Dutch national flag problem
You are encouraged to solve this task according to the task description, using any language you may know.
The Dutch national flag is composed of three coloured bands in the order:
- red (top)
- then white, and
- lastly blue (at the bottom).
The problem posed by Edsger Dijkstra is:
- Given a number of red, blue and white balls in random order, arrange them in the order of the colours in the Dutch national flag.
When the problem was first posed, Dijkstra then went on to successively refine a solution, minimising the number of swaps and the number of times the colour of a ball needed to determined and restricting the balls to end in an array, ...
- Task
- Generate a randomized order of balls ensuring that they are not in the order of the Dutch national flag.
- Sort the balls in a way idiomatic to your language.
- Check the sorted balls are in the order of the Dutch national flag.
- C.f.
- Dutch national flag problem
- Probabilistic analysis of algorithms for the Dutch national flag problem by Wei-Mei Chen. (pdf)
ABAP
This works for ABAP Version 7.40 and above, the color blue is excluded as an option for the last entry to insure an unsorted sequence.
<lang ABAP> report z_dutch_national_flag_problem.
interface sorting_problem.
methods:
generate_unsorted_sequence
importing
lenght_of_sequence type int4
returning
value(unsorted_sequence) type string,
sort_sequence
changing
sequence_to_be_sorted type string,
is_sorted
importing
sequence_to_check type string
returning
value(sorted) type abap_bool.
endinterface.
class dutch_national_flag_problem definition.
public section.
interfaces:
sorting_problem.
constants:
begin of dutch_flag_colors,
red type char1 value 'R',
white type char1 value 'W',
blue type char1 value 'B',
end of dutch_flag_colors.
endclass.
class dutch_national_flag_problem implementation.
method sorting_problem~generate_unsorted_sequence.
data(random_int_generator) = cl_abap_random_int=>create(
seed = cl_abap_random=>seed( )
min = 0
max = 2 ).
do lenght_of_sequence - 1 times.
data(random_int) = random_int_generator->get_next( ).
data(next_color) = cond char1(
when random_int eq 0 then dutch_flag_colors-red
when random_int eq 1 then dutch_flag_colors-white
when random_int eq 2 then dutch_flag_colors-blue ).
unsorted_sequence = |{ unsorted_sequence }{ next_color }|.
enddo.
if strlen( unsorted_sequence ) > 0.
random_int = random_int_generator->get_next( ).
next_color = cond char1(
when random_int eq 0 or random_int eq 2 then dutch_flag_colors-red
when random_int eq 1 then dutch_flag_colors-white ).
unsorted_sequence = |{ unsorted_sequence }{ next_color }|.
endif.
endmethod.
method sorting_problem~sort_sequence. data(low_index) = 0. data(middle_index) = 0. data(high_index) = strlen( sequence_to_be_sorted ) - 1.
while middle_index <= high_index.
data(current_color) = sequence_to_be_sorted+middle_index(1).
if current_color eq dutch_flag_colors-red.
data(buffer) = sequence_to_be_sorted+low_index(1).
sequence_to_be_sorted = replace(
val = sequence_to_be_sorted
off = middle_index
len = 1
with = buffer ).
sequence_to_be_sorted = replace(
val = sequence_to_be_sorted
off = low_index
len = 1
with = current_color ).
low_index = low_index + 1.
middle_index = middle_index + 1.
elseif current_color eq dutch_flag_colors-blue.
buffer = sequence_to_be_sorted+high_index(1).
sequence_to_be_sorted = replace(
val = sequence_to_be_sorted
off = middle_index
len = 1
with = buffer ).
sequence_to_be_sorted = replace(
val = sequence_to_be_sorted
off = high_index
len = 1
with = current_color ).
high_index = high_index - 1.
else.
middle_index = middle_index + 1.
endif.
endwhile.
endmethod.
method sorting_problem~is_sorted. sorted = abap_true.
do strlen( sequence_to_check ) - 1 times.
data(current_character_index) = sy-index - 1.
data(current_color) = sequence_to_check+current_character_index(1).
data(next_color) = sequence_to_check+sy-index(1).
sorted = cond abap_bool(
when ( current_color eq dutch_flag_colors-red and
( next_color eq current_color or
next_color eq dutch_flag_colors-white or
next_color eq dutch_flag_colors-blue ) )
or
( current_color eq dutch_flag_colors-white and
( next_color eq current_color or
next_color eq dutch_flag_colors-blue ) )
or
( current_color eq dutch_flag_colors-blue and
current_color eq next_color )
then sorted
else abap_false ).
check sorted eq abap_false.
return.
enddo.
endmethod.
endclass.
start-of-selection.
data dutch_national_flag_problem type ref to sorting_problem.
dutch_national_flag_problem = new dutch_national_flag_problem( ).
data(sequence) = dutch_national_flag_problem->generate_unsorted_sequence( 20 ).
write:|{ sequence }, is sorted? -> { dutch_national_flag_problem->is_sorted( sequence ) }|, /.
dutch_national_flag_problem->sort_sequence( changing sequence_to_be_sorted = sequence ).
write:|{ sequence }, is sorted? -> { dutch_national_flag_problem->is_sorted( sequence ) }|, /.
</lang>
- Output:
RBWRWWRBWWRWBBRBRRWR, is sorted? -> RRRRRRRRWWWWWWWBBBBB, is sorted? -> X
Ada
<lang Ada>with Ada.Text_IO, Ada.Numerics.Discrete_Random, Ada.Command_Line;
procedure Dutch_National_Flag is
type Colour_Type is (Red, White, Blue);
Number: Positive range 2 .. Positive'Last :=
Positive'Value(Ada.Command_Line.Argument(1));
-- no sorting if the Number of balls is less than 2
type Balls is array(1 .. Number) of Colour_Type;
function Is_Sorted(B: Balls) return Boolean is
-- checks if balls are in order
begin
for I in Balls'First .. Balls'Last-1 loop
if B(I) > B(I+1) then
return False;
end if;
end loop;
return True;
end Is_Sorted;
function Random_Balls return Balls is
-- generates an array of random balls, ensuring they are not in order
package Random_Colour is new Ada.Numerics.Discrete_Random(Colour_Type);
Gen: Random_Colour.Generator;
B: Balls;
begin
Random_Colour.Reset(Gen);
loop
for I in Balls'Range loop
B(I) := Random_Colour.Random(Gen);
end loop;
exit when (not Is_Sorted(B));
-- ... ensuring they are not in order
end loop;
return B;
end Random_Balls;
procedure Print(Message: String; B: Balls) is
begin
Ada.Text_IO.Put(Message);
for I in B'Range loop
Ada.Text_IO.Put(Colour_Type'Image(B(I)));
if I < B'Last then
Ada.Text_IO.Put(", ");
else
Ada.Text_IO.New_Line;
end if;
end loop;
end Print;
procedure Sort(Bls: in out Balls) is
-- sort Bls in O(1) time
Cnt: array(Colour_Type) of Natural := (Red => 0, White => 0, Blue => 0);
Col: Colour_Type;
procedure Move_Colour_To_Top(Bls: in out Balls;
Colour: Colour_Type;
Start: Positive;
Count: Natural) is
This: Positive := Start;
Tmp: Colour_Type;
begin
for N in Start .. Start+Count-1 loop
while Bls(This) /= Colour loop
This := This + 1;
end loop; -- This is the first index >= N with B(This) = Colour
Tmp := Bls(N); Bls(N) := Bls(This); Bls(This) := Tmp; -- swap
This := This + 1;
end loop;
end Move_Colour_To_Top;
begin
for Ball in Balls'Range loop
-- count how often each colour is found
Col := Bls(Ball);
Cnt(Col) := Cnt(Col) + 1;
end loop;
Move_Colour_To_Top(Bls, Red, Start => 1, Count => Cnt(Red));
Move_Colour_To_Top(Bls, White, Start => 1+Cnt(Red), Count => Cnt(White));
-- all the remaining balls are blue
end Sort;
A: Balls := Random_Balls;
begin
Print("Original Order: ", A);
pragma Assert(not Is_Sorted(A)); -- Check if A is unsorted
Sort(A); -- A = ((Red**Cnt(Red)= & (White**Cnt(White)) & (Blue**Cnt(Blue)))
pragma Assert(Is_Sorted(A)); -- Check if A is actually sorted
Print("After Sorting: ", A);
end Dutch_National_Flag;</lang>
- Output:
>./dutch_national_flag 5 Original Order: RED, RED, BLUE, RED, BLUE After Sorting: RED, RED, RED, BLUE, BLUE >./dutch_national_flag 5 Original Order: BLUE, RED, RED, WHITE, RED After Sorting: RED, RED, RED, WHITE, BLUE >./dutch_national_flag 7 Original Order: WHITE, WHITE, BLUE, WHITE, BLUE, BLUE, WHITE After Sorting: WHITE, WHITE, WHITE, WHITE, BLUE, BLUE, BLUE
AutoHotkey
<lang AutoHotKey>RandGen(MaxBalls){ Random,k,3,MaxBalls Loop,% k{ Random,k,1,3 o.=k }return o } While((!InStr(o,1)||!InStr(o,2)||!InStr(o,3))||!RegExReplace(o,"\b1+2+3+\b")) o:=RandGen(3) Loop,% StrLen(o) F.=SubStr(o,A_Index,1) "," F:=RTrim(F,",") Sort,F,N D`, MsgBox,% F:=RegExReplace(RegExReplace(RegExReplace(F,"(1)","Red"),"(2)","White"),"(3)","Blue")</lang>
AutoIt
Given each color a value in descending order ( Red = 1, White = 2 And Blue = 3) <lang Autoit>
- include <Array.au3>
Dutch_Flag(50) Func Dutch_Flag($arrayitems) Local $avArray[$arrayitems] For $i = 0 To UBound($avArray) - 1 $avArray[$i] = Random(1, 3, 1) Next Local $low = 2, $high = 3, $i = 0 Local $arraypos = -1 Local $p = UBound($avArray) - 1 While $i < $p if $avArray[$i] < $low Then $arraypos += 1 _ArraySwap($avArray[$i], $avArray[$arraypos]) $i += 1 ElseIf $avArray[$i] >= $high Then _ArraySwap($avArray[$i], $avArray[$p]) $p -= 1 Else $i += 1 EndIf WEnd _ArrayDisplay($avArray) EndFunc ;==>Dutch_Flag </lang>
AWK
<lang awk> BEGIN {
weight[1] = "red"; weight[2] = "white"; weight[3] = "blue"; # ballnr must be >= 3. Using very high numbers here may make your computer # run out of RAM. (10 millions balls ~= 2.5GiB RAM on x86_64) ballnr = 10
srand()
# Generating a random pool of balls. This python-like loop is actually
# a prettyfied one-liner
do
for (i = 1; i <= ballnr; i++)
do
balls[i] = int(3 * rand() + 1)
# These conditions ensure the 3 first balls contains
# a white, blue and red ball. Removing 'i < 4' would
# hit performance a lot.
while ( (i < 4 && i > 1 && balls[i] == balls[i - 1]) ||
(i < 4 && i > 2 && balls[i] == balls[i - 2]) )
while (is_dnf(balls, ballnr))
printf("BEFORE: ")
print_balls(balls, ballnr, weight)
# Using gawk default quicksort. Using variants of PROCINFO["sorted_in"]
# wasn't faster than a simple call to asort().
asort(balls)
printf("\n\nAFTER : ")
print_balls(balls, ballnr, weight)
sorting = is_dnf(balls, ballnr) ? "valid" : "invalid"
print("\n\nSorting is " sorting ".")
