,: & (0&{)"2 t
5 4 _ 2 2
4 2
5 _ 6 2
_ 4 6 2
4 _ _ 3
5 _ 6 2 3
6 _ _ 3 1
_ 4 2 3 3 1
_ _ _ 3 1
1 6 2 _ _ 1
_ 2 3 1
_ _ 2 _ _ _
4 2 3 1
_ 5 6 2 _ 3 _ _
4 _ _ 2 3 1
_ _ 3 _ _
5 6 2 3 1
4 _ _ 3 _ 1
4 _ 2 3 1 _
_ 6 2 _ 3 3 1 1
5 6 2 3 _ 1 _
2 _ 3 _ 1
5 6 _ _ 3 1 _
6 2 3 _ 1
2 _ _ 1 _
2 _ 3 3 1
2 3 1 _
3 _
3 _ _ 1
3 1 1
NB. data is reversed integer list
show 30 plt l ,: & (1&{)"2 t
6 4 3 1
5 4 3 2 1
_ _ 4 3 _ 2 1
_ 3 2 1
6 4 _ 2 _
1 3 _
_ _ _ 2 1
6 4 3 _ _
1 _ 2 1
6 _ 3 2 _
_ 2 _ 1
6 1 2 _
_ 5 2 1
3 2 _ 1
_ 4 _ 2 _
3 _ 1
3 5 2 _ 1
4 _ 2 1 _
4 5 2 _ 1
_ 1
5 _ 2 1 _
5 _ 2 1
2 1 _
2
2 _
2 1
_
_ 1
_ 1
1
NB. data is random
show 30 plt l ,: & (2&{)"2 t
6 5 4 3 2 1
_ 4 3 2 1
_ 5 4 3 2 1
_ 3 2 1
6 5 4 _ _ _
4 3 2 1
_ _ _ _ _ 1
6 4 3 1
1 _ 2 1
6 _ 3 _ _
_ 2 1
6 1 2 1
_ 5 _ 1 _
3 _ 2 1
_ 4 5 2 1
3 _ 5 2 _ 1 _
3 4 2
_ 2 _ _
4 _ 1
5 2 _
_ 1
5 _ 2 _
2 1
2 _
2 _ 1
1
1
1
The first version of the code set only a time limit. The builtin sort violated this only when the data overflowed RAM into virtual space, causing a large jump in time affecting also the next data set as the OS restored itself. The timing might be interesting for some other exercise. Here, a maximum data size test was inserted. Arbitrary time is the reasonable choice without details of the J interpreter nor of specific hardware. The radix sort involves putting data directly into the right spot. It is quick!
The data fit curves of the character cell graph were combined with GCD +. function. This explains "1"s or other strange values where these curves intersect. Finally the scatter plots were multiplied by infinity and added to the best fit curves. The points didn't show up well using the same values as the curves.
Julia
Julia comes with the InsertionSort, MergeSort, and QuickSort routines built into the Base.Sort module. Here is a comparison using those system algorithms and with integers. <lang julia> function comparesorts(tosort)
a = shuffle(["i", "m", "q"])
iavg = mavg = qavg = 0.0
for c in a
if c == "i"
iavg = sum(i -> @elapsed(sort(tosort, alg=InsertionSort)), 1:100) / 100.0
elseif c == "m"
mavg = sum(i -> @elapsed(sort(tosort, alg=MergeSort)), 1:100) / 100.0
elseif c == "q"
qavg = sum(i -> @elapsed(sort(tosort, alg=QuickSort)), 1:100) / 100.0
end
end
iavg, mavg, qavg
end
allones = fill(1, 40000) sequential = collect(1:40000) randomized = collect(shuffle(1:40000))
comparesorts(allones) comparesorts(allones) iavg, mavg, qavg = comparesorts(allones) println("Average sort times for 40000 ones:") println("\tinsertion sort:\t$iavg\n\tmerge sort:\t$mavg\n\tquick sort\t$qavg")
comparesorts(sequential) comparesorts(sequential) iavg, mavg, qavg = comparesorts(sequential) println("Average sort times for 40000 presorted:") println("\tinsertion sort:\t$iavg\n\tmerge sort:\t$mavg\n\tquick sort\t$qavg")
comparesorts(randomized) comparesorts(randomized) iavg, mavg, qavg = comparesorts(randomized) println("Average sort times for 40000 randomized:") println("\tinsertion sort:\t$iavg\n\tmerge sort:\t$mavg\n\tquick sort\t$qavg") </lang>
Average sort times for 40000 ones:
insertion sort: 0.00036058316000000005
merge sort: 0.00040099004999999996
quick sort 0.0003586394400000001
Average sort times for 40000 presorted:
insertion sort: 0.0003141142199999999
merge sort: 0.0007967360000000003
quick sort 0.0005601127399999998
Average sort times for 40000 randomized:
insertion sort: 0.2190664327599999
merge sort: 0.0028818907399999986
quick sort 0.0023325933899999997
Kotlin
This mostly reuses the code from the sorting sub-tasks except that:
1. All sorting functions have been adjusted where necessary so that they sort an IntArray 'in place'. This ensures that the timings are not affected by time spent copying arrays.
2. The bubble sort function, which is very slow when sorting 100,000 random numbers, has been optimized somewhat to try and reduce overall execution time, though the program is still taking about 5 minutes to run on my machine.
Unfortunately the code used to measure CPU time in the 'Time a function' sub-task no longer works properly on my present Windows 10 machine (many results are inexplicably zero). I've therefore had to use the Kotlin library function, measureNanoTime(), instead which measures system time elapsed. Consequently, the results are a bit erratic even when averaged over 10 runs.
