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Ingy döt Net 2023-07-01 11:58:00 -04:00
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2
Task/Bell-numbers/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Bell_numbers

31
Task/Bell-numbers/00-TASK.txt Normal file
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[[wp:Bell number|Bell or exponential numbers]] are enumerations of the number of different ways to partition a set that has exactly '''n''' elements. Each element of the sequence '''B<sub>n</sub>''' is the number of partitions of a set of size '''n''' where order of the elements and order of the partitions are non-significant. E.G.: '''{a b}''' is the same as '''{b a}''' and '''{a} {b}''' is the same as '''{b} {a}'''.
;So:
:'''B<sub>0</sub> = 1''' trivially. There is only one way to partition a set with zero elements. '''{ }'''
:'''B<sub>1</sub> = 1''' There is only one way to partition a set with one element. '''{a}'''
:'''B<sub>2</sub> = 2''' Two elements may be partitioned in two ways. '''{a} {b}, {a b}'''
:'''B<sub>3</sub> = 5''' Three elements may be partitioned in five ways '''{a} {b} {c}, {a b} {c}, {a} {b c}, {a c} {b}, {a b c}'''
: and so on.
A simple way to find the Bell numbers is construct a '''[[wp:Bell_triangle|Bell triangle]]''', also known as an '''Aitken's array''' or '''Peirce triangle''', and read off the numbers in the first column of each row. There are other generating algorithms though, and you are free to choose the best / most appropriate for your case.
;Task:
Write a routine (function, generator, whatever) to generate the Bell number sequence and call the routine to show here, on this page at least the '''first 15''' and (if your language supports big Integers) '''50th''' elements of the sequence.
If you ''do'' use the Bell triangle method to generate the numbers, also show the '''first ten rows''' of the Bell triangle.
;See also:
:* '''[[oeis:A000110|OEIS:A000110 Bell or exponential numbers]]'''
:* '''[[oeis:A011971|OEIS:A011971 Aitken's array]]'''

20
Task/Bell-numbers/11l/bell-numbers.11l Normal file
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F bellTriangle(n)
[[BigInt]] tri
L(i) 0 .< n
tri.append([BigInt(0)] * i)
tri[1][0] = 1
L(i) 2 .< n
tri[i][0] = tri[i - 1][i - 2]
L(j) 1 .< i
tri[i][j] = tri[i][j - 1] + tri[i - 1][j - 1]
R tri
V bt = bellTriangle(51)
print(‘First fifteen and fiftieth Bell numbers:’)
L(i) 1..15
print(‘#2: #.’.format(i, bt[i][0]))
print(‘50: ’bt[50][0])
print()
print(‘The first ten rows of Bell's triangle:’)
L(i) 1..10
print(bt[i])

21
Task/Bell-numbers/ALGOL-68/bell-numbers.alg Normal file
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BEGIN # show some Bell numbers #
PROC show bell = ( INT n, LONG LONG INT bell number )VOID:
print( ( whole( n, -2 ), ": ", whole( bell number, 0 ), newline ) );
INT max bell = 50;
[ 0 : max bell - 2 ]LONG LONG INT a; FOR i TO UPB a DO a[ i ] := 0 OD;
a[ 0 ] := 1;
show bell( 1, a[ 0 ] );
FOR n FROM 0 TO UPB a DO
# replace a with the next line of the triangle #
a[ n ] := a[ 0 ];
FOR j FROM n BY -1 TO 1 DO
a[ j - 1 ] +:= a[ j ]
OD;
IF n < 14 THEN
show bell( n + 2, a[ 0 ] )
ELIF n = UPB a THEN
print( ( "...", newline ) );
show bell( n + 2, a[ 0 ] )
FI
OD
END

36
Task/Bell-numbers/ALGOL-M/bell-numbers.alg Normal file
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begin
integer function index(row, col);
integer row, col;
index := row * (row-1)/ 2 + col;
integer ROWS; ROWS := 15;
begin
decimal(11) array bell[0:ROWS*(ROWS+1)/2];
integer i, j;
bell[index(1, 0)] := 1.;
for i := 2 step 1 until ROWS do
begin
bell[index(i, 0)] := bell[index(i-1, i-2)];
for j := 1 step 1 until i-1 do
bell[index(i,j)] := bell[index(i,j-1)] + bell[index(i-1,j-1)];
end;
write("First fifteen Bell numbers:");
for i := 1 step 1 until ROWS do
begin
write(i);
writeon(": ");
writeon(bell[index(i,0)]);
end;
write("");
write("First ten rows of Bell's triangle:");
for i := 1 step 1 until 10 do
begin
write("");
for j := 0 step 1 until i-1 do
writeon(bell[index(i,j)]);
end;
end;
end