}
function print_balls(balls, ballnr, weight ,i) {
for (i = 1; i <= ballnr; i++)
printf("%-7s", weight[balls[i]])
}
function is_dnf(balls, ballnr) {
# Checking if the balls are sorted in the Dutch national flag order,
# using a simple scan with weight comparison
for (i = 2; i <= ballnr; i++)
if (balls[i - 1] > balls[i])
return 0
return 1
} </lang>
Output:
<lang> BEFORE: blue red white red white blue red white blue white
AFTER : red red red white white white white blue blue blue
Sorting is valid. </lang>
BaCon
<lang qbasic>DECLARE color$[] = { "red", "white", "blue" }
DOTIMES 16
ball$ = APPEND$(ball$, 0, color$[RANDOM(3)] )
DONE
PRINT "Unsorted: ", ball$
PRINT " Sorted: ", REPLACE$(SORT$(REPLACE$(ball$, "blue", "z")), "z", "blue")</lang>
- Output:
Unsorted: red white blue blue red white white white blue white blue red blue red white red Sorted: red red red red red white white white white white white blue blue blue blue blue
BBC BASIC
<lang bbcbasic> INSTALL @lib$+"SORTLIB"
Sort% = FN_sortinit(0,0)
nBalls% = 12
DIM Balls$(nBalls%-1), Weight%(nBalls%-1), DutchFlag$(2)
DutchFlag$() = "Red ", "White ", "Blue "
REM. Generate random list of balls, ensuring not sorted:
REPEAT
prev% = 0 : sorted% = TRUE
FOR ball% = 0 TO nBalls%-1
index% = RND(3) - 1
Balls$(ball%) = DutchFlag$(index%)
IF index% < prev% THEN sorted% = FALSE
prev% = index%
NEXT
UNTIL NOT sorted%
PRINT "Random list: " SUM(Balls$())
REM. Assign Dutch Flag weightings to ball colours:
DutchFlag$ = SUM(DutchFlag$())
FOR ball% = 0 TO nBalls%-1
Weight%(ball%) = INSTR(DutchFlag$, Balls$(ball%))
NEXT
REM. Sort into Dutch Flag colour sequence:
C% = nBalls%
CALL Sort%, Weight%(0), Balls$(0)
PRINT "Sorted list: " SUM(Balls$())
REM Final check:
prev% = 0 : sorted% = TRUE
FOR ball% = 0 TO nBalls%-1
weight% = INSTR(DutchFlag$, Balls$(ball%))
IF weight% < prev% THEN sorted% = FALSE
prev% = weight%
NEXT
IF NOT sorted% PRINT "Error: Balls are not in correct order!"</lang>
- Output:
Random list: Red White Red Blue White Red White Blue Red Red Blue Red Sorted list: Red Red Red Red Red Red White White White Blue Blue Blue
C
<lang c>#include <stdio.h> //printf()
- include <stdlib.h> //srand(), rand(), RAND_MAX, qsort()
- include <stdbool.h> //true, false
- include <time.h> //time()
- define NUMBALLS 5 //NUMBALLS>1
int compar(const void *a, const void *b){ char c1=*(const char*)a, c2=*(const char*)b; //first cast void* to char*, then dereference return c1-c2; }
_Bool issorted(char *balls){ int i,state; state=0; for(i=0;i<NUMBALLS;i++){ if(balls[i]<state)return false; if(balls[i]>state)state=balls[i]; } return true; }
void printout(char *balls){ int i; char str[NUMBALLS+1]; for(i=0;i<NUMBALLS;i++)str[i]=balls[i]==0?'r':balls[i]==1?'w':'b'; printf("%s\n",str); }
int main(void) { char balls[NUMBALLS]; //0=r, 1=w, 2=b int i; srand(time(NULL)); //not a good seed but good enough for the example rand(); //rand() always starts with the same values for certain seeds, making // testing pretty irritating // Generate balls for(i=0;i<NUMBALLS;i++)balls[i]=(double)rand()/RAND_MAX*3; while(issorted(balls)){ //enforce that we start with non-sorted balls printf("Accidentally still sorted: "); printout(balls); for(i=0;i<NUMBALLS;i++)balls[i]=(double)rand()/RAND_MAX*3; } printf("Non-sorted: "); printout(balls); qsort(balls,NUMBALLS,sizeof(char),compar); //sort them using quicksort (stdlib) if(issorted(balls)){ //unnecessary check but task enforces it printf("Sorted: "); printout(balls); } else { printf("Sort failed: "); printout(balls); } return 0; }</lang>
- Output:
Accidentally still sorted:rrrww Non-sorted: rbwww Sorted: rwwwb
C_sharp
<lang csharp>using System; using System.Collections.Generic; using System.Linq; using System.Text;
namespace RosettaCode {
class Program
{
static void QuickSort(IComparable[] elements, int left, int right)
{
int i = left, j = right;
IComparable pivot = elements[left + (right - left) / 2];
while (i <= j)
{
while (elements[i].CompareTo(pivot) < 0) i++;
while (elements[j].CompareTo(pivot) > 0) j--;
if (i <= j)
{
// Swap
IComparable tmp = elements[i];
elements[i] = elements[j];
elements[j] = tmp;
i++;
j--;
}
}
// Recursive calls
if (left < j) QuickSort(elements, left, j);
if (i < right) QuickSort(elements, i, right);
}
const int NUMBALLS = 5;
static void Main(string[] args)
{
Func<string[], bool> IsSorted = (ballList) =>
{
int state = 0;
for (int i = 0; i < NUMBALLS; i++)
{
if (int.Parse(ballList[i]) < state)
return false;
if (int.Parse(ballList[i]) > state)
state = int.Parse(ballList[i]);
}
return true;
};
Func<string[], string> PrintOut = (ballList2) =>
{
StringBuilder str = new StringBuilder();
for (int i = 0; i < NUMBALLS; i++)
str.Append(int.Parse(ballList2[i]) == 0 ? "r" : int.Parse(ballList2[i]) == 1 ? "w" : "b");
return str.ToString();
};
bool continueLoop = true;
string[] balls = new string[NUMBALLS]; // 0 = r, 1 = w, 2 = b
Random numberGenerator = new Random();
do // Enforce that we start with non-sorted balls
{
// Generate balls
for (int i = 0; i < NUMBALLS; i++)
balls[i] = numberGenerator.Next(3).ToString();
continueLoop = IsSorted(balls);
if (continueLoop)
Console.WriteLine("Accidentally still sorted: {0}", PrintOut(balls));
} while (continueLoop);
Console.WriteLine("Non-sorted: {0}", PrintOut(balls));
QuickSort(balls, 0, NUMBALLS - 1); // Sort them using quicksort
Console.WriteLine("{0}: {1}", IsSorted(balls) ? "Sorted" : "Sort failed", PrintOut(balls));
}
}
} </lang>
C++
<lang cpp>#include <algorithm>
- include <iostream>
// Dutch national flag problem template <typename BidIt, typename T> void dnf_partition(BidIt first, BidIt last, const T& low, const T& high) {
for (BidIt next = first; next != last; ) {
if (*next < low) {
std::iter_swap(first++, next++);
} else if (!(*next < high)) {
std::iter_swap(next, --last);
} else {
++next;
}
}
}
enum Colors { RED, WHITE, BLUE };
void print(const Colors *balls, size_t size) {
static const char *label[] = { "red", "white", "blue" };
std::cout << "Balls:";
for (size_t i = 0; i < size; ++i) {
std::cout << ' ' << label[balls[i]];
}
std::cout << "\nSorted: " << std::boolalpha << std::is_sorted(balls, balls + size) << '\n';
}
int main() {
Colors balls[] = { RED, WHITE, BLUE, RED, WHITE, BLUE, RED, WHITE, BLUE };
std::random_shuffle(balls, balls + 9); print(balls, 9);
dnf_partition(balls, balls + 9, WHITE, BLUE); print(balls, 9);
}</lang>
- Output:
Balls: blue white red blue red blue white red white Sorted: false Balls: red red red white white white blue blue blue Sorted: true
Ceylon
Be sure to add ceylon.random in your module.ceylon file. <lang ceylon>import ceylon.random {
DefaultRandom }
abstract class Colour(name, ordinal) of red | white | blue satisfies Comparable<Colour> { shared String name; shared Integer ordinal; string => name; compare(Colour other) => this.ordinal <=> other.ordinal; }
object red extends Colour("red", 0) {} object white extends Colour("white", 1) {} object blue extends Colour("blue", 2) {}
Colour[] allColours = `Colour`.caseValues;
shared void run() {
function ordered({Colour*} colours) => colours.paired.every(([c1, c2]) => c1 <= c2);
value random = DefaultRandom();
function randomBalls(Integer length = 15) { while (true) { value balls = random.elements(allColours).take(length); if (!ordered(balls)) { return balls.sequence(); } } }
function dutchSort({Colour*} balls, Colour mid = white) { value array = Array { *balls }; if (array.empty) { return []; } variable value i = 0; variable value j = 0; variable value n = array.size - 1; while (j <= n) { assert (exists ball = array[j]); if (ball < mid) { array.swap(i, j); i ++; j ++; } else if (ball > mid) { array.swap(n, j); n --; } else { j ++; } } return array; }
function idiomaticSort({Colour*} balls) => balls.sort(increasing);
value initialBalls = randomBalls();
"the initial balls are not randomized" assert (!ordered(initialBalls));
print(initialBalls); value sortedBalls1 = idiomaticSort(initialBalls); value sortedBalls2 = dutchSort(initialBalls); "the idiomatic sort didn't work" assert (ordered(sortedBalls1)); "the dutch sort didn't work" assert (ordered(sortedBalls2)); print(sortedBalls1); print(sortedBalls2);
}</lang>
D
<lang d>import std.stdio, std.random, std.algorithm, std.traits, std.array;
enum DutchColors { red, white, blue }
void dutchNationalFlagSort(DutchColors[] items) pure nothrow @nogc {
int lo, mid, hi = items.length - 1;
while (mid <= hi)
final switch (items[mid]) {
case DutchColors.red:
swap(items[lo++], items[mid++]);
break;
case DutchColors.white:
mid++;
break;
case DutchColors.blue:
swap(items[mid], items[hi--]);
break;
}
}
void main() {
DutchColors[12] balls;
foreach (ref ball; balls)
ball = uniform!DutchColors;
writeln("Original Ball order:\n", balls);
balls.dutchNationalFlagSort;
writeln("\nSorted Ball Order:\n", balls);
assert(balls[].isSorted, "Balls not sorted.");
}</lang>
- Output:
Original Ball order: [red, white, white, blue, white, red, red, red, red, red, blue, red] Sorted Ball Order: [red, red, red, red, red, red, red, white, white, white, blue, blue]
Bidirectional Range Version
<lang d>import std.stdio, std.random, std.algorithm, std.range,
std.array, std.traits;
/* This implementation has less requirements, it works with just a Bidirectional Range instead of a Random Access Range.
(Comments modified from "Notes on Programming" by Alexander
Stepanov.)
Let us assume that somehow we managed to solve the problem up to some middle point s:
0000001111?????22222222
^ ^ ^
f s l (first, second, last)
If s points to an item with value 0 (red) we swap it with an element pointed at by f and advance both f and s. If s refers to an item 1 (white) we just advance s. If s refers to an item 2 (blue) we swap elements pointed by l and s and we decrement l.
In D/Phobos we use Ranges, that are like pairs of iterators. So 'secondLast' represents the s and l iterators, and the 'first' range contains f plus an unused end.
secondLast represents the inclusive range of items not yet seen. When it's empty, the algorithm has finished.
Loop variant: in each iteration of the for loop the length of secondLast decreases by 1. So the algorithm terminates.