Although it would be easy enough to plot the results graphically using an external library such as JFreePlot, there doesn't seem much point when we can no longer upload images to RC. I've therefore presented the results in tabular form on the terminal which is good enough to detect significant trends. <lang scala>// Version 1.2.31
import java.util.Random import kotlin.system.measureNanoTime
typealias Sorter = (IntArray) -> Unit
val rand = Random()
fun onesSeq(n: Int) = IntArray(n) { 1 }
fun ascendingSeq(n: Int) = shuffledSeq(n).sorted().toIntArray()
fun shuffledSeq(n: Int) = IntArray(n) { 1 + rand.nextInt(10 * n) }
fun bubbleSort(a: IntArray) {
var n = a.size
do {
var n2 = 0
for (i in 1 until n) {
if (a[i - 1] > a[i]) {
val tmp = a[i]
a[i] = a[i - 1]
a[i - 1] = tmp
n2 = i
}
}
n = n2
} while (n != 0)
}
fun insertionSort(a: IntArray) {
for (index in 1 until a.size) {
val value = a[index]
var subIndex = index - 1
while (subIndex >= 0 && a[subIndex] > value) {
a[subIndex + 1] = a[subIndex]
subIndex--
}
a[subIndex + 1] = value
}
}
fun quickSort(a: IntArray) {
fun sorter(first: Int, last: Int) {
if (last - first < 1) return
val pivot = a[first + (last - first) / 2]
var left = first
var right = last
while (left <= right) {
while (a[left] < pivot) left++
while (a[right] > pivot) right--
if (left <= right) {
val tmp = a[left]
a[left] = a[right]
a[right] = tmp
left++
right--
}
}
if (first < right) sorter(first, right)
if (left < last) sorter(left, last)
}
sorter(0, a.lastIndex)
}
fun radixSort(a: IntArray) {
val tmp = IntArray(a.size)
for (shift in 31 downTo 0) {
tmp.fill(0)
var j = 0
for (i in 0 until a.size) {
val move = (a[i] shl shift) >= 0
val toBeMoved = if (shift == 0) !move else move
if (toBeMoved)
tmp[j++] = a[i]
else {
a[i - j] = a[i]
}
}
for (i in j until tmp.size) tmp[i] = a[i - j]
for (i in 0 until a.size) a[i] = tmp[i]
}
}
val gaps = listOf(701, 301, 132, 57, 23, 10, 4, 1) // Marcin Ciura's gap sequence
fun shellSort(a: IntArray) {
for (gap in gaps) {
for (i in gap until a.size) {
val temp = a[i]
var j = i
while (j >= gap && a[j - gap] > temp) {
a[j] = a[j - gap]
j -= gap
}
a[j] = temp
}
}
}
fun main(args: Array<String>) {
val runs = 10
val lengths = listOf(1, 10, 100, 1_000, 10_000, 100_000)
val sorts = listOf<Sorter>(
::bubbleSort, ::insertionSort, ::quickSort, ::radixSort, ::shellSort
)
/* allow JVM to compile sort functions before timings start */ for (sort in sorts) sort(intArrayOf(1))
val sortTitles = listOf("Bubble", "Insert", "Quick ", "Radix ", "Shell ")
val seqTitles = listOf("All Ones", "Ascending", "Shuffled")
val totals = List(seqTitles.size) { List(sorts.size) { LongArray(lengths.size) } }
for ((k, n) in lengths.withIndex()) {
val seqs = listOf(onesSeq(n), ascendingSeq(n), shuffledSeq(n))
repeat(runs) {
for (i in 0 until seqs.size) {
for (j in 0 until sorts.size) {
val seq = seqs[i].copyOf()
totals[i][j][k] += measureNanoTime { sorts[j](seq) }
}
}
}
}
println("All timings in micro-seconds\n")
print("Sequence length")
for (len in lengths) print("%8d ".format(len))
println("\n")
for (i in 0 until seqTitles.size) {
println(" ${seqTitles[i]}:")
for (j in 0 until sorts.size) {
print(" ${sortTitles[j]} ")
for (k in 0 until lengths.size) {
val time = totals[i][j][k] / runs / 1_000
print("%8d ".format(time))
}
println()
}
println("\n")
}
}</lang>
- Output:
All timings in micro-seconds
Sequence length 1 10 100 1000 10000 100000
All Ones:
Bubble 1 2 6 24 26 264
Insert 1 16 10 14 48 518
Quick 2 7 18 46 397 5181
Radix 38 79 501 3720 864 9096
Shell 11 15 43 189 407 4105
Ascending:
Bubble 1 2 6 8 24 270
Insert 0 2 9 14 47 496
Quick 1 6 19 33 282 3347
Radix 38 71 264 415 1869 21403
Shell 7 10 42 171 399 4052
Shuffled:
Bubble 1 5 436 3292 275224 27730705
Insert 0 3 176 754 24759 2546180
Quick 1 7 24 106 1281 14982
Radix 28 73 622 317 1891 21617
Shell 11 19 88 408 1946 36980
Conclusions
As expected quick sort is faster than the other methods when applied to random data of a reasonable size though radix and shell sort are also respectable performers for large amounts of random data. In contrast, bubble and insertion sorts are orders of magnitude slower, particularly the former.
On the other hand, bubble and insertion sorts are much quicker than the other methods for constant data and for data which is already sorted in an ascending direction, bubble sort being the faster of the two.
Nim
This is a direct translation of the Kotlin program. We have added the sorting algorithm provided by Nim standard library which is a merge sort. For this reason, we have been constrained to annotate the sorting functions with the pragma {.locks: "unknown".} to make their type compatible with that of the standard sort function.
We have also added the array as first parameter of the internal function “sorter” as Nim compiler doesn’t allow direct access to this mutable array in function “quicksort” (memory safety violation).