7
Task/Bell-numbers/APL/bell-numbers.apl Normal file
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bell←{
tr←↑(⊢,(⊂⊃∘⌽+0,+\)∘⊃∘⌽)⍣14⊢,⊂,1
⎕←'First 15 Bell numbers:'
⎕←tr[;1]
⎕←'First 10 rows of Bell''s triangle:'
⎕←tr[⍳10;⍳10]
}

29
Task/Bell-numbers/ASIC/bell-numbers.asic Normal file
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REM Bell numbers
DIM A&(13)
FOR I = 0 TO 13
A&(I) = 0
NEXT I
N = 0
A&(0) = 1
GOSUB DisplayRow:
WHILE N <= 13
A&(N) = A&(0)
J = N
WHILE J >= 1
JM1 = J - 1
A&(JM1) = A&(JM1) + A&(J)
J = J - 1
WEND
N = N + 1
GOSUB DisplayRow:
WEND
END
DisplayRow:
PRINT "B(";
SN$ = STR$(N)
SN$ = RIGHT$(SN$, 2)
PRINT SN$;
PRINT ") =";
PRINT A&(0)
RETURN

59
Task/Bell-numbers/Ada/bell-numbers.ada Normal file
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with Ada.Text_IO; use Ada.Text_IO;
procedure Main is
type Bell_Triangle is array(Positive range <>, Positive range <>) of Natural;
procedure Print_Rows (Row : in Positive; Triangle : in Bell_Triangle) is
begin
if Row in Triangle'Range(1) then
for I in Triangle'First(1) .. Row loop
Put_Line (Triangle (I, 1)'Image);
end loop;
end if;
end Print_Rows;
procedure Print_Triangle (Num : in Positive; Triangle : in Bell_Triangle) is
begin
if Num in Triangle'Range then
for I in Triangle'First(1) .. Num loop
for J in Triangle'First(2) .. Num loop
if Triangle (I, J) /= 0 then
Put (Triangle (I, J)'Image);
end if;
end loop;
New_Line;
end loop;
end if;
end Print_Triangle;
procedure Bell_Numbers is
Triangle : Bell_Triangle(1..15, 1..15) := (Others => (Others => 0));
Temp : Positive := 1;
begin
Triangle (1, 1) := 1;
for I in Triangle'First(1) + 1 .. Triangle'Last(1) loop
Triangle (I, 1) := Temp;
for J in Triangle'First(2) .. Triangle'Last(2) - 1 loop
if Triangle (I - 1, J) /= 0 then
Triangle (I, J + 1) := Triangle (I, J) + Triangle (I - 1, J);
else
Temp := Triangle (I, J);
exit;
end if;
end loop;
end loop;
Put_Line ("First 15 Bell numbers:");
Print_Rows (15, Triangle);
New_Line;
Put_Line ("First 10 rows of the Bell triangle:");
Print_Triangle (10, Triangle);
end Bell_Numbers;
begin
Bell_Numbers;
end Main;