- /
void dutchNationalFlagSort(Range, T)(Range secondLast,
in T lowVal, in T highVal)
pure nothrow if (isBidirectionalRange!Range &&
hasSwappableElements!Range &&
is(ElementType!Range == T)) {
for (auto first = secondLast; !secondLast.empty; )
if (secondLast.front == lowVal) {
swap(first.front, secondLast.front);
first.popFront();
secondLast.popFront();
} else if (secondLast.front == highVal) {
swap(secondLast.front, secondLast.back);
secondLast.popBack();
} else
secondLast.popFront();
}
void main() {
enum DutchColors { red, white, blue }
DutchColors[12] balls;
foreach (ref ball; balls)
ball = [EnumMembers!DutchColors][uniform(0, $)];
writeln("Original Ball order:\n", balls);
balls[].dutchNationalFlagSort(DutchColors.red,
DutchColors.blue);
writeln("\nSorted Ball Order:\n", balls);
assert(balls[].isSorted(), "Balls not sorted");
// More tests:
foreach (i; 0 .. 100_000) {
int n = uniform(0, balls.length);
foreach (ref ball; balls[0 .. n])
ball = [EnumMembers!DutchColors][uniform(0, $)];
balls[0 .. n].dutchNationalFlagSort(DutchColors.red,
DutchColors.blue);
assert(balls[0 .. n].isSorted());
}
}</lang> The output is the same.
More Verified Version
This version uses more contract programming and asserts to verify the code correctness. With hints from: toccata.lri.fr/gallery/flag.en.html <lang d>import std.stdio, std.random, std.algorithm, std.traits, std.range;
enum Color : ubyte { blue, white, red }
immutable isMonochrome = (in Color[] a, in size_t i, in size_t j, in Color c)
pure nothrow @safe @nogc => iota(i, j).all!(k => a[k] == c);
bool isPermutation(in Color[] a1, in Color[] a2) pure nothrow @safe @nogc {
size_t[EnumMembers!Color.length] counts1, counts2;
foreach (immutable x; a1)
counts1[x]++;
foreach (immutable x; a2)
counts2[x]++;
return counts1 == counts2;
}
void dutchNationalFlagSort(Color[] a) pure nothrow @safe @nogc
// This function is not @nogc in -debug builds. /* Scan of the array 'a' from left to right using 'i' and we maintain this invariant, using indices 'b' and 'r':
0 b i r +---------+----------+-----------+-------+ | blue | white | ? | red | +---------+----------+-----------+-------+ */
out {
// Find b and r.
immutable bRaw = a.countUntil!q{a != b}(Color.blue);
immutable size_t b = (bRaw == -1) ? a.length : bRaw;
immutable rRaw = a.retro.countUntil!q{a != b}(Color.red);
immutable size_t r = (rRaw == -1) ? 0 : (a.length - rRaw);
assert(isMonochrome(a, 0, b, Color.blue)); assert(isMonochrome(a, b, r, Color.white)); assert(isMonochrome(a, r, a.length, Color.red)); // debug assert(isPermutation(a, a.old));
} body {
size_t b = 0, i = 0, r = a.length;
debug {
/*ghost*/ immutable aInit = a.idup; // For loop invariant.
/*ghost*/ size_t riPred = r - i; // For loop variant.
}
while (i < r) {
/*invariant*/ assert(0 <= b && b <= i && i <= r && r <= a.length);
/*invariant*/ assert(isMonochrome(a, 0, b, Color.blue));
/*invariant*/ assert(isMonochrome(a, b, i, Color.white));
/*invariant*/ assert(isMonochrome(a, r, a.length, Color.red));
/*invariant*/ debug assert(isPermutation(a, aInit));
final switch (a[i]) with (Color) {
case blue:
a[b].swap(a[i]);
b++;
i++;
break;
case white:
i++;
break;
case red:
r--;
a[r].swap(a[i]);
break;
}
debug {
/*variant*/ assert((r - i) < riPred);
riPred = r - i;
}
}
}
void main() {
Color[12] balls;
// Test special cases.
foreach (immutable color; [EnumMembers!Color]) {
balls[] = color;
balls.dutchNationalFlagSort;
assert(balls[].isSorted, "Balls not sorted.");
}
foreach (ref b; balls)
b = uniform!Color;
writeln("Original Ball order:\n", balls);
balls.dutchNationalFlagSort;
writeln("\nSorted Ball Order:\n", balls);
assert(balls[].isSorted, "Balls not sorted.");
}</lang> The output is the same.
Elixir
<lang elixir>defmodule Dutch_national_flag do
defp ball(:red), do: 1
defp ball(:white), do: 2
defp ball(:blue), do: 3
defp random_ball, do: Enum.random([:red, :white, :blue])
defp random_ball(n), do: (for _ <- 1..n, do: random_ball())
defp is_dutch([]), do: true
defp is_dutch([_]), do: true
defp is_dutch([b,h|l]), do: ball(b) < ball(h) and is_dutch([h|l])
defp is_dutch(_), do: false
def dutch(list), do: dutch([], [], [], list)
defp dutch(r, w, b, []), do: r ++ w ++ b
defp dutch(r, w, b, [:red | list]), do: dutch([:red | r], w, b, list)
defp dutch(r, w, b, [:white | list]), do: dutch(r, [:white | w], b, list)
defp dutch(r, w, b, [:blue | list]), do: dutch(r, w, [:blue | b], list)
def problem(n \\ 10) do
list = random_ball(n)
if is_dutch(list) do
IO.puts "The random sequence #{inspect list} is already in the order of the Dutch flag!"
else
IO.puts "The starting random sequence is #{inspect list};"
IO.puts "The ordered sequence is #{inspect dutch(list)}."
end
end
end
Dutch_national_flag.problem</lang>
- Output:
The starting random sequence is [:blue, :white, :blue, :red, :red, :white, :blue , :white, :white, :blue]; The ordered sequence is [:red, :red, :white, :white, :white, :white, :blue, :blu e, :blue, :blue].
Erlang
<lang erlang>-module(dutch). -export([random_balls/1, is_dutch/1, dutch/1]).
ball(red) -> 1; ball(white) -> 2; ball(blue) -> 3.
random_ball() -> lists:nth(random:uniform(3), [red, white, blue]).
random_balls(N) -> random_balls(N,[]). random_balls(0,L) -> L; random_balls(N,L) when N > 0 ->
B = random_ball(), random_balls(N-1, [B|L]).
is_dutch([]) -> true; is_dutch([_]) -> true; is_dutch([B|[H|L]]) -> (ball(B) < ball(H)) and is_dutch([H|L]); is_dutch(_) -> false.
dutch(L) -> dutch([],[],[],L).
dutch(R, W, B, []) -> R ++ W ++ B; dutch(R, W, B, [red | L]) -> dutch([red|R], W, B, L); dutch(R, W, B, [white | L]) -> dutch(R, [white|W], B, L); dutch(R, W, B, [blue | L]) -> dutch(R, W, [blue|B], L).</lang>
Sample usage: <lang erlang>main(_) ->
L = random_balls(10),
case is_dutch(L) of
true -> io:format("The random sequence ~p is already in the order of the Dutch flag!~n", [L]);
false -> io:format("The starting random sequence is ~p;~nThe ordered sequence is ~p.~n", [L, dutch(L)])
end.</lang>
- Output:
The starting random sequence is [white,white,blue,blue,white,red,white,blue,
blue,white];
The ordered sequence is [red,white,white,white,white,white,blue,blue,blue,
blue].
F#
<lang fsharp>(* Since the task description here does not impose Dijsktra's original restrictions
* Changing the order is only allowed by swapping 2 elements * Every element must only be inspected once we have several options ... One way -- especially when we work with immutable data structures -- is to scan the unordered list, collect the different colours on our way and append the 3 sub-lists in the correct order.
- )
let rnd = System.Random()
type color = | Red | White | Blue
let isDutch s =
Seq.forall2 (fun last this ->
match (last, this) with
| (Red, Red) | (Red, White) | (White, White) | (White, Blue) | (Blue, Blue) -> true | _ -> false
) s (Seq.skip 1 s)
[<EntryPoint>] let main argv =
let n = 10
let rec getBallsToSort n s =
let sn = Seq.take n s
if (isDutch sn) then (getBallsToSort n (Seq.skip 1 s)) else sn
let balls = getBallsToSort n (Seq.initInfinite (fun _ -> match (rnd.Next(3)) with | 0 -> Red | 1 -> White | _ -> Blue))
printfn "Sort the sequence of %i balls: %A" n (Seq.toList balls)
let (rs,ws,bs) =
balls
|> Seq.fold (fun (rs,ws,bs) b ->
match b with | Red -> (b::rs,ws,bs) | White -> (rs,b::ws,bs) | Blue -> (rs,ws,b::bs))
([],[],[])
let sorted = rs @ ws @ bs
printfn "The sequence %A is sorted: %b" sorted (isDutch sorted)
0</lang>
- Output:
Sort the sequence of 10 balls: [Red; White; Red; Blue; White; White; Blue; Blue; White; White] The sequence [Red; Red; White; White; White; White; White; Blue; Blue; Blue] is sorted: true
Forth
This demo is by no means exemplary however there was no other Forth entry. This code runs on the infamous TI-99, one of the slowest computers ever. This demo uses Dijkstra's three colour algorithm to sort four different inputs. The flag is sorted on the screen so you can see it happen. The input data patterns are: random, checker-board, Russian flag and French (imperfect) flag. Using three variables for the screen position pointers (vs stack juggling) makes the Dijkstra algorithm translate nicely into Forth.
A video of the results can be seen here:
https://github.com/bfox9900/CAMEL99-V2/blob/master/Video/DIJKSTRAFLAG%20.mp4
<lang>\ Dutch flag DEMO for CAMEL99 Forth \ *SORTS IN PLACE FROM Video MEMORY*
INCLUDE DSK1.GRAFIX.F INCLUDE DSK1.RANDOM.F INCLUDE DSK1.CASE.F
\ TMS9918 Video chip Specific code HEX FFFF FFFF FFFF FFFF PATTERN: SQUARE
\ define colors and characters DECIMAL 24 32 * CONSTANT SIZE \ flag will fill GRAPHICS screen SIZE 3 / CONSTANT #256 \ 256 chars per segment of flag 1 CONSTANT REDSQR \ red character 9 CONSTANT WHTSQR \ white character 19 CONSTANT BLUSQR \ blue character
\ color constants 1 CONSTANT TRANS 7 CONSTANT RED 5 CONSTANT BLU 16 CONSTANT WHT
SQUARE REDSQR CHARDEF SQUARE BLUSQR CHARDEF SQUARE WHTSQR CHARDEF
\ charset FG BG
0 RED TRANS COLOR 1 WHT TRANS COLOR 2 BLU TRANS COLOR
\ screen fillers
- RNDI ( -- n ) SIZE 1+ RND ; \ return a random VDP screen address
- NOTRED ( -- n ) \ return rnd index that is not RED
BEGIN
RNDI DUP VC@ REDSQR =
WHILE DROP
REPEAT ;
- NOTREDWHT ( -- n ) \ return rnd index that is not RED or WHITE
BEGIN RNDI DUP
VC@ DUP REDSQR =
SWAP WHTSQR = OR
WHILE
DROP
REPEAT ;
- RNDRED ( -- ) \ Random RED on VDP screen
#256 0 DO REDSQR NOTRED VC! LOOP ;
- RNDWHT ( -- ) \ place white where there is no red or white
#256 0 DO WHTSQR NOTREDWHT VC! LOOP ;
- BLUSCREEN ( -- )
0 768 BLUSQR VFILL ;
\ load the screen with random red,white&blue squares
- RNDSCREEN ( -- )
BLUSCREEN RNDRED RNDWHT ;
- CHECKERED ( -- ) \ red,wht,blue checker board
SIZE 0
DO
BLUSQR I VC!
WHTSQR I 1+ VC!
REDSQR I 2+ VC!