<lang Nim>import algorithm import random import sequtils import times
- Data.
proc oneSeq(n: int): seq[int] = repeat(1, n)
- ---------------------------------------------------------------------------------------------------
proc shuffledSeq(n: int): seq[int] =
result.setLen(n) for item in result.mitems: item = rand(1..(10 * n))
- ---------------------------------------------------------------------------------------------------
proc ascendingSeq(n: int): seq[int] = sorted(shuffledSeq(n))
- Algorithms.
func bubbleSort(a: var openArray[int]) {.locks: "unknown".} =
var n = a.len
while true:
var n2 = 0
for i in 1..<n:
if a[i - 1] > a[i]:
swap a[i], a[i - 1]
n2 = i
n = n2
if n == 0: break
- ---------------------------------------------------------------------------------------------------
func insertionSort(a: var openArray[int]) {.locks: "unknown".} =
for index in 1..a.high:
let value = a[index]
var subIndex = index - 1
while subIndex >= 0 and a[subIndex] > value:
a[subIndex + 1] = a[subIndex]
dec subIndex
a[subIndex + 1] = value
- ---------------------------------------------------------------------------------------------------
func quickSort(a: var openArray[int]) {.locks: "unknown".} =
func sorter(a: var openArray[int]; first, last: int) =
if last - first < 1: return
let pivot = a[first + (last - first) div 2]
var left = first
var right = last
while left <= right:
while a[left] < pivot: inc left
while a[right] > pivot: dec right
if left <= right:
swap a[left], a[right]
inc left
dec right
if first < right: a.sorter(first, right)
if left < last: a.sorter(left, last)
a.sorter(0, a.high)
- ---------------------------------------------------------------------------------------------------
func radixSort(a: var openArray[int]) {.locks: "unknown".} =
var tmp = newSeq[int](a.len)
for shift in countdown(63, 0):
for item in tmp.mitems: item = 0
var j = 0
for i in 0..a.high:
let move = a[i] shl shift >= 0
let toBeMoved = if shift == 0: not move else: move
if toBeMoved:
tmp[j] = a[i]
inc j
else:
a[i - j] = a[i]
for i in j..tmp.high: tmp[i] = a[i - j]
for i in 0..a.high: a[i] = tmp[i]
- ---------------------------------------------------------------------------------------------------
func shellSort(a: var openArray[int]) {.locks: "unknown".} =
const Gaps = [701, 301, 132, 57, 23, 10, 4, 1]
for gap in Gaps:
for i in gap..a.high:
let temp = a[i]
var j = i
while j >= gap and a[j - gap] > temp:
a[j] = a[j - gap]
dec j, gap
a[j] = temp
- ---------------------------------------------------------------------------------------------------
func standardSort(a: var openArray[int]) =
a.sort()
- Main code.
import strformat
const
Runs = 10 Lengths = [1, 10, 100, 1_000, 10_000, 100_000]
Sorts = [bubbleSort, insertionSort, quickSort, radixSort, shellSort, standardSort]
const
SortTitles = ["Bubble", "Insert", "Quick ", "Radix ", "Shell ", "Standard"] SeqTitles = ["All Ones", "Ascending", "Shuffled"]
var totals: array[SeqTitles.len, array[Sorts.len, array[Lengths.len, Duration]]]
randomize()
for k, n in Lengths:
let seqs = [oneSeq(n), ascendingSeq(n), shuffledSeq(n)]
for _ in 1..Runs:
for i, s in seqs:
for j, sort in Sorts:
var s = s
let t0 = getTime()
s.sort()
totals[i][j][k] += getTime() - t0
echo "All timings in microseconds\n" stdout.write "Sequence length " for length in Lengths:
stdout.write &"{length:6d} "
echo '\n' for i in 0..SeqTitles.high:
echo &" {SeqTitles[i]}:"
for j in 0..Sorts.high:
stdout.write &" {SortTitles[j]:8s} "
for k in 0..Lengths.high:
let time = totals[i][j][k].inMicroseconds div Runs
stdout.write &"{time:8d} "
echo ""
echo '\n'</lang>
- Output:
All timings in microseconds Sequence length 1 10 100 1000 10000 100000 All Ones: Bubble 0 0 0 0 6 64 Insert 0 0 0 1 9 90 Quick 0 0 3 9 105 1201 Radix 1 4 34 103 848 8354 Shell 0 0 2 10 97 946 Standard 0 2 2 6 45 380 Ascending: Bubble 0 0 0 0 6 61 Insert 0 0 0 1 9 94 Quick 0 0 3 11 88 919 Radix 1 5 47 154 1435 15519 Shell 0 0 2 10 95 954 Standard 0 0 2 7 47 463 Shuffled: Bubble 0 0 38 1026 133729 16181412 Insert 0 0 8 152 10010 1133210 Quick 0 0 9 63 607 7199 Radix 1 5 46 157 1405 15557 Shell 0 0 8 69 708 10236 Standard 0 0 18 96 992 12394
Conclusions
Compared to the results obtained by the Kotlin program, the radix sort seems less efficient and the shell sort more efficient. Maybe some optimizations could improve the radix sort, but it seems also that the shell sort is well optimized by the Nim compiler and the C compiler.
The standard sort behaves well if the list is already sorted. For random list, it is less efficient than the quick sort or the shell sort, but is still a good performer.