41
Task/Bell-numbers/Applesoft-BASIC/bell-numbers.basic Normal file
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100 LET ROWS = 15
110 LET M$ = CHR$ (13)
120 LET N = ROWS: GOSUB 500"BELLTRIANGLE"
130 PRINT "FIRST FIFTEEN BELL NUMBERS:"
140 FOR I = 1 TO ROWS
150 LET BR = I:BC = 0: GOSUB 350"GETBELL"
160 HTAB T * 13 + 1
170 PRINT RIGHT$ (" " + STR$ (I),2)": "BV; MID$ (M$,1,T = 2);
180 LET T = T + 1 - (T = 2) * 3
190 NEXT I
200 PRINT M$"THE FIRST TEN ROWS OF BELL'S TRIANGLE:";
210 FOR I = 1 TO 10
220 LET BR = I:BC = 0: GOSUB 350"GETBELL"
230 PRINT M$BV;
240 FOR J = 1 TO I - 1
250 IF I - 1 > = J THEN BR = I:BC = J: GOSUB 350"GETBELL": PRINT " "BV;
260 NEXT J,I
270 END
300 LET BI = BR * (BR - 1) / 2 + BC
310 RETURN
350 GOSUB 300"BELLINDEX"
360 LET BV = TRI(BI)
370 RETURN
400 GOSUB 300"BELLINDEX"
410 LET TRI(BI) = BV
420 RETURN
500 DIM TRI(N * (N + 1) / 2)
510 LET BR = 1:BC = 0:BV = 1: GOSUB 400"SETBELL"
520 FOR I = 2 TO N
530 LET BR = I - 1:BC = I - 2: GOSUB 350"GETBELL"
540 LET BR = I:BC = 0: GOSUB 400"SETBELL"
550 FOR J = 1 TO I - 1
560 LET BR = I:BC = J - 1: GOSUB 350"GETBELL":V = BV
570 LET BR = I - 1:BC = J - 1: GOSUB 350"GETBELL"
580 LET BR = I:BC = J:BV = V + BV: GOSUB 400"SETBELL"
590 NEXT J,I
600 RETURN

21
Task/Bell-numbers/Arturo/bell-numbers.arturo Normal file
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bellTriangle: function[n][
tri: map 0..n-1 'x [ map 0..n 'y -> 0 ]
set get tri 1 0 1
loop 2..n-1 'i [
set get tri i 0 get (get tri i-1) i-2
loop 1..i-1 'j [
set get tri i j (get (get tri i) j-1) + ( get (get tri i-1) j-1)
]
]
return tri
]
bt: bellTriangle 51
loop 1..15 'x ->
print [x "=>" first bt\[x]]
print ["50 =>" first last bt]
print ""
print "The first ten rows of Bell's triangle:"
loop 1..10 'i ->
print filter bt\[i] => zero?

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Task/Bell-numbers/AutoHotkey/bell-numbers-1.ahk Normal file
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;-----------------------------------
Bell_triangle(maxRows){
row := 1, col := 1, Arr := []
Arr[row, col] := 1
while (Arr.Count() < maxRows){
row++
max := Arr[row-1].Count()
Loop % max{
if (col := A_Index) =1
Arr[row, col] := Arr[row-1, max]
Arr[row, col+1] := Arr[row, col] + Arr[row-1, col]
}
}
return Arr
}
;-----------------------------------
Show_Bell_Number(Arr){
for i, obj in Arr{
res .= obj.1 "`n"
}
return Trim(res, "`n")
}
;-----------------------------------
Show_Bell_triangle(Arr){
for i, obj in Arr{
for j, v in obj
res .= v ", "
res := Trim(res, ", ") . "`n"
}
return Trim(res, "`n")
}
;-----------------------------------

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Task/Bell-numbers/AutoHotkey/bell-numbers-2.ahk Normal file
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MsgBox % Show_Bell_Number(Bell_triangle(15))
MsgBox % Show_Bell_triangle(Bell_triangle(10))
return

51
Task/Bell-numbers/C++/bell-numbers.cpp Normal file
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#include <iostream>
#include <vector>
#ifdef HAVE_BOOST
#include <boost/multiprecision/cpp_int.hpp>
typedef boost::multiprecision::cpp_int integer;
#else
typedef unsigned int integer;
#endif
auto make_bell_triangle(int n) {
std::vector<std::vector<integer>> bell(n);
for (int i = 0; i < n; ++i)
bell[i].assign(i + 1, 0);
bell[0][0] = 1;
for (int i = 1; i < n; ++i) {
std::vector<integer>& row = bell[i];
std::vector<integer>& prev_row = bell[i - 1];
row[0] = prev_row[i - 1];
for (int j = 1; j <= i; ++j)
row[j] = row[j - 1] + prev_row[j - 1];
}
return bell;
}
int main() {
#ifdef HAVE_BOOST
const int size = 50;
#else
const int size = 15;
#endif
auto bell(make_bell_triangle(size));
const int limit = 15;
std::cout << "First " << limit << " Bell numbers:\n";
for (int i = 0; i < limit; ++i)
std::cout << bell[i][0] << '\n';
#ifdef HAVE_BOOST
std::cout << "\n50th Bell number is " << bell[49][0] << "\n\n";
#endif
std::cout << "First 10 rows of the Bell triangle:\n";
for (int i = 0; i < 10; ++i) {
std::cout << bell[i][0];
for (int j = 1; j <= i; ++j)
std::cout << ' ' << bell[i][j];
std::cout << '\n';
}
return 0;
}