3 +LOOP ;
- RUSSIAN \ Russian flag
0 0 WHTSQR 256 HCHAR
0 8 BLUSQR 256 HCHAR
0 16 REDSQR 256 HCHAR ;
- FRENCH \ kind of a French flag
0 0 BLUSQR 256 VCHAR
10 16 WHTSQR 256 VCHAR
21 8 REDSQR 256 VCHAR ;
\ ======================================================= \ Algorithm Dijkstra(A) \ A is an array of three colors \ begin \ r <- 1; \ b <- n; \ w <- n; \ while (w>=r) \ check the color of A[w] \ case 1: red \ swap(A[r],A [w]); \ r<-r+1; \ case 2: white \ w<-w-1 \ case 3: blue \ swap(A[w],A[b]); \ w<-w-1; \ b<-b-1; \ end
\ ====================================================== \ Dijkstra three color Algorithm in Forth
\ screen address pointers VARIABLE R VARIABLE B VARIABLE W
- XCHG ( vadr1 vadr2 -- ) \ Exchange chars in Video RAM
OVER VC@ OVER VC@ ( -- addr1 addr2 char1 char2)
SWAP ROT VC! SWAP VC! ; \ exchange chars in Video RAM
- DIJKSTRA ( -- )
0 R !
SIZE 1- DUP B ! W !
BEGIN
W @ R @ 1- >
WHILE
W @ VC@ ( fetch Video char at pointer W)
CASE
REDSQR OF R @ W @ XCHG
1 R +! ENDOF
WHTSQR OF -1 W +! ENDOF
BLUSQR OF W @ B @ XCHG
-1 W +!
-1 B +! ENDOF
ENDCASE
REPEAT ;
- WAIT ( -- ) 11 11 AT-XY ." Finished!" 1500 MS ;
- RUN ( -- )
PAGE
CR ." Dijkstra Dutch flag Demo" CR
CR ." Sorted in-place in Video RAM" CR
CR
CR ." Using the 3 colour algorithm" CR
CR ." Press any key to begin" KEY DROP
RNDSCREEN DIJKSTRA WAIT
CHECKERED DIJKSTRA WAIT
RUSSIAN DIJKSTRA WAIT
FRENCH DIJKSTRA WAIT
0 23 AT-XY
CR ." Completed"
</lang>
Fortran
Please find the example run along with compilation instructions on a GNU/linux platform in the comments at the beginning of the FORTRAN 2008 program source. The Netherlands program, using equal numbers of colors, solved the problem at three sample sizes. Swaps number 2/3 the total of samples, convincingly demonstrating the O(n) time behavior that's directly provable by inspection. The color strings are chosen for ASCII sort. Feature not used.
Abhor code duplication. I've repeated code anyway to demonstrate FORTRAN pointers, which behave like an alias. A subroutine with traditional arguments including the number of valid elements of the array is appropriate. I'd use one long array instead of 3 arrays and the size intrinsic. <lang> !-*- mode: compilation; default-directory: "/tmp/" -*- !Compilation started at Mon Jun 3 11:18:24 ! !a=./f && make FFLAGS='-O0 -g' $a && OMP_NUM_THREADS=2 $a < unixdict.txt !gfortran -std=f2008 -O0 -g -Wall -fopenmp -ffree-form -fall-intrinsics -fimplicit-none f.f08 -o f ! Original and flag sequences ! WHITE RED blue blue RED WHITE WHITE WHITE blue RED RED blue ! RED RED RED RED WHITE WHITE WHITE WHITE blue blue blue blue ! 12 items, 8 swaps. ! 999 items, 666 swaps. ! 9999 items, 6666 swaps. ! !Compilation finished at Mon Jun 3 11:18:24
program Netherlands
character(len=6), parameter, dimension(3) :: colors = (/'RED ', 'WHITE ', 'blue '/) integer, dimension(12) :: sort_me integer, dimension(999), target :: a999 integer, dimension(9999), target :: a9999 integer, dimension(:), pointer :: pi integer :: i, swaps data sort_me/4*1,4*2,4*3/ call shuffle(sort_me, 5) write(6,*)'Original and flag sequences' write(6,*) (colors(sort_me(i)), i = 1, size(sort_me)) call partition3way(sort_me, 2, swaps) write(6,*) (colors(sort_me(i)), i = 1, size(sort_me)) write(6,*) 12,'items,',swaps,' swaps.' pi => a999 do i=1, size(pi) pi(i) = 1 + L(size(pi)/3 .lt. i) + L(2*size(pi)/3 .lt. i) end do call shuffle(pi, size(pi)/3+1) call partition3way(pi, 2, swaps) write(6,*) size(pi),'items,',swaps,' swaps.' pi => a9999 do i=1, size(pi) pi(i) = 1 + L(size(pi)/3 .lt. i) + L(2*size(pi)/3 .lt. i) end do call shuffle(pi, size(pi)/3+1) call partition3way(pi, 2, swaps) write(6,*) size(pi),'items,',swaps,' swaps.'
contains
integer function L(q)
! In Ken Iverson's spirit, APL logicals are more useful as integers.
logical, intent(in) :: q
if (q) then
L = 1
else
L = 0
end if
end function L
subroutine swap(a,i,j) integer, dimension(:), intent(inout) :: a integer, intent(in) :: i, j integer :: t t = a(i) a(i) = a(j) a(j) = t end subroutine swap
subroutine partition3way(a, pivot, swaps)
integer, dimension(:), intent(inout) :: a
integer, intent(in) :: pivot
integer, intent(out) :: swaps
integer :: i, j, k
swaps = 0
i = 0
j = 1
k = size(a) + 1
do while (j .lt. k)
if (pivot .eq. a(j)) then
j = j+1
swaps = swaps-1
else if (pivot .lt. a(j)) then
k = k-1
call swap(a, k, j)
else
i = i+1
call swap(a, i, j)
j = j+1
end if
swaps = swaps+1
end do
end subroutine partition3way
subroutine shuffle(a, n) ! a rather specialized shuffle not for general use
integer, intent(inout), dimension(:) :: a
integer, intent(in) :: n
integer :: i, j, k
real :: harvest
do i=1, size(a)-1
call random_number(harvest)
harvest = harvest - epsilon(harvest)*L(harvest.eq.1)
k = L(i.eq.1)*(n-1) + i
j = i + int((size(a) - k) * harvest)
call swap(a, i, j)
end do
end subroutine shuffle
end program Netherlands </lang>
FreeBASIC
<lang freebasic> ' El problema planteado por Edsger Dijkstra es: ' "Dado un número de bolas rojas, azules y blancas en orden aleatorio, ' ordénelas en el orden de los colores de la bandera nacional holandesa."
Dim As String c = "RBW", n = "121509" Dim As Integer bolanum = 9 Dim As Integer d(bolanum), k, i, j Randomize Timer
Color 15: Print "Aleatorio: "; For k = 1 To bolanum
d(k) = Int(Rnd * 3) + 1 Color Val(Mid(n, d(k), 2)) Print Mid(c, d(k), 1) & Chr(219);
Next k
Color 15: Print : Print "Ordenado: "; For i = 1 To 3
For j = 1 To bolanum
If d(j) = i Then Color Val(Mid(n, i, 2)): Print Mid(c, i, 1) & Chr(219);
Next j
Next i End </lang>
Gambas
Click this link to run this code <lang gambas>Public Sub Main() Dim Red As String = "0" Dim White As String = "1" Dim Blue As String = "2" Dim siCount As Short Dim sColours As New String[] Dim sTemp As String
For siCount = 1 To 20
sColours.Add(Rand(Red, Blue))
Next
Print "Random: - ";
For siCount = 1 To 2
For Each sTemp In sColours If sTemp = Red Then Print "Red "; If sTemp = White Then Print "White "; If sTemp = Blue Then Print "Blue "; Next sColours.Sort Print If siCount = 1 Then Print "Sorted: - ";
Next
End</lang> Output:
Random: - Blue Red Red White White White White Red Blue White Red Red White Blue White White Blue Red White Blue Sorted: - Red Red Red Red Red Red White White White White White White White White White Blue Blue Blue Blue Blue
Go
<lang go>package main
import (
"fmt" "math/rand" "time"
)
// constants define order of colors in Dutch national flag const (
red = iota white blue nColors
)
// zero object of type is valid red ball. type ball struct {
color int
}
// order of balls based on DNF func (b1 ball) lt(b2 ball) bool {
return b1.color < b2.color
}
// type for arbitrary ordering of balls type ordering []ball
// predicate tells if balls are ordered by DNF func (o ordering) ordered() bool {
var b0 ball
for _, b := range o {
if b.lt(b0) {
return false
}
b0 = b
}
return true
}
func init() {
rand.Seed(time.Now().Unix())
}
// constructor returns new ordering of balls which is randomized but // guaranteed to be not in DNF order. function panics for n < 2. func outOfOrder(n int) ordering {
if n < 2 {
panic(fmt.Sprintf("%d invalid", n))
}
r := make(ordering, n)
for {
for i, _ := range r {
r[i].color = rand.Intn(nColors)
}
if !r.ordered() {
break
}
}
return r
}
// O(n) algorithm // http://www.csse.monash.edu.au/~lloyd/tildeAlgDS/Sort/Flag/ func (a ordering) sort3() {
lo, mid, hi := 0, 0, len(a)-1
for mid <= hi {
switch a[mid].color {
case red:
a[lo], a[mid] = a[mid], a[lo]
lo++
mid++
case white:
mid++
default:
a[mid], a[hi] = a[hi], a[mid]
hi--
}
}
}
func main() {
f := outOfOrder(12) fmt.Println(f) f.sort3() fmt.Println(f)
}</lang>
- Output:
[{1} {0} {0} {2} {1} {1} {1} {2} {2} {0} {1} {2}]
[{0} {0} {0} {1} {1} {1} {1} {1} {2} {2} {2} {2}]
Haskell
With the Color data type we take care that no other values than Red, White and Blue can be used. The "deriving" clause is a key aspect: We want Haskell to make Color automatically an instance of the classes Show, Eq, Ord and Enum. - Show means that Haskell can convert the data constructors Red, White and Blue to text. - Eq means that two values of type Color can be compared for equality, as if they were numbers or characters. - Ord means that one can sort a list of values of type Color according to the order in which the constructors Red, White and Blue were declared. We don't need to check if the order of the colors is right - it just is. - Enum menas that Red, White and Blue are automatically enumerated: every constructor is assigned to an integer.
The function "sort" works with anything that belongs to the Eq and Ord classes. The function "randomRIO" takes a range of two integers to give a random value within the range. We make Color an instance of Enum so that we can give Red, White and Blue as integers to randomRIO and convert the random number back to Red, White or Blue. <lang Haskell>import Data.List (sort) import System.Random (randomRIO) import System.IO.Unsafe (unsafePerformIO)
data Color = Red | White | Blue deriving (Show, Eq, Ord, Enum)
dutch :: [Color] -> [Color] dutch = sort
isDutch :: [Color] -> Bool isDutch x = x == dutch x
randomBalls :: Int -> [Color] randomBalls 0 = [] randomBalls n = toEnum (unsafePerformIO (randomRIO (fromEnum Red,
fromEnum Blue))) : randomBalls (n - 1)
main :: IO () main = do
let a = randomBalls 20
case isDutch a of
True -> putStrLn $ "The random sequence " ++ show a ++
" is already in the order of the Dutch national flag!"