Phix
-- demo\rosetta\Compare_sorting_algorithms.exw constant XQS = 01 -- (set to 1 to exclude quick_sort and shell_sort from ones) include pGUI.e Ihandle dlg, tabs, plot Ihandles plots function quick_sort2(sequence x) integer n = length(x) if n<2 then return x -- already sorted (trivial case) end if integer mid = floor((n+1)/2), midn = 1 object midval = x[mid] sequence left = {}, right = {} x[mid] = x[1] for i=2 to n do object xi = x[i] integer c = compare(xi,midval) if c<0 then left = append(left,xi) elsif c>0 then right = append(right,xi) else midn += 1 end if end for return quick_sort2(left) & repeat(midval,midn) & quick_sort2(right) end function function quick_sort(sequence s) sequence qstack = repeat(0,floor((length(s)/5)+10)) -- create a stack integer first = 1, last = length(s), stackptr = 0 while true do while first<last do object pivot = s[floor(last+first)/2], si, sj integer I = first, J = last while true do while true do si = s[I] if si>=pivot then exit end if I += 1 end while while true do sj = s[J] if sj<=pivot then exit end if J -= 1 end while if I>J then exit end if if I<J then if si=sj then {I,J} = {J+1,I-1} exit end if s[I] = sj s[J] = si end if I += 1 J -= 1 if I>J then exit end if end while if I<last then qstack[stackptr+1] = I qstack[stackptr+2] = last stackptr += 2 end if last = J end while if stackptr=0 then exit end if stackptr -= 2 first = qstack[stackptr+1] last = qstack[stackptr+2] end while return s end function function radixSortn(sequence s, integer n) sequence buckets = repeat({},10) sequence res = {} for i=1 to length(s) do integer digit = remainder(floor(s[i]/power(10,n-1)),10)+1 buckets[digit] = append(buckets[digit],s[i]) end for for i=1 to length(buckets) do integer len = length(buckets[i]) if len!=0 then if len=1 or n=1 then res &= buckets[i] else res &= radixSortn(buckets[i],n-1) end if end if end for return res end function function split_by_sign(sequence s) sequence buckets = {{},{}} for i=1 to length(s) do integer si = s[i] if si<0 then buckets[1] = append(buckets[1],-si) else buckets[2] = append(buckets[2],si) end if end for return buckets end function function radix_sort(sequence s) -- NB this is an integer-only sort integer mins = min(s), passes = floor(log10(max(max(s),abs(mins))))+1 if mins<0 then sequence buckets = split_by_sign(s) buckets[1] = reverse(sq_uminus(radixSortn(buckets[1],passes))) buckets[2] = radixSortn(buckets[2],passes) s = buckets[1]&buckets[2] else s = radixSortn(s,passes) end if return s end function function shell_sort(sequence s) integer gap = floor(length(s)/2) while gap>0 do for i=gap to length(s) do object temp = s[i] integer j = i-gap while j>=1 and temp<=s[j] do s[j+gap] = s[j] j -= gap end while s[j+gap] = temp end for gap = floor(gap/2) end while return s end function function shell_sort2(sequence x) integer last = length(x), gap = floor(last/10)+1 while TRUE do integer first = gap+1 for i=first to last do object xi = x[i] integer j = i-gap while TRUE do object xj = x[j] if xi>=xj then j += gap exit end if x[j+gap] = xj if j<=gap then exit end if j -= gap end while x[j] = xi end for if gap=1 then return x else gap = floor(gap/3.5)+1 end if end while end function function siftDown(sequence arr, integer s, integer last) integer root = s while root*2<=last do integer child = root*2 if child<last and arr[child]<arr[child+1] then child += 1 end if if arr[root]>=arr[child] then exit end if object tmp = arr[root] arr[root] = arr[child] arr[child] = tmp root = child end while return arr end function function heapify(sequence arr, integer count) integer s = floor(count/2) while s>0 do arr = siftDown(arr,s,count) s -= 1 end while return arr end function function heap_sort(sequence arr) integer last = length(arr) arr = heapify(arr,last) while last>1 do object tmp = arr[1] arr[1] = arr[last] arr[last] = tmp last -= 1 arr = siftDown(arr,1,last) end while return arr end function include builtins/sort.e enum ONES = 1, SORTED = 2, RANDOM = 3, REVERSE = 4 constant tabtitles = {"ones","sorted","random","reverse"} integer tabidx = 3 integer STEP function tr(sequence name, integer rid=routine_id(name)) return {name,rid} end function constant tests = {tr("quick_sort"), tr("quick_sort2"), tr("radix_sort"), tr("shell_sort"), tr("shell_sort2"), tr("heap_sort"), tr("sort"), -- builtin } sequence results = repeat(repeat({}, length(tests)),length(tabtitles)) sequence dsdx = repeat(repeat(0,length(tests)),length(tabtitles)) integer ds_index function idle_action_cb() atom best = -1, -- fastest last besti = 0, -- 1..length(tests) bestt = 0, -- 1..length(tabtitles) len -- -- Search for something to do, active/visible tab first. -- Any result set of length 0 -> just do one. -- Of all result sets<8, pick the lowest [$]. -- sequence todo = {tabidx} for t=1 to length(tabtitles) do if t!=tabidx then todo &= t end if end for for t=1 to length(tabtitles) do integer ti = todo[t] for i=1 to length(results[ti]) do len = length(results[ti][i]) if len=0 then best = 0 besti = i bestt = ti exit elsif len<8 then if (best=-1) or (best>results[ti][i][$]) then best = results[ti][i][$] besti = i bestt = ti end if end if end for if (t=1) and (besti!=0) then exit end if end for if best>10 then -- cop out if it is getting too slow besti = 0 end if if besti!=0 then STEP = iff(not XQS and bestt=ONES?1000:100000) len = (length(results[bestt][besti])+1)*STEP sequence test = iff(bestt=ONES?repeat(1,len): iff(bestt=SORTED?tagset(len): iff(bestt=RANDOM?shuffle(tagset(len)): iff(bestt=REVERSE?reverse(tagset(len)):9/0)))) ds_index = dsdx[bestt][besti] atom t0 = time() sequence check = call_func(tests[besti][2],{test}) t0 = time()-t0 -- if check!=sort(test) then ?9/0 end if plot = plots[bestt] IupPlotInsert(plot, ds_index, -1, len, t0) results[bestt][besti] = append(results[bestt][besti],t0) IupSetAttribute(plot,"REDRAW",NULL) sequence progress = {bestt} for i=1 to length(results[bestt]) do progress &= length(results[bestt][i]) end for IupSetStrAttribute(dlg,"TITLE","Compare sorting algorithms %s",{sprint(progress)}) return IUP_CONTINUE end if IupSetAttribute(dlg,"TITLE","Compare sorting algorithms (all done, idle)") return IUP_IGNORE -- all done, remove callback end function constant cb_idle_action = Icallback("idle_action_cb") function tabchange_cb(Ihandle /*self*/, Ihandle /*new_tab*/) tabidx = IupGetInt(tabs,"VALUEPOS")+1 plot = plots[tabidx] return IUP_DEFAULT; end function procedure main() IupOpen() plots = {} for i=1 to length(tabtitles) do if XQS then -- results[ONES][1] = repeat(0,8) results[ONES][4] = repeat(0,8) end if plot = IupPlot() IupSetAttribute(plot,"MENUITEMPROPERTIES","YES") IupSetAttribute(plot,"TABTITLE",tabtitles[i]) IupSetAttribute(plot,"GRID","YES") IupSetAttribute(plot,"MARGINLEFT","50") IupSetAttribute(plot,"MARGINBOTTOM","40") IupSetAttribute(plot,"LEGEND","YES") IupSetAttribute(plot,"LEGENDPOS","TOPLEFT") -- IupSetAttribute(plot,"AXS_YSCALE","LOG10") -- IupSetAttribute(plot,"AXS_XSCALE","LOG10") for j=1 to length(tests) do IupPlotBegin(plot) dsdx[i][j] = IupPlotEnd(plot) IupSetAttribute(plot,"DS_NAME",tests[j][1]) end for plots = append(plots,plot) end for tabs = IupTabs(plots) IupSetCallback(tabs, "TABCHANGE_CB", Icallback("tabchange_cb")) dlg = IupDialog(tabs, "RASTERSIZE=800x480") IupSetAttribute(dlg, "TITLE", "Compare sorting algorithms") IupShow(dlg) IupSetInt(tabs, "VALUEPOS", tabidx-1) IupSetGlobalFunction("IDLE_ACTION", cb_idle_action) if platform()!=JS then IupMainLoop() IupClose() end if end procedure main()
Conclusions
I knew bubblesort and insertion sort would be bad, but not so bad that you cannot meaningfully plot them against better sorts. (logarithmic scale helps, but is still not enough) I had no idea that (these particular implementations of) quicksort and shellsort would be so bad on a sequence of all 1s. (so bad in fact that I had to cap that test length to 8,000 instead of 800,000 as used for the other tests) The builtin sort and shell_sort2 were the clear winners, until I found a non-recursive quicksort that seems quite good. IupPlot is brilliant! It is actually quite fun to watch the graphs grow as you get more results in! There is a point where you realise you are currently wasting your life fretting over 0.015 seconds...
