Compare sorting algorithms' performance
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.
Phix
<lang 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), c, mid, midn object xi, midval sequence left = {}, right = {}
if n<2 then
return x -- already sorted (trivial case)
end if
mid = floor((n+1)/2)
midval = x[mid]
x[mid] = x[1]
midn = 1
for i=2 to n do
xi = x[i]
c = compare(xi,midval)
if c<0 then
left &= xi
elsif c>0 then
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 integer first, last, stackptr, I, J, tmp, pivot
qstack = repeat(0,floor((length(s)/5)+10)) -- create a stack
first = 1
last = length(s)
stackptr = 0
while 1 do
while first<last do
pivot = s[floor(last+first)/2]
I = first
J = last
while 1 do
while s[I]<pivot do
I += 1
end while
while s[J]>pivot do
J -= 1
end while
if I>J then exit end if
if I<J then
tmp = s[I]
s[I] = s[J]
s[J] = tmp
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) integer mins = min(s) integer passes = max(max(s),abs(mins))
passes = floor(log10(passes))+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), j object temp
while gap>0 do
for i=gap to length(s) do
temp = s[i]
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 gap, j, first, last object xi, xj
last = length(x)
gap = floor(last/10)+1
while TRUE do
first = gap+1
for i=first to last do
xi = x[i]
j = i-gap
while TRUE do
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
sequence todo
--
-- 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 [$].
--
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
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if return IUP_CONTINUE
end function
procedure main()
IupOpen(join_path({"..","pGUI"},1))
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)
IupSetAttributes(dlg, "RASTERSIZE=%dx%d", {640, 480})
IupSetAttribute(dlg, "TITLE", "Compare sorting algorithms")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupShow(dlg)
IupSetInt(tabs, "VALUEPOS", tabidx-1)
IupSetGlobalFunction("IDLE_ACTION", cb_idle_action)
IupMainLoop()
IupClose()
end procedure
main()</lang>
Conclusions
I knew bubblesort and insertion sort would be bad, but no 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