False -> do
putStrLn $ "The starting random sequence is " ++ show a ++ "\n"
putStrLn $ "The ordered sequence is " ++ show (dutch a)</lang>
- Output:
The starting random sequence is [White,Blue,Blue,Blue,Blue,Blue,Blue,Red,Red, White,White,Blue,White,White,Red,White,Blue,White,Red,Red] The ordered sequence is [Red,Red,Red,Red,Red,White,White,White,White,White, White,White,Blue,Blue,Blue,Blue,Blue,Blue,Blue,Blue]
To understand why Dijsktra was interested in the problem, here's an example showing difficiency of using generic sort: <lang haskell>inorder n = and $ zipWith (<=) n (tail n) -- or use Data.List.Ordered
mk012 :: Int -> Int -> [Int] -- definitely unordered mk012 n = (++[0]).(2:).map (`mod` 3).take n.frr where -- frr = Fast Rubbish Randoms frr = tail . iterate (\n -> n * 7 + 13)
dutch1 n = (filter (==0) n)++(filter (==1) n)++(filter (==2) n)
dutch2 n = a++b++c where (a,b,c) = foldl f ([],[],[]) n -- scan list once; it *may* help f (a,b,c) x = case x of 0 -> (0:a, b, c) 1 -> (a, x:b, c) 2 -> (a, b, x:c)
main = do -- 3 methods, comment/uncomment each for speed comparisons -- print $ inorder $ sort s -- O(n log n) -- print $ inorder $ dutch1 s -- O(n) print $ inorder $ dutch2 s -- O(n) where s = mk012 10000000 42</lang>
Icon and Unicon
The following solution works in both languages.
The problem statement isn't clear on whether the randomized list of balls has to contain at least one of each color. The approach below assumes that you can have no balls of a given color (including no balls at all - though that makes ensuring they're not properly sorted at the start hard...). To force at least one of each color ball, change "?n-1" to "?n" in the 3rd line.
<lang unicon>procedure main(a)
n := integer(!a) | 20
every (nr|nw|nb) := ?n-1
sIn := repl("r",nw)||repl("w",nb)||repl("b",nr)
write(sRand := bestShuffle(sIn))
write(sOut := map(csort(map(sRand,"rwb","123")),"123","rwb"))
if sIn ~== sOut then write("Eh? Not in correct order!")
end
procedure bestShuffle(s) # (Taken from the Best Shuffle task)
t := s
every !t :=: ?t # Uncommented to get a random best shuffling
every i := 1 to *t do
every j := (1 to i-1) | (i+1 to *t) do
if (t[i] ~== s[j]) & (s[i] ~== t[j]) then break t[i] :=: t[j]
return t
end
procedure csort(w)
every (s := "") ||:= (find(c := !cset(w),w),c) return s
end</lang>
A few sample runs:
->dutch bwwwwwwwwwrrrrrrbbbrrbrwwwrw rrrrrrrrrrwwwwwwwwwwwwwbbbbb ->dutch bbbbbbrbbbbbbrwwrwwrwwwwrw rrrrrwwwwwwwwwbbbbbbbbbbbb ->dutch bbbbbbbbbwbbwrrrrrrrrrwrrwwrr rrrrrrrrrrrrrwwwwwbbbbbbbbbbb ->dutch wbrbrrwwrbrbwrrrrrrwrrrrrrrrr rrrrrrrrrrrrrrrrrrrrwwwwwbbbb ->
J
We shall define a routine to convert the values 0 1 2 to ball names: <lang J>i2b=: {&(;:'red white blue')</lang> and its inverse <lang J>b2i=: i2b inv</lang> Next, we need a random assortment of balls: <lang J> BALLS=: i2b ?20#3
BALLS
┌────┬───┬────┬───┬───┬─────┬─────┬─────┬────┬────┬─────┬────┬────┬───┬────┬───┬─────┬───┬────┬───┐ │blue│red│blue│red│red│white│white│white│blue│blue│white│blue│blue│red│blue│red│white│red│blue│red│ └────┴───┴────┴───┴───┴─────┴─────┴─────┴────┴────┴─────┴────┴────┴───┴────┴───┴─────┴───┴────┴───┘</lang> And we want to sort them in their canonical order: <lang J> /:~&.b2i BALLS ┌───┬───┬───┬───┬───┬───┬───┬─────┬─────┬─────┬─────┬─────┬────┬────┬────┬────┬────┬────┬────┬────┐ │red│red│red│red│red│red│red│white│white│white│white│white│blue│blue│blue│blue│blue│blue│blue│blue│ └───┴───┴───┴───┴───┴───┴───┴─────┴─────┴─────┴─────┴─────┴────┴────┴────┴────┴────┴────┴────┴────┘</lang> Note that if we were not using J's built in sort, we would probably want to use bin sort here.
Anyways, we can test that they are indeed sorted properly: <lang J> assert@(-: /:~)&b2i /:~&.b2i BALLS</lang>
Java
The elements of an enum implement Comparable so the build-in sort works. You can also use this comparability to check the sort has worked.
<lang java>import java.util.Arrays;
import java.util.Random;
public class DutchNationalFlag {
enum DutchColors {
RED, WHITE, BLUE
}
public static void main(String[] args){
DutchColors[] balls = new DutchColors[12];
DutchColors[] values = DutchColors.values();
Random rand = new Random();
for (int i = 0; i < balls.length; i++)
balls[i]=values[rand.nextInt(values.length)];
System.out.println("Before: " + Arrays.toString(balls));
Arrays.sort(balls);
System.out.println("After: " + Arrays.toString(balls));
boolean sorted = true;
for (int i = 1; i < balls.length; i++ ){
if (balls[i-1].compareTo(balls[i]) > 0){
sorted=false;
break;
}
}
System.out.println("Correctly sorted: " + sorted);
}
}</lang>
- Output:
Before: [WHITE, RED, BLUE, RED, WHITE, WHITE, WHITE, RED, WHITE, RED, WHITE, WHITE] After: [RED, RED, RED, RED, WHITE, WHITE, WHITE, WHITE, WHITE, WHITE, WHITE, BLUE] Correctly sorted: true
JavaScript
ES6
<lang javascript>const dutchNationalFlag = () => {
/**
* Return the name of the given number in this way:
* 0 = Red
* 1 = White
* 2 = Blue
* @param {!number} e
*/
const name = e => e > 1 ? 'Blue' : e > 0 ? 'White' : 'Red';
/**
* Given an array of numbers return true if each number is bigger than
* or the same as the previous
* @param {!Array<!number>} arr
*/
const isSorted = arr => arr.every((e,i) => e >= arr[Math.max(i-1, 0)]);
/**
* Generator that keeps yielding a random int between 0(inclusive) and
* max(exclusive), up till n times, and then is done.
* @param max
* @param n
*/
function* randomGen (max, n) {
let i = 0;
while (i < n) {
i += 1;
yield Math.floor(Math.random() * max);
}
}
/**
* An array of random integers between 0 and 3
* @type {[!number]}
*/
const mixedBalls = [...(randomGen(3, 22))];
/** * Sort the given array into 3 sub-arrays and then concatenate those. */ const sortedBalls = mixedBalls .reduce((p,c) => p[c].push(c) && p, [[],[],[]]) .reduce((p,c) => p.concat(c), []);
/**
* A verbatim implementation of the Wikipedia pseudo-code
* @param {!Array<!number>} A
* @param {!number} mid The value of the 'mid' number. In our case 1 as
* low is 0 and high is 2
*/
const dutchSort = (A, mid) => {
let i = 0;
let j = 0;
let n = A.length - 1;
while(j <= n) {
if (A[j] < mid) {
[A[i], A[j]] = [A[j], A[i]];
i += 1;
j += 1;
} else if (A[j] > mid) {
[A[j], A[n]] = [A[n], A[j]];
n -= 1
} else {
j += 1;
}
}
};
console.log(`Mixed balls : ${mixedBalls.map(name).join()}`);
console.log(`Is sorted: ${isSorted(mixedBalls)}`);
console.log(`Sorted balls : ${sortedBalls.map(name).join()}`);
console.log(`Is sorted: ${isSorted(sortedBalls)}`);
// Only do the dutch sort now as it mutates the mixedBalls array in place.
dutchSort(mixedBalls, 1);
console.log(`Dutch Sorted balls: ${mixedBalls.map(name).join()}`);
console.log(`Is sorted: ${isSorted(mixedBalls)}`);
}; dutchNationalFlag(); </lang>
- Output:
Mixed balls : Red,Red,Blue,Red,White,Red,White,Blue,Blue,White,White,Blue,Red,Blue,Blue,Red,White,Red,Red,Red,White,White Is sorted: false Sorted balls : Red,Red,Red,Red,Red,Red,Red,Red,Red,White,White,White,White,White,White,White,Blue,Blue,Blue,Blue,Blue,Blue Is sorted: true Dutch Sorted balls: Red,Red,Red,Red,Red,Red,Red,Red,Red,White,White,White,White,White,White,White,Blue,Blue,Blue,Blue,Blue,Blue Is sorted: true
Julia
Here the task is solved two ways, with a specialized routine and using the sort built-in. dutchsort is a specialized sort based upon the three-way-partition pseudocode provided in the Wikipedia article referenced in the task description. Timing each shows that dutchsort is about two orders of magnitude faster than sort. (This relative performance result holds for a variety of color array sizes.)
Function <lang Julia> const COLORS = ["red", "white", "blue"]
function dutchsort!(a::Array{ASCIIString,1}, lo=COLORS[1], hi=COLORS[end])
i = 1
j = 1
n = length(a)
while j <= n
if a[j] == lo
a[i], a[j] = a[j], a[i]
i += 1
j += 1
elseif a[j] == hi
a[j], a[n] = a[n], a[j]
n -= 1
else
j += 1
end
end
return a
end
function dutchsort(a::Array{ASCIIString,1}, lo=COLORS[1], hi=COLORS[end])
dutchsort!(copy(a), lo, hi)
end </lang>
Main <lang Julia> function formatdf(a::Array{ASCIIString,1})
i = 0
s = " "
for c in a
s *= @sprintf "%6s" c
i += 1
i %= 8
if i == 0
s *= "\n "
end
end
return s
end
cnum = 20 d = [COLORS[rand(1:3)] for i in 1:cnum] while d == dutchsort(d)
d = [COLORS[rand(1:3)] for i in 1:cnum]
end
println("The original list is:") println(formatdf(d))
print("Sorting with dutchsort, ") @time e = dutchsort(d) println(formatdf(e))
print("Sorting conventionally, ") @time e = sort(d, by=x->findfirst(COLORS, x)) println(formatdf(e)) </lang>
- Output:
The original list is:
red blue red blue white blue white white
blue white white blue white white blue white
white blue blue blue
Sorting with dutchsort, elapsed time: 0.000520454 seconds (14104 bytes allocated)
red red white white white white white white
white white white blue blue blue blue blue
blue blue blue blue
Sorting conventionally, elapsed time: 0.062974782 seconds (1688896 bytes allocated)
red red white white white white white white
white white white blue blue blue blue blue
blue blue blue blue
Kotlin
<lang scala>// version 1.1.4
import java.util.Random
enum class DutchColors { RED, WHITE, BLUE }
fun Array<DutchColors>.swap(i: Int, j: Int) {
val temp = this[i] this[i] = this[j] this[j] = temp
}
fun Array<DutchColors>.sort() {
var lo = 0 var mid = 0 var hi = this.lastIndex
while (mid <= hi) {
when (this[mid]) {
DutchColors.RED -> this.swap(lo++, mid++)
DutchColors.WHITE -> mid++
DutchColors.BLUE -> this.swap(mid, hi--)
}
}
}
fun Array<DutchColors>.isSorted(): Boolean {
return (1 until this.size)
.none { this[it].ordinal < this[it - 1].ordinal }
}
const val NUM_BALLS = 9
fun main(args: Array<String>) {
val r = Random()
val balls = Array(NUM_BALLS) { DutchColors.RED }
val colors = DutchColors.values()
// give balls random colors whilst ensuring they're not already sorted
do {
for (i in 0 until NUM_BALLS) balls[i] = colors[r.nextInt(3)]
}
while (balls.isSorted())
// print the colors of the balls before sorting
println("Before sorting : ${balls.contentToString()}")
// sort the balls in DutchColors order balls.sort()
// print the colors of the balls after sorting
println("After sorting : ${balls.contentToString()}")
}</lang>
Sample output:
Before sorting : [WHITE, RED, RED, WHITE, BLUE, WHITE, BLUE, RED, RED] After sorting : [RED, RED, RED, RED, WHITE, WHITE, WHITE, BLUE, BLUE]
Lasso
<lang Lasso>define orderdutchflag(a) => { local(r = array, w = array, b = array) with i in #a do => { match(#i) => { case('Red') #r->insert(#i) case('White') #w->insert(#i) case('Blue') #b->insert(#i) } } return #r + #w + #b }
orderdutchflag(array('Red', 'Red', 'Blue', 'Blue', 'Blue', 'Red', 'Red', 'Red', 'White', 'Blue'))</lang>
- Output:
array(Red, Red, Red, Red, Red, White, Blue, Blue, Blue, Blue)
Logo
<lang logo>; We'll just use words for the balls make "colors {red white blue}
- to get a mapping from colors back to a numeric value,
- we make variables out of the color names (e.g. the variable
- "red" has value "1").