The ultimate conclusion is, of course, that there are some differences, but as long as you weed out the really bad algorithms, and at least in the majority of cases, you will probably never notice whether sorting 800,000 items takes 0.25s or 0.1s - more significant gains are likely to be found elsewhere.
Python
Examples of sorting routines
<lang python>def builtinsort(x):
x.sort()
def partition(seq, pivot):
low, middle, up = [], [], []
for x in seq:
if x < pivot:
low.append(x)
elif x == pivot:
middle.append(x)
else:
up.append(x)
return low, middle, up
import random def qsortranpart(seq):
size = len(seq) if size < 2: return seq low, middle, up = partition(seq, random.choice(seq)) return qsortranpart(low) + middle + qsortranpart(up)</lang>
Sequence generators
<lang python>def ones(n):
return [1]*n
def reversedrange(n):
return reversed(range(n))
def shuffledrange(n):
x = range(n) random.shuffle(x) return x</lang>
Write timings
<lang python>def write_timings(npoints=10, maxN=10**4, sort_functions=(builtinsort,insertion_sort, qsort),
sequence_creators = (ones, range, shuffledrange)):
Ns = range(2, maxN, maxN//npoints)
for sort in sort_functions:
for make_seq in sequence_creators:
Ts = [usec(sort, (make_seq(n),)) for n in Ns]
writedat('%s-%s-%d-%d.xy' % (sort.__name__, make_seq.__name__, len(Ns), max(Ns)), Ns, Ts)</lang>
Where writedat() is defined in the Write float arrays to a text file, usec() - Query Performance, insertion_sort() - Insertion sort, qsort - Quicksort subtasks, correspondingly.
Plot timings
<lang python>import operator import numpy, pylab def plotdd(dictplotdict):
"""See ``plot_timings()`` below."""
symbols = ('o', '^', 'v', '<', '>', 's', '+', 'x', 'D', 'd',
'1', '2', '3', '4', 'h', 'H', 'p', '|', '_')
colors = list('bgrcmyk') # split string on distinct characters
for npoints, plotdict in dictplotdict.iteritems():
for ttle, lst in plotdict.iteritems():
pylab.hold(False)
for i, (label, polynom, x, y) in enumerate(sorted(lst,key=operator.itemgetter(0))):
pylab.plot(x, y, colors[i % len(colors)] + symbols[i % len(symbols)], label='%s %s' % (polynom, label))
pylab.hold(True)
y = numpy.polyval(polynom, x)
pylab.plot(x, y, colors[i % len(colors)], label= '_nolegend_')
pylab.legend(loc='upper left')
pylab.xlabel(polynom.variable)
pylab.ylabel('log2( time in microseconds )')
pylab.title(ttle, verticalalignment='bottom')
figname = '_%(npoints)03d%(ttle)s' % vars()
pylab.savefig(figname+'.png')
pylab.savefig(figname+'.pdf')
print figname</lang>
See Plot x, y arrays and Polynomial Fitting subtasks for a basic usage of pylab.plot() and numpy.polyfit().
<lang python>import collections, itertools, glob, re import numpy def plot_timings():
makedict = lambda: collections.defaultdict(lambda: collections.defaultdict(list))
df = makedict()
ds = makedict()
# populate plot dictionaries
for filename in glob.glob('*.xy'):
m = re.match(r'([^-]+)-([^-]+)-(\d+)-(\d+)\.xy', filename)
print filename
assert m, filename
funcname, seqname, npoints, maxN = m.groups()
npoints, maxN = int(npoints), int(maxN)
a = numpy.fromiter(itertools.imap(float, open(filename).read().split()), dtype='f')
Ns = a[::2] # sequences lengths
Ts = a[1::2] # corresponding times
assert len(Ns) == len(Ts) == npoints
assert max(Ns) <= maxN
#
logsafe = numpy.logical_and(Ns>0, Ts>0)
Ts = numpy.log2(Ts[logsafe])
Ns = numpy.log2(Ns[logsafe])
coeffs = numpy.polyfit(Ns, Ts, deg=1)
poly = numpy.poly1d(coeffs, variable='log2(N)')
#
df[npoints][funcname].append((seqname, poly, Ns, Ts))
ds[npoints][seqname].append((funcname, poly, Ns, Ts))
# actual plotting
plotdd(df)
plotdd(ds) # see ``plotdd()`` above</lang>
Figures: log2( time in microseconds ) vs. log2( sequence length )
<lang python>sort_functions = [
builtinsort, # see implementation above insertion_sort, # see Insertion sort insertion_sort_lowb, # insertion_sort, where sequential search is replaced # by lower_bound() function qsort, # see Quicksort qsortranlc, # qsort with randomly choosen pivot # and the filtering via list comprehension qsortranpart, # qsortranlc with filtering via partition function qsortranpartis, # qsortranpart, where for a small input sequence lengths ] # insertion_sort is called
if __name__=="__main__":
import sys
sys.setrecursionlimit(10000)
write_timings(npoints=100, maxN=1024, # 1 <= N <= 2**10 an input sequence length
sort_functions=sort_functions,
sequence_creators = (ones, range, shuffledrange))
plot_timings()</lang>
Executing above script we get belowed figures.