foreach arraytolist :colors [
make ? #
]
- Make a random list of a given size
to random_balls :n
local "balls make "balls array n repeat n [ setitem # :balls pick :colors ] output :balls
end
- Test for Dutchness
to dutch? :array
output dutchlist? arraytolist :array
end
- List is easier than array to test
to dutchlist? :list
output cond [ [(less? count :list 2) "true] [(greater? thing first :list thing item 2 :list) "false ] [else dutchlist? butfirst :list] ]
end
- But array is better for sorting algorithm
to dutch :array
local "lo
make "lo 0
local "hi
make "hi sum 1 count :array
local "i
make "i 1
while [:i < :hi] [
case (item :i :array) [
[[red]
make "lo sum :lo 1
swap :array :lo :i
make "i sum :i 1
]
[[white]
make "i sum :i 1
]
[[blue]
make "hi difference :hi 1
swap :array :hi :i
]
]
]
output :array
end
- utility routine to swap array elements
to swap :array :a :b
local "temp make "temp item :a :array setitem :a :array item :b :array setitem :b :array :temp
end</lang>
Test code: <lang>do.while [
make "list random_balls 10
] [dutch? :list]
print (sentence [Start list:] arraytolist :list) print (sentence [Sorted:] arraytolist dutch :list) bye</lang>
- Output:
Start list: white blue red red red white blue red red white Sorted: red red red red red white white white blue blue
Mathematica / Wolfram Language
<lang Mathematica>flagSort[data_List] := Sort[data, (#1 === RED || #2 === BLUE) &]</lang>
- Output:
flagSort[{WHITE, RED, RED, WHITE, WHITE, BLUE, WHITE, BLUE, BLUE, WHITE, WHITE, BLUE}]
{RED, RED, WHITE, WHITE, WHITE, WHITE, WHITE, WHITE, BLUE, BLUE, BLUE, BLUE}
PARI/GP
A counting sort might be more appropriate here, but that would conceal the details of the sort. <lang parigp>compare(a,b)={
if (a==b, 0 , if(a=="red" || b=="blue", -1, 1) )
}; r(n)=vector(n,i,if(random(3),if(random(2),"red","white"),"blue")); inorder(v)=for(i=2,#v,if(compare(v[i-1],v[i])>0,return(0)));1;
v=r(10); while(inorder(v), v=r(10)); v=vecsort(v,compare); inorder(v)</lang>
- Output:
1
Perl
The task is probably not to just sort an array. The wikipedia links has a slightly better explanation that leads to the following code: <lang perl>use warnings; use strict; use 5.010; # //
use List::Util qw( shuffle );
my @colours = qw( blue white red );
sub are_ordered {
my $balls = shift;
my $last = 0;
for my $ball (@$balls) {
return if $ball < $last;
$last = $ball;
}
return 1;
}
sub show {
my $balls = shift;
print join(' ', map $colours[$_], @$balls), "\n";
}
sub debug {
return unless $ENV{DEBUG};
my ($pos, $top, $bottom, $balls) = @_;
for my $i (0 .. $#$balls) {
my ($prefix, $suffix) = (q()) x 2;
($prefix, $suffix) = qw/( )/ if $i == $pos;
$prefix .= '>' if $i == $top;
$suffix .= '<' if $i == $bottom;
print STDERR " $prefix$colours[$balls->[$i]]$suffix"; } print STDERR "\n";
}
my $count = shift // 10;
die "$count: Not enough balls\n" if $count < 3;
my $balls = [qw( 2 1 0 )]; push @$balls, int rand 3 until @$balls == $count; do { @$balls = shuffle @$balls } while are_ordered($balls);
show($balls);
my $top = 0; my $bottom = $#$balls;
my $i = 0; while ($i <= $bottom) {
debug($i, $top, $bottom, $balls);
my $col = $colours[ $balls->[$i] ];
if ('red' eq $col and $i < $bottom) {
@{$balls}[$bottom, $i] = @{$balls}[$i, $bottom];
$bottom--;
} elsif ('blue' eq $col and $i > $top) {
@{$balls}[$top, $i] = @{$balls}[$i, $top];
$top++;
} else {
$i++;
}
} debug($i, $top, $bottom, $balls);
show($balls); are_ordered($balls) or die "Incorrect\n";</lang> You can run it with no parameters, it sorts 10 balls in such a case. If you provide one parameter, it is used as the number of balls. The second parameter turns on debugging that shows how the balls are being swapped.
Perl 6
Here are five ways to do it, all one liners (apart from the test apparatus). <lang perl6>enum NL <red white blue>; my @colors;
sub how'bout (&this-way) {
sub show {
say @colors;
say "Ordered: ", [<=] @colors;
}
@colors = NL.roll(20); show; this-way; show; say ;
}
say "Using functional sort"; how'bout { @colors = sort *.value, @colors }
say "Using in-place sort"; how'bout { @colors .= sort: *.value }
say "Using a Bag"; how'bout { @colors = flat red, white, blue Zxx bag(@colors».key)<red white blue> }
say "Using the classify method"; how'bout { @colors = flat (.list for %(@colors.classify: *.value){0,1,2}) }
say "Using multiple greps"; how'bout { @colors = flat (.grep(red), .grep(white), .grep(blue) given @colors) }</lang>
- Output:
Using functional sort red red white white red red red red red red red white red white red red red white white white Ordered: False red red red red red red red red red red red red red white white white white white white white Ordered: True Using in-place sort red blue white red white blue white blue red white blue blue blue red white white red blue red blue Ordered: False red red red red red red white white white white white white blue blue blue blue blue blue blue blue Ordered: True Using a Bag red blue blue blue white red white red white blue blue red red red red blue blue red white blue Ordered: False red red red red red red red red white white white white blue blue blue blue blue blue blue blue Ordered: True Using the classify method blue red white blue blue white white red blue red red white red blue white white red blue red white Ordered: False red red red red red red red white white white white white white white blue blue blue blue blue blue Ordered: True Using multiple greps red white blue white white red blue white red white red white white white white white red red blue red Ordered: False red red red red red red red white white white white white white white white white white blue blue blue Ordered: True
Phix
Minimizes the number of read and swap operations, straight translation of the wikipedia pseudocode: <lang Phix>function three_way_partition(sequence s, integer mid) integer i=1, j=1, n = length(s)
while j < n do
if s[j] < mid then
{s[i],s[j]} = {s[j],s[i]}
i += 1
j += 1
elsif s[j] > mid then
{s[j],s[n]} = {s[n],s[j]}
n -= 1
else
j += 1
end if
end while
return s
end function
constant colours = {"red","white","blue"} enum /*red,*/ white = 2, blue, maxc = blue
procedure show(string msg, sequence s)
for i=1 to length(s) do
s[i] = colours[s[i]]
end for
printf(1,"%s: %s\n",{msg,join(s)})
end procedure
sequence unsorted, sorted
while 1 do
unsorted = sq_rand(repeat(maxc,12))
-- sorted = sort(unsorted) -- (works just as well)
sorted = three_way_partition(unsorted, white)
if unsorted!=sorted then exit end if
?"oops"
end while
show("Unsorted",unsorted)
show("Sorted",sorted)</lang>
I thought of unsorted=shuffle(unsorted) in the "oops" loop, but of course that'd repeat forever should they all be the same colour.
- Output:
Unsorted: blue blue blue blue red white white red white red white blue Sorted: red red red white white white white blue blue blue blue blue
PicoLisp
<lang PicoLisp>(def 'Colors
(list
(def 'RED 1)
(def 'WHITE 2)
(def 'BLUE 3) ) )
(let (L (make (do 9 (link (get Colors (rand 1 3))))) S (by val sort L))
(prin "Original balls ") (print L) (prinl (unless (= L S) " not sorted")) (prin "Sorted balls ") (print S) (prinl " are sorted") )</lang>
- Output:
Original balls (RED BLUE WHITE BLUE BLUE RED WHITE WHITE WHITE) not sorted Sorted balls (RED RED WHITE WHITE WHITE WHITE BLUE BLUE BLUE) are sorted
PowerShell
<lang PowerShell> $Colors = 'red', 'white','blue'
- Select 10 random colors
$RandomBalls = 1..10 | ForEach { $Colors | Get-Random }
- Ensure we aren't finished before we start. For some reason. It's in the task requirements.
While ( $RandomBalls -eq $RandomBalls | Sort { $Colors.IndexOf( $_ ) } )
{ $RandomBalls = 1..10 | ForEach { $Colors | Get-Random } }
- Sort the colors
$SortedBalls = $RandomBalls | Sort { $Colors.IndexOf( $_ ) }
- Display the results
$RandomBalls $SortedBalls </lang>
- Output:
white blue blue blue white red white blue red red red red red white white white blue blue blue blue
Prolog
Works with SWI-Prolog 6.1.11
Prolog spirit
<lang Prolog>dutch_flag(N) :- length(L, N), repeat, maplist(init,L), \+is_dutch_flag(L) , writeln(L), test_sorted(L), sort_dutch_flag(L, TmpFlag), append(TmpFlag, Flag), writeln(Flag), test_sorted(Flag).
sort_dutch_flag([], [[], [], []]).
sort_dutch_flag([blue | T], [R, W, [blue|B]]) :- sort_dutch_flag(T, [R, W, B]).
sort_dutch_flag([red | T], [[red|R], W, B]) :- sort_dutch_flag(T, [R, W, B]).
sort_dutch_flag([white | T], [R, [white | W], B]) :-
sort_dutch_flag(T, [R, W, B]).
init(C) :-
R is random(3),
nth0(R, [blue, red, white], C).
test_sorted(Flag) :-
( is_dutch_flag(Flag)
-> write('it is a dutch flag')
; write('it is not a dutch flag')),
nl,nl.
% First color must be red is_dutch_flag([red | T]) :- is_dutch_flag_red(T).
is_dutch_flag_red([red|T]) :-
is_dutch_flag_red(T);
% second color must be white
T = [white | T1],
is_dutch_flag_white(T1).
is_dutch_flag_white([white | T]) :-
is_dutch_flag_white(T);
% last one must be blue
T = [blue | T1],
is_dutch_flag_blue(T1).
is_dutch_flag_blue([blue | T]) :- is_dutch_flag_blue(T).
is_dutch_flag_blue([]). </lang>
- Output:
?- dutch_flag(20). [blue,white,white,blue,blue,blue,red,blue,red,blue,blue,blue,white,red,red,blue,blue,red,blue,red] it is not a dutch flag [red,red,red,red,red,red,white,white,white,blue,blue,blue,blue,blue,blue,blue,blue,blue,blue,blue] it is a dutch flag true .