ones
ones.png (143KiB)
builtinsort - O(N) insertion_sort - O(N) qsort - O(N**2) qsortranpart - O(N)
range
range.png (145KiB)
builtinsort - O(N) insertion_sort - O(N) qsort - O(N**2) qsortranpart - O(N*log(N))
shuffled range
shuffledrange.png (152KiB)
builtinsort - O(N) insertion_sort - O(N**4) ??? qsort - O(N*log(N)) qsortranpart - O(N) ???
Ruby
<lang ruby>class Array
def radix_sort(base=10) # negative value is inapplicable.
ary = dup
rounds = (Math.log(ary.max)/Math.log(base)).ceil
rounds.times do |i|
buckets = Array.new(base){[]}
base_i = base**i
ary.each do |n|
digit = (n/base_i) % base
buckets[digit] << n
end
ary = buckets.flatten
end
ary
end
def quick_sort
return self if size <= 1
pivot = sample
g = group_by{|x| x<=>pivot}
g.default = []
g[-1].quick_sort + g[0] + g[1].quick_sort
end
def shell_sort
inc = size / 2
while inc > 0
(inc...size).each do |i|
value = self[i]
while i >= inc and self[i - inc] > value
self[i] = self[i - inc]
i -= inc
end
self[i] = value
end
inc = (inc == 2 ? 1 : (inc * 5.0 / 11).to_i)
end
self
end
def insertion_sort
(1...size).each do |i|
value = self[i]
j = i - 1
while j >= 0 and self[j] > value
self[j+1] = self[j]
j -= 1
end
self[j+1] = value
end
self
end
def bubble_sort
(1...size).each do |i|
(0...size-i).each do |j|
self[j], self[j+1] = self[j+1], self[j] if self[j] > self[j+1]
end
end
self
end
end
data_size = [1000, 10000, 100000, 1000000] data = [] data_size.each do |size|
ary = *1..size data << [ [1]*size, ary, ary.shuffle, ary.reverse ]
end data = data.transpose
data_type = ["set to all ones", "ascending sequence", "randomly shuffled", "descending sequence"] print "Array size: " puts data_size.map{|size| "%9d" % size}.join
data.each_with_index do |arys,i|
puts "\nData #{data_type[i]}:"
[:sort, :radix_sort, :quick_sort, :shell_sort, :insertion_sort, :bubble_sort].each do |m|
printf "%20s ", m
flag = true
arys.each do |ary|
if flag
t0 = Time.now
ary.dup.send(m)
printf " %7.3f", (t1 = Time.now - t0)
flag = false if t1 > 2
else
print " --.---"
end
end
puts
end
end</lang> Array#sort is a built-in method.
- Output:
Array size: 1000 10000 100000 1000000
Data set to all ones:
sort 0.000 0.001 0.005 0.043
radix_sort 0.000 0.002 0.012 0.084
quick_sort 0.000 0.002 0.020 0.197
shell_sort 0.002 0.018 0.234 2.897
insertion_sort 0.000 0.002 0.020 0.198
bubble_sort 0.064 6.328 --.--- --.---
Data ascending sequence:
sort 0.000 0.000 0.002 0.020
radix_sort 0.001 0.010 0.128 1.546
quick_sort 0.004 0.058 0.521 5.996
shell_sort 0.001 0.019 0.234 2.882
insertion_sort 0.000 0.002 0.021 0.195
bubble_sort 0.065 6.453 --.--- --.---
Data randomly shuffled:
sort 0.000 0.002 0.024 0.263
radix_sort 0.001 0.011 0.126 1.529
quick_sort 0.004 0.081 0.522 6.192
shell_sort 0.003 0.033 0.498 5.380
insertion_sort 0.027 2.627 --.--- --.---
bubble_sort 0.122 11.779 --.--- --.---
Data descending sequence:
sort 0.000 0.001 0.001 0.021
radix_sort 0.001 0.012 0.125 1.560
quick_sort 0.004 0.061 0.522 5.873
shell_sort 0.003 0.028 0.316 3.829
insertion_sort 0.053 5.298 --.--- --.---
bubble_sort 0.206 17.232 --.--- --.---
Tcl
Background
The lsort command is Tcl's built-in sorting engine. It is implemented in C as a mergesort, so while it is theoretically slower than quicksort, it is a stable sorting algorithm too, which produces results that tend to be less surprising in practice. This task will be matching it against multiple manually-implemented sorting procedures.
Observations
Obviously, the built-in compiled sort command will be much faster than any Tcl-coded implementation. The Tcl-coded mergesort is up to 3 orders of magnitude slower.
The shellsort implementation suffers, relative to other algorithms, in the case where the list is already sorted.