Functional spirit
Use of filters. <lang Prolog>dutch_flag(N) :- length(L, N),
% create the list to sort repeat, maplist(init,L), \+is_dutch_flag(L) , writeln(L), test_sorted(L),
foldl(\X^Y^Z^(Y = [Red, White, Blue], ( X = blue -> append_dl(Blue, [X|U]-U, Blue1), Z = [Red, White, Blue1] ; X = red -> append_dl(Red, [X|U]-U, Red1), Z = [Red1, White, Blue] ; append_dl(White, [X|U]-U, White1), Z = [Red, White1, Blue])), L, [R-R, W-W, B-B], [R1, W1, B1]), append_dl(R1, W1, B1, Flag-[]), write(Flag), nl, test_sorted(Flag).
% append lists in O(1) append_dl(A-B, B-C, A-C). append_dl(A-B, B-C, C-D, A-D).
init(C) :-
R is random(3),
nth0(R, [blue, red, white], C).
test_sorted(Flag) :-
( is_dutch_flag(Flag)
-> write('it is a dutch flag')
; write('it is not a dutch flag')),
nl,nl.
% First color must be red is_dutch_flag([red | T]) :- is_dutch_flag_red(T).
is_dutch_flag_red([red|T]) :-
is_dutch_flag_red(T);
% second color must be white
T = [white | T1],
is_dutch_flag_white(T1).
is_dutch_flag_white([white | T]) :-
is_dutch_flag_white(T);
% last one must be blue
T = [blue | T1],
is_dutch_flag_blue(T1).
is_dutch_flag_blue([blue | T]) :- is_dutch_flag_blue(T).
is_dutch_flag_blue([]). </lang>
Python
Python: Sorted
The heart of the idiomatic Dutch sort in python is the call to function sorted in function dutch_flag_sort.
<lang python>import random
colours_in_order = 'Red White Blue'.split()
def dutch_flag_sort(items, order=colours_in_order):
'return sort of items using the given order' reverse_index = dict((x,i) for i,x in enumerate(order)) return sorted(items, key=lambda x: reverse_index[x])
def dutch_flag_check(items, order=colours_in_order):
'Return True if each item of items is in the given order' reverse_index = dict((x,i) for i,x in enumerate(order)) order_of_items = [reverse_index[item] for item in items] return all(x <= y for x, y in zip(order_of_items, order_of_items[1:]))
def random_balls(mx=5):
'Select from 1 to mx balls of each colour, randomly'
balls = sum([[colour] * random.randint(1, mx)
for colour in colours_in_order], [])
random.shuffle(balls)
return balls
def main():
# Ensure we start unsorted
while True:
balls = random_balls()
if not dutch_flag_check(balls):
break
print("Original Ball order:", balls)
sorted_balls = dutch_flag_sort(balls)
print("Sorted Ball Order:", sorted_balls)
assert dutch_flag_check(sorted_balls), 'Whoops. Not sorted!'
if __name__ == '__main__':
main()</lang>
- Sample output:
Original Ball order: ['Red', 'Red', 'Blue', 'Blue', 'Blue', 'Red', 'Red', 'Red', 'White', 'Blue'] Sorted Ball Order: ['Red', 'Red', 'Red', 'Red', 'Red', 'White', 'Blue', 'Blue', 'Blue', 'Blue']
Python: sum of filters
This follows the critics section of the wikipedia article by using a sum of filters.
Replace the function/function call dutch_flag_sort above, with dutch_flag_sort2 defined as: <lang python>from itertools import chain def dutch_flag_sort2(items, order=colours_in_order):
'return summed filter of items using the given order'
return list(chain.from_iterable(filter(lambda c: c==colour, items)
for colour in order))</lang>
Or equivalently using a list comprehension (though perhaps less clear): <lang python>def dutch_flag_sort2(items, order=colours_in_order):
'return summed filter of items using the given order' return [c for colour in order for c in items if c==colour]</lang>
Output follows that of the sorting solution above.
Python: Construct from ball counts
This reconstructs the correct output by counting how many of each colour there are.
Replace the function/function call dutch_flag_sort above, with dutch_flag_sort3 defined as: <lang python>def dutch_flag_sort3(items, order=colours_in_order):
'counts each colour to construct flag' return sum([[colour] * items.count(colour) for colour in order], [])</lang>
Output follows that of the sorting solution above.
Python: Explicit in-place sort
<lang python>import random
colours_in_order = 'Red White Blue'.split()
def dutch_flag_sort(items):
\ In-place sort of list items using the given order. Python idiom is to return None when argument is modified in-place
O(n)? Algorithm from Go language implementation of http://www.csse.monash.edu.au/~lloyd/tildeAlgDS/Sort/Flag/
lo, mid, hi = 0, 0, len(items)-1
while mid <= hi:
colour = items[mid]
if colour == 'Red':
items[lo], items[mid] = items[mid], items[lo]
lo += 1
mid += 1
elif colour == 'White':
mid += 1
else:
items[mid], items[hi] = items[hi], items[mid]
hi -= 1
def dutch_flag_check(items, order=colours_in_order):
'Return True if each item of items is in the given order' order_of_items = [order.index(item) for item in items] return all(x <= y for x, y in zip(order_of_items, order_of_items[1:]))
def random_balls(mx=5):
'Select from 1 to mx balls of each colour, randomly'
balls = sum(([[colour] * random.randint(1, mx)
for colour in colours_in_order]), [])
random.shuffle(balls)
return balls
def main():
# Ensure we start unsorted
while 1:
balls = random_balls()
if not dutch_flag_check(balls):
break
print("Original Ball order:", balls)
dutch_flag_sort(balls)
print("Sorted Ball Order:", balls)
assert dutch_flag_check(balls), 'Whoops. Not sorted!'
if __name__ == '__main__':
main()</lang>
Output follows that of the sorting solution above.
Racket
<lang Racket>
- lang racket
(define dutch-colors '(red white blue))
(define (dutch-order? balls)
;; drop each color from the front, should end up empty
(null? (for/fold ([r balls]) ([color dutch-colors])
(dropf r (curry eq? color)))))
(define (random-balls)
(define balls
(for/list ([i (random 20)])
(list-ref dutch-colors (random (length dutch-colors)))))
(if (dutch-order? balls) (random-balls) balls))
- first method
- use a key to map colors to integers
(define (order->key order)
(let ([alist (for/list ([x order] [i (in-naturals)]) (cons x i))]) (λ(b) (cdr (assq b alist)))))
(define (sort-balls/key balls)
(sort balls < #:key (order->key dutch-colors)))
- second method
- use a comparator built from the ordered list
(define ((order<? ord) x y)
(memq y (cdr (memq x ord))))
(define (sort-balls/compare balls)
(sort balls (order<? dutch-colors)))
(define (test sort)
(define balls (random-balls))
(define sorted (sort balls))
(printf "Testing ~a:\n Random: ~s\n Sorted: ~s\n ==> ~s\n"
(object-name sort)
balls sorted (if (dutch-order? sorted) 'OK 'BAD)))
(for-each test (list sort-balls/key sort-balls/compare)) </lang>
- Output:
Testing sort-balls/order:
Random: (red blue blue white red blue red red blue blue red red white blue)
Sorted: (red red red red red red white white blue blue blue blue blue blue)
==> OK
Testing sort-balls/compare:
Random: (red blue white blue white white white blue red blue blue blue white)
Sorted: (red red white white white white white blue blue blue blue blue blue)
==> OK
REXX
colors (as words)
This version uses a version of a bin sort with counts, and has been generalized to allow any number of colors.
The REXX solution could've been simplified somewhat by the use of the countstr BIF (but some older REXX interpreters don't have).
<lang rexx>/*REXX program reorders a set of random colored balls into a correct order, which is the*/ /*────────────────────────────────── order of colors on the Dutch flag: red white blue.*/ parse arg N colors /*obtain optional arguments from the CL*/ if N= | N="," then N=15 /*Not specified? Then use the default.*/ if colors= then colors= 'red white blue' /* " " " " " " */
- =words(colors) /*count the number of colors specified.*/
@=word(colors, #) word(colors, 1) /*ensure balls aren't already in order.*/
do g=3 to N /*generate a random # of colored balls.*/ @=@ word( colors, random(1, #) ) /*append a random color to the @ list.*/ end /*g*/
say 'number of colored balls generated = ' N ; say say center(' original ball order ', length(@), "─") say @ ; say $=; do j=1 for #;
_=word(colors, j); $=$ copies(_' ', countWords(_, @))
end /*j*/
say say center(' sorted ball order ', length(@), "─") say space($) say
do k=2 to N /*verify the balls are in correct order*/ if wordpos(word($,k), colors) >= wordpos(word($,k-1), colors) then iterate say "The list of sorted balls isn't in proper order!"; exit 13 end /*k*/
say say 'The sorted colored ball list has been confirmed as being sorted correctly.' exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ countWords: procedure; parse arg ?,hay; s=1
do r=0 until _==0; _=wordpos(?, hay, s); s=_+1; end /*r*/; return r</lang>
output when using the default input:
number of colored balls generated = 15 ────────────────────────── original ball order ─────────────────────────── blue red white blue white white red blue blue blue red blue red blue white ─────────────────────────── sorted ball order ─────────────────────────── red red red red white white white white blue blue blue blue blue blue blue The sorted colored ball list has been confirmed as being sorted correctly.
colors (as letters)
<lang rexx>/*REXX program reorders a set of random colored balls into a correct order, which is the*/ /*────────────────────────────────── order of colors on the Dutch flag: red white blue.*/ parse arg N colors /*obtain optional arguments from the CL*/ if N= | N="," then N=15 /*Not specified? Then use the default.*/ if colors= then colors= "RWB" /*use default: R=red, W=white, B=blue */
- =length(colors) /*count the number of colors specified.*/
@=right(colors, 1)left(colors, 1) /*ensure balls aren't already in order.*/
do g=3 to N /*generate a random # of colored balls.*/ @=@ ||substr( colors, random(1, #), 1) /*append a color (1char) to the @ list.*/ end /*g*/
say 'number of colored balls generated = ' N ; say say center(' original ball order ', max(30,2*#), "─") say @ ; say $=; do j=1 for #; _=substr(colors, j, 1)
#=length(@) - length( space( translate(@, , _), 0) )
$=$ || copies(_, #)
end /*j*/
say center(' sorted ball order ', max(30, 2*#), "─") say $ say
do k=2 to N /*verify the balls are in correct order*/ if pos(substr($,k,1), colors) >= pos(substr($,k-1,1), colors) then iterate say "The list of sorted balls isn't in proper order!"; exit 13 end /*k*/
say say 'The sorted colored ball list has been confirmed as being sorted correctly.' exit /*stick a fork in it, we're all done. */</lang> output when using the default input:
number of colored balls generated = 15 ──── original ball order ───── BRRRRBWWRBWRRBR ───── sorted ball order ───── RRRRRRRRWWWBBBB The sorted colored ball list has been confirmed as being sorted correctly.