Code
<lang tcl>###############################################################################
- measure and plot times
package require Tk package require struct::list namespace path ::tcl::mathfunc
proc create_log10_plot {title xlabel ylabel xs ys labels shapes colours} {
set w [toplevel .[clock clicks]] wm title $w $title pack [canvas $w.c -background white] pack [canvas $w.legend -background white] update plot_log10 $w.c $w.legend $title $xlabel $ylabel $xs $ys $labels $shapes $colours $w.c config -scrollregion [$w.c bbox all] update
}
proc plot_log10 {canvas legend title xlabel ylabel xs ys labels shapes colours} {
global xfac yfac
set log10_xs [map {_ {log10 $_}} $xs]
foreach series $ys {
lappend log10_ys [map {_ {log10 $_}} $series]
}
set maxx [max {*}$log10_xs]
set yvalues [lsort -real [struct::list flatten $log10_ys]]
set firstInf [lsearch $yvalues Inf]
set maxy [lindex $yvalues [expr {$firstInf == -1 ? [llength $yvalues] - 1 : $firstInf - 1}]]
set xfac [expr {[winfo width $canvas] * 0.8/$maxx}]
set yfac [expr {[winfo height $canvas] * 0.8/$maxy}]
scale $canvas x 0 $maxx $xfac "log10($xlabel)" scale $canvas y 0 $maxy $yfac "log10($ylabel)" $maxx $xfac
$legend create text 30 0 -text $title -anchor nw
set count 1
foreach series $log10_ys shape $shapes colour $colours label $labels {
plotxy $canvas $log10_xs $series $shape $colour
legenditem $legend [incr count] $shape $colour $label
}
}
proc map {lambda list} {
set res [list]
foreach item $list {lappend res [apply $lambda $item]}
return $res
}
proc legenditem {legend pos shape colour label} {
set y [expr {$pos * 15}]
$shape $legend 20 $y -fill $colour
$legend create text 30 $y -text $label -anchor w
}
- The actual plotting engine
proc plotxy {canvas _xs _ys shape colour} {
global xfac yfac
foreach x $_xs y $_ys {
if {$y < Inf} {
lappend xs $x
lappend ys $y
}
}
set coords [list]
foreach x $xs y $ys {
set coord_x [expr {$x*$xfac}]
set coord_y [expr {-$y*$yfac}]
$shape $canvas $coord_x $coord_y -fill $colour
lappend coords $coord_x $coord_y
}
$canvas create line $coords -smooth true
}
- Rescales the contents of the given canvas
proc scale {canvas direction from to fac label {other_to 0} {other_fac 0}} {
set f [expr {$from*$fac}]
set t [expr {$to*$fac}]
switch -- $direction {
x {
set f [expr {$from * $fac}]
set t [expr {$to * $fac}]
# create x-axis
$canvas create line $f 0 $t 0
$canvas create text $f 0 -anchor nw -text $from
$canvas create text $t 0 -anchor n -text [format "%.1f" $to]
$canvas create text [expr {($f+$t)/2}] 0 -anchor n -text $label
}
y {
set f [expr {$from * -$fac}]
set t [expr {$to * -$fac}]
# create y-axis
$canvas create line 0 $f 0 $t
$canvas create text 0 $f -anchor se -text $from
$canvas create text 0 $t -anchor e -text [format "%.1f" $to]
$canvas create text 0 [expr {($f+$t)/2}] -anchor e -text $label
# create gridlines
set xmax [expr {$other_to * $other_fac}]
for {set i 1} {$i < $to} {incr i} {
set y [expr {$i * -$fac}]
$canvas create line 0 $y $xmax $y -dash .
}
}
}
}
- Helper to make points, which are otherwise not a native item type
proc dot {canvas x y args} {
set id [$canvas create oval [expr {$x-3}] [expr {$y-3}] \
[expr {$x+3}] [expr {$y+3}]]
$canvas itemconfigure $id {*}$args
} proc square {canvas x y args} {
set id [$canvas create rectangle [expr {$x-3}] [expr {$y-3}] \
[expr {$x+3}] [expr {$y+3}]]
$canvas itemconfigure $id {*}$args
} proc cross {canvas x y args} {
set l1 [$canvas create line [expr {$x-3}] $y [expr {$x+3}] $y]
set l2 [$canvas create line $x [expr {$y-3}] $x [expr {$y+3}]]
$canvas itemconfigure $l1 {*}$args
$canvas itemconfigure $l2 {*}$args
} proc x {canvas x y args} {
set l1 [$canvas create line [expr {$x-3}] [expr {$y-3}] [expr {$x+3}] [expr {$y+3}]]
set l2 [$canvas create line [expr {$x+3}] [expr {$y-3}] [expr {$x-3}] [expr {$y+3}]]
$canvas itemconfigure $l1 {*}$args
$canvas itemconfigure $l2 {*}$args
} proc triangleup {canvas x y args} {
set id [$canvas create polygon $x [expr {$y-4}] \
[expr {$x+4}] [expr {$y+4}] \
[expr {$x-4}] [expr {$y+4}]]
$canvas itemconfigure $id {*}$args
} proc triangledown {canvas x y args} {
set id [$canvas create polygon $x [expr {$y+4}] \
[expr {$x+4}] [expr {$y-4}] \
[expr {$x-4}] [expr {$y-4}]]
$canvas itemconfigure $id {*}$args
}
wm withdraw .
- list creation procedures
proc ones n {
lrepeat $n 1
} proc reversed n {
while {[incr n -1] >= 0} {
lappend result $n
}
return $result
} proc random n {
for {set i 0} {$i < $n} {incr i} {
lappend result [expr {int($n * rand())}]
}
return $result
}
set algorithms {lsort quicksort shellsort insertionsort bubblesort mergesort} set sizes {1 10 100 1000 10000 100000} set types {ones reversed random} set shapes {dot square cross triangleup triangledown x} set colours {red blue black brown yellow black}
- create some lists to be used by all sorting algorithms
array set lists {} foreach size $sizes {
foreach type $types {
set lists($type,$size) [$type $size]
}
}
set runs 10
- header
fconfigure stdout -buffering none puts -nonewline [format "%-16s" "list length:"] foreach size $sizes {
puts -nonewline [format " %10d" $size]
} puts ""
- perform the sort timings and output results
foreach type $types {
puts "\nlist type: $type"
set times [list]
foreach algo $algorithms {
set errs [list]
set thesetimes [list]
$algo {} ;# call it once to ensure it's compiled
puts -nonewline [format " %-13s" $algo]
foreach size $sizes {
# some implementations are just too slow
if {$type ne "ones" && (
($algo eq "insertionsort" && $size > 10000) ||
($algo eq "bubblesort" && $size > 1000))
} {
set time Inf
} else {
# OK, do it
if {[catch {time [list $algo $lists($type,$size)] $runs} result] != 0} {
set time Inf
lappend errs $result
} else {
set time [lindex [split $result] 0]
}
}
lappend thesetimes $time
puts -nonewline [format " %10s" $time]
}
puts ""
if {[llength $errs] > 0} {
puts [format " %s" [join $errs "\n "]]
}
lappend times $thesetimes
}
create_log10_plot "Sorting a '$type' list" size time $sizes $times $algorithms $shapes $colours
} puts "\ntimes in microseconds, average of $runs runs"</lang>
Output
list length: 1 10 100 1000 10000 100000 list type: ones lsort 0.8 1.2 7.2 71.9 1042.7 11428.9 quicksort 1.1 9.0 40.6 369.5 3696.4 37478.4 shellsort 1.4 26.0 249.1 4003.4 56278.7 717790.6 insertionsort 1.1 6.4 59.0 528.1 5338.9 54913.0 bubblesort 1.9 5.1 31.9 308.8 3259.1 31991.2 mergesort 1.3 61.1 704.2 9275.4 224784.4 14599414.6 list type: reversed lsort 1.0 1.6 9.9 112.1 1434.9 20181.0 quicksort 1.5 55.3 495.6 6705.9 79984.0 963975.0 shellsort 1.5 25.9 457.0 7118.6 92497.5 1210143.9 insertionsort 1.2 21.0 1645.0 159262.2 15859610.8 Inf bubblesort 1.9 445.0 46526.6 4665550.4 Inf Inf mergesort 1.4 61.7 842.8 9572.1 215536.6 16938651.0 list type: random lsort 1.0 1.7 15.7 300.9 3275.0 58779.5 quicksort 1.2 28.0 429.1 5609.5 71743.3 923630.4 shellsort 1.6 26.7 571.0 9031.1 140526.9 2244152.7 insertionsort 1.3 15.4 832.6 79018.0 7893722.6 Inf bubblesort 1.8 256.2 23753.1 2422926.0 Inf Inf mergesort 1.9 60.2 883.5 12505.6 399672.6 49225509.8 times in microseconds, average of 10 runs
Wren
The quick, insertion and shell sorts all use the 'in place' implementations in the Wren-sort module.
The radix sort is lifted from the task of that name and, although more complicated, appears to be much faster than the Kotlin version.
For the bubble sort, I have used the optimized Kotlin implementation.
I've limited the size of the arrays to 50,000 though even then the program takes the best part of half an hour to run, due to the extreme slowness of the bubble and insertion sorts for large amounts of shuffled data.
Results presented in tabular form as Wren doesn't have a plotting library available at the present time. <lang ecmascript>import "random" for Random import "/sort" for Sort import "/fmt" for Fmt
var rand = Random.new()
var onesSeq = Fn.new { |n| List.filled(n, 1) }
var shuffledSeq = Fn.new { |n|
var seq = List.filled(n, 0) for (i in 0...n) seq[i] = 1 + rand.int(10 * n) return seq
}
var ascendingSeq = Fn.new { |n|
var seq = shuffledSeq.call(n) seq.sort() return seq
}
var bubbleSort = Fn.new { |a|
var n = a.count
while (true) {
var n2 = 0
for (i in 1...n) {
if (a[i - 1] > a[i]) {
a.swap(i, i - 1)
n2 = i
}
}
n = n2
if (n == 0) break
}
}
// 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 measureTime = Fn.new { |sort, seq|
var start = System.clock sort.call(seq) return ((System.clock - start) * 1e6).round // microseconds
}
var runs = 10 var lengths = [1, 10, 100, 1000, 10000, 50000] var sorts = [
bubbleSort,
Fn.new { |a| Sort.insertion(a) },
Fn.new { |a| Sort.quick(a) },
radixSort,
Fn.new { |a| Sort.shell(a) }
]
var sortTitles = ["Bubble", "Insert", "Quick ", "Radix ", "Shell "] var seqTitles = ["All Ones", "Ascending", "Shuffled"] var totals = List.filled(seqTitles.count, null) for (i in 0...totals.count) {
totals[i] = List.filled(sorts.count, null) for (j in 0...sorts.count) totals[i][j] = List.filled(lengths.count, 0)
} var k = 0 for (n in lengths) {
var seqs = [onesSeq.call(n), ascendingSeq.call(n), shuffledSeq.call(n)]
for (r in 0...runs) {
for (i in 0...seqs.count) {
for (j in 0...sorts.count) {
var seq = seqs[i].toList
totals[i][j][k] = totals[i][j][k] + measureTime.call(sorts[j], seq)
}
}
}
k = k + 1
} System.print("All timings in microseconds\n") System.write("Sequence length") for (len in lengths) Fmt.write("$8d ", len) System.print("\n") for (i in 0...seqTitles.count) {
System.print(" %(seqTitles[i]):")
for (j in 0...sorts.count) {
System.write(" %(sortTitles[j]) ")
for (k in 0...lengths.count) {
var time = (totals[i][j][k] / runs).round
Fmt.write("$8d ", time)
}
System.print()
}
System.print("\n")
}</lang>
- Output:
All timings in microseconds
Sequence length 1 10 100 1000 10000 50000
All Ones:
Bubble 1 2 9 61 643 3225
Insert 1 3 16 118 1256 6338
Quick 1 8 92 983 14746 87660
Radix 6 13 62 460 4823 24379
Shell 1 5 59 770 9542 48873
Ascending:
Bubble 1 2 8 61 637 3221
Insert 1 3 16 118 1251 6371
Quick 1 7 65 643 9149 54199
Radix 7 23 169 1648 21428 130609
Shell 1 5 60 779 9537 49041
Shuffled:
Bubble 1 7 451 37271 4025966 99834073
Insert 0 7 295 24040 2597162 64875212
Quick 1 8 101 1149 16256 95590
Radix 5 24 163 1688 22443 136228
Shell 1 8 111 1514 25180 230897
The results are much the same as one might have expected beforehand.
As far as the shuffled data is concerned, quick sort is the fastest though radix and shell sorts are also reasonable performers. Bubble and insertion sorts are very slow indeed for large amounts of data.
Conversely, if the data is already sorted into ascending order, bubble and insertion sorts are much faster than the others and radix sort is the slowest.
If all data is the same, a similar pattern emerges except that radix sort performs better than both shell and quick sorts, the latter being the slowest.