Ring
<lang ring>
- Project : Dutch national flag problem
flag = ["Red","White","Blue"] balls = list(10)
see "Random: |" for i = 1 to 10
color = random(2) + 1
balls[i] = flag[color]
see balls[i] + " |"
next see nl
see "Sorted: |" for i = 1 to 3
color = flag[i]
for j = 1 to 10
if balls[j] = color
see balls[j] + " |"
ok
next
next </lang> Output:
Random: |Red |Blue |Red |White |Red |Blue |White |Blue |Red |White | Sorted: |Red |Red |Red |Red |White |White |White |Blue |Blue |Blue |
Ruby
<lang ruby>class Ball
FLAG = {red: 1, white: 2, blue: 3}
def initialize
@color = FLAG.keys.sample
end
def color @color end
def <=>(other) # needed for sort, results in -1 for <, 0 for == and 1 for >. FLAG[self.color] <=> FLAG[other.color] end
def inspect @color end
end
balls = [] balls = Array.new(8){Ball.new} while balls == balls.sort
puts "Random: #{balls}" puts "Sorted: #{balls.sort}"
</lang>
- Output:
Random: [blue, red, red, red, blue, blue, white, red] Sorted: [red, red, red, red, white, blue, blue, blue]
Run BASIC
<lang runbasic>flag$ = "Red,White,Blue"
print "Random: |"; for i = 1 to 10 color = rnd(0) * 3 + 1 balls$(i) = word$(flag$,color,",") print balls$(i);" |"; next i
print :print "Sorted: |"; for i = 1 to 3
color$ = word$(flag$,i,",") for j = 1 to 10 if balls$(j) = color$ then print balls$(j);" |"; end if
next j next i</lang>
Random: |White |Blue |White |Red |Red |White |Red |Blue |Red |White | Sorted: |Red |Red |Red |Red |White |White |White |White |Blue |Blue |
Rust
<lang rust>extern crate rand;
use rand::Rng;
// Color enums will be sorted by their top-to-bottom declaration order
- [derive(Eq,Ord,PartialOrd,PartialEq,Debug)]
enum Color {
Red, White, Blue
}
fn is_sorted(list: &Vec<Color>) -> bool {
let mut state = &Color::Red;
for current in list.iter() {
if current < state { return false; }
if current > state { state = current; }
}
true
}
fn main() {
let mut rng = rand::thread_rng(); let mut colors: Vec<Color> = Vec::new();
for _ in 1..10 {
let r = rng.gen_range(0, 3);
if r == 0 { colors.push(Color::Red); }
else if r == 1 { colors.push(Color::White); }
else if r == 2 { colors.push(Color::Blue); }
}
while is_sorted(&colors) {
rng.shuffle(&mut colors);
}
println!("Before: {:?}", colors);
colors.sort();
println!("After: {:?}", colors);
if !is_sorted(&colors) {
println!("Oops, did not sort colors correctly!");
}
}</lang>
Scala
<lang scala>object FlagColor extends Enumeration {
type FlagColor = Value val Red, White, Blue = Value
}
val genBalls = (1 to 10).map(i => FlagColor(scala.util.Random.nextInt(FlagColor.maxId))) val sortedBalls = genBalls.sorted val sorted = if (genBalls == sortedBalls) "sorted" else "not sorted"
println(s"Generated balls (${genBalls mkString " "}) are $sorted.") println(s"Sorted balls (${sortedBalls mkString " "}) are sorted.")</lang>
- Output:
Generated balls (Blue Blue Blue White Blue Blue Red Red Blue White) are not sorted. Sorted balls (Red Red White White Blue Blue Blue Blue Blue Blue) are sorted.
SQL
<lang SQL>-- Create and populate tables create table colours (id integer primary key, name varchar(5)); insert into colours (id, name) values ( 1, 'red' ); insert into colours (id, name) values ( 2, 'white'); insert into colours (id, name) values ( 3, 'blue' );
create table balls ( colour integer references colours ); insert into balls ( colour ) values ( 2 ); insert into balls ( colour ) values ( 2 ); insert into balls ( colour ) values ( 3 ); insert into balls ( colour ) values ( 2 ); insert into balls ( colour ) values ( 1 ); insert into balls ( colour ) values ( 3 ); insert into balls ( colour ) values ( 3 ); insert into balls ( colour ) values ( 2 );
-- Show the balls are unsorted select colours.name from balls join colours on balls.colour = colours.id;
-- Show the balls in dutch flag order select colours.name from balls join colours on balls.colour = colours.id order by colours.id;
-- Tidy up drop table balls; drop table colours;</lang>
- Output:
COLOUR ------ white white blue white red blue blue white COLOUR ------ red white white white white blue blue blue
- Generating a randomized order of balls ensuring that they are not in the order of the Dutch national flag. Hmm - just loaded some data - could do better here...
- Sort the balls in a way idiomatic to your language. Yup!
- Check the sorted balls are in the order of the Dutch national flag. Not checked beyond eyeballing - is there a db implementation that gets order by wrong??
Tcl
This isn't very efficient in terms of the sorting itself (and it happens to use lsearch twice in the comparator!) but it is very simple to write like this.
<lang tcl># The comparison function
proc dutchflagcompare {a b} {
set colors {red white blue}
return [expr {[lsearch $colors $a] - [lsearch $colors $b]}]
}
- The test function (evil shimmer of list to string!)
proc isFlagSorted lst {
expr {![regexp {blue.*(white|red)} $lst] && ![regexp {white.*red} $lst]}
}
- A ball generator
proc generateBalls n {
for {set i 0} {$i<$n} {incr i} {
lappend result [lindex {red white blue} [expr {int(rand()*3)}]]
} return $result
}
- Do the challenge with 20 balls
set balls [generateBalls 20] if {[isFlagSorted $balls]} {
error "already a sorted flag"
} set sorted [lsort -command dutchflagcompare $balls] if {[isFlagSorted $sorted]} {
puts "Sorted the flag\n$sorted"
} else {
puts "sort failed\n$sorted"
}</lang>
- Output:
Sorted the flag red red red red red red red white white white white white white white white white blue blue blue blue
UNIX Shell
<lang bash>COLORS=(red white blue)
- to go from name to number, we make variables out of the color names
- (e.g. the variable "$red" has value "1").
for (( i=0; i<${#COLORS[@]}; ++i )); do
eval ${COLORS[i]}=$i
done
- Make a random list
function random_balls {
local -i n="$1"
local -i i
local balls=()
for (( i=0; i < n; ++i )); do
balls+=("${COLORS[RANDOM%${#COLORS[@]}]}")
done
echo "${balls[@]}"
}
- Test for Dutchness
function dutch? {
if (( $# < 2 )); then
return 0
else
local first="$1"
shift
if eval "(( $first > $1 ))"; then
return 1
else
dutch? "$@"
fi
fi
}
- Sort into order
function dutch {
local -i lo=-1 hi=$# i=0
local a=("$@")
while (( i < hi )); do
case "${a[i]}" in
red)
let lo+=1
local t="${a[lo]}"
a[lo]="${a[i]}"
a[i]="$t"
let i+=1
;;
white) let i+=1;;
blue)
let hi-=1
local t="${a[hi]}"
a[hi]="${a[i]}"
a[i]="$t"
;;
esac
done
echo "${a[@]}"
}</lang>
Test code: <lang bash>declare -i len=${1:-10} balls=() while (( ${#balls[@]} < len )) || dutch? "${balls[@]}"; do
balls=($(random_balls "$len"))
done echo "Initial list: ${balls[@]}" balls=($(dutch "${balls[@]}")) echo "Sorted: ${balls[@]}"</lang>
- Output:
Initial list: blue blue red blue red blue blue white blue red Sorted: red red red white blue blue blue blue blue blue
VBScript
<lang vb> 'Solution derived from http://www.geeksforgeeks.org/sort-an-array-of-0s-1s-and-2s/.
'build an unsorted array with n elements Function build_unsort(n) flag = Array("red","white","blue") Set random = CreateObject("System.Random") Dim arr() ReDim arr(n) For i = 0 To n arr(i) = flag(random.Next_2(0,3)) Next build_unsort = arr End Function
'sort routine Function sort(arr) lo = 0 mi = 0 hi = UBound(arr) Do While mi <= hi Select Case arr(mi) Case "red" tmp = arr(lo) arr(lo) = arr(mi) arr(mi) = tmp lo = lo + 1 mi = mi + 1 Case "white" mi = mi + 1 Case "blue" tmp = arr(mi) arr(mi) = arr(hi) arr(hi) = tmp hi = hi - 1 End Select Loop sort = Join(arr,",") End Function
unsort = build_unsort(11) WScript.StdOut.Write "Unsorted: " & Join(unsort,",") WScript.StdOut.WriteLine WScript.StdOut.Write "Sorted: " & sort(unsort) WScript.StdOut.WriteLine </lang>
- Output:
Unsorted: blue,white,white,blue,red,red,blue,red,red,red,white,white Sorted: red,red,red,red,red,white,white,white,white,blue,blue,blue
Visual FoxPro
SQL Version
<lang vfp> CLOSE DATABASES ALL LOCAL lcCollate As String, i As Integer, n As Integer lcCollate = SET("Collate") SET COLLATE TO "Machine"
- !* Colours table
CREATE CURSOR colours (id I UNIQUE, colour V(5)) INSERT INTO colours VALUES (1, "Red") INSERT INTO colours VALUES (2, "White") INSERT INTO colours VALUES (3, "Blue")
- !* Balls table
CREATE CURSOR balls (colour I, rowid I AUTOINC) INDEX ON colour TAG colour SET ORDER TO 0
- !* Make sure there is at least 1 of each colour
INSERT INTO balls (colour) VALUES(3) INSERT INTO balls (colour) VALUES(1) INSERT INTO balls (colour) VALUES(2) RAND(-1) && Initialise random number generator n = 24 FOR i = 4 TO n INSERT INTO balls (colour) VALUES (RanInt()) ENDFOR
- !* Show unsorted
SELECT bb.rowid, cc.colour FROM colours cc JOIN balls bb ON cc.id = bb.colour
- !* Select by correct order
SELECT bb.rowid, cc.colour FROM colours cc JOIN balls bb ON cc.id = bb.colour ; ORDER BY cc.id INTO CURSOR dutchflag
- !* Show sorted records
BROWSE NOMODIFY IN SCREEN SET COLLATE TO lcCollate
FUNCTION RanInt() As Integer RETURN INT(3*RAND()) + 1 ENDFUNC </lang>
Array Version
<lang vfp> LOCAL i As Integer, n As Integer, colours As String, k As Integer colours = "Red,White,Blue" n = 15 LOCAL ARRAY balls[n,2]
- !* Make sure there is at least 1 of each colour
balls[1,1] = "Blue" balls[1,2] = 3 balls[2,1] = "Red" balls[2,2] = 1 balls[3,1] = "White" balls[3,2] = 2 RAND(-1) && Initialise random number generator FOR i = 4 TO n k = RanInt() balls[i,1] = GETWORDNUM(colours, k, ",") balls[i,2] = k ENDFOR
- !* Show the unsorted array
CLEAR ? "Unsorted..." FOR i = 1 TO n ? balls[i,1], balls[i,2] ENDFOR
- !* Sort the array on column 2
ASORT(balls, 2)
- !* And show it...
? ? "Sorted..." FOR i = 1 TO n ? balls[i,1], balls[i,2] ENDFOR
FUNCTION RanInt() As Integer RETURN INT(3*RAND()) + 1 ENDFUNC </lang>
zkl
<lang zkl>const RED=0, WHITE=1, BLUE=2; var BALLS=T(RED,WHITE,BLUE); fcn colorBalls(balls){ balls.apply(T("red","white","blue").get).concat(", "); }
reg balls, sortedBalls; do{
balls=(0).pump(12,List,fcn{ BALLS[(0).random(3)] }); // create list of 12 random balls
sortedBalls=balls.sort(); // balls is read only, sort creates new list
}while(balls==sortedBalls); // make sure sort does something println("Original ball order:\n", colorBalls(balls)); println("\nSorted ball order:\n", colorBalls(sortedBalls));</lang>
- Output:
Original ball order: white, white, red, blue, red, red, red, red, blue, red, white, blue Sorted ball order: red, red, red, red, red, red, white, white, white, blue, blue, blue
ZX Spectrum Basic
<lang zxbasic>10 LET r$="Red": LET w$="White": LET b$="Blue" 20 LET c$="RWB" 30 DIM b(10) 40 PRINT "Random:" 50 FOR n=1 TO 10 60 LET b(n)=INT (RND*3)+1 70 PRINT VAL$ (c$(b(n))+"$");" "; 80 NEXT n 90 PRINT "Sorted:" 100 FOR i=1 TO 3 110 FOR j=1 TO 10 120 IF b(j)=i THEN PRINT VAL$ (c$(i)+"$");" "; 130 NEXT j 140 NEXT i</lang>
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