55
Task/Bell-numbers/C-sharp/bell-numbers.cs Normal file
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using System;
using System.Numerics;
namespace BellNumbers {
public static class Utility {
public static void Init<T>(this T[] array, T value) {
if (null == array) return;
for (int i = 0; i < array.Length; ++i) {
array[i] = value;
}
}
}
class Program {
static BigInteger[][] BellTriangle(int n) {
BigInteger[][] tri = new BigInteger[n][];
for (int i = 0; i < n; ++i) {
tri[i] = new BigInteger[i];
tri[i].Init(BigInteger.Zero);
}
tri[1][0] = 1;
for (int i = 2; i < n; ++i) {
tri[i][0] = tri[i - 1][i - 2];
for (int j = 1; j < i; ++j) {
tri[i][j] = tri[i][j - 1] + tri[i - 1][j - 1];
}
}
return tri;
}
static void Main(string[] args) {
var bt = BellTriangle(51);
Console.WriteLine("First fifteen and fiftieth Bell numbers:");
for (int i = 1; i < 16; ++i) {
Console.WriteLine("{0,2}: {1}", i, bt[i][0]);
}
Console.WriteLine("50: {0}", bt[50][0]);
Console.WriteLine();
Console.WriteLine("The first ten rows of Bell's triangle:");
for (int i = 1; i < 11; ++i) {
//Console.WriteLine(bt[i]);
var it = bt[i].GetEnumerator();
Console.Write("[");
if (it.MoveNext()) {
Console.Write(it.Current);
}
while (it.MoveNext()) {
Console.Write(", ");
Console.Write(it.Current);
}
Console.WriteLine("]");
}
}
}
}

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Task/Bell-numbers/C/bell-numbers.c Normal file
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#include <stdio.h>
#include <stdlib.h>
// row starts with 1; col < row
size_t bellIndex(int row, int col) {
return row * (row - 1) / 2 + col;
}
int getBell(int *bellTri, int row, int col) {
size_t index = bellIndex(row, col);
return bellTri[index];
}
void setBell(int *bellTri, int row, int col, int value) {
size_t index = bellIndex(row, col);
bellTri[index] = value;
}
int *bellTriangle(int n) {
size_t length = n * (n + 1) / 2;
int *tri = calloc(length, sizeof(int));
int i, j;
setBell(tri, 1, 0, 1);
for (i = 2; i <= n; ++i) {
setBell(tri, i, 0, getBell(tri, i - 1, i - 2));
for (j = 1; j < i; ++j) {
int value = getBell(tri, i, j - 1) + getBell(tri, i - 1, j - 1);
setBell(tri, i, j, value);
}
}
return tri;
}
int main() {
const int rows = 15;
int *bt = bellTriangle(rows);
int i, j;
printf("First fifteen Bell numbers:\n");
for (i = 1; i <= rows; ++i) {
printf("%2d: %d\n", i, getBell(bt, i, 0));
}
printf("\nThe first ten rows of Bell's triangle:\n");
for (i = 1; i <= 10; ++i) {
printf("%d", getBell(bt, i, 0));
for (j = 1; j < i; ++j) {
printf(", %d", getBell(bt, i, j));
}
printf("\n");
}
free(bt);
return 0;
}

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Task/Bell-numbers/CLU/bell-numbers.clu Normal file
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bell = cluster is make, get
rep = array[int]
idx = proc (row, col: int) returns (int)
return (row * (row - 1) / 2 + col)
end idx
get = proc (tri: cvt, row, col: int) returns (int)
return (tri[idx(row, col)])
end get
make = proc (rows: int) returns (cvt)
length: int := rows * (rows+1) / 2
arr: rep := rep$fill(0, length, 0)
arr[idx(1,0)] := 1
for i: int in int$from_to(2, rows) do
arr[idx(i,0)] := arr[idx(i-1, i-2)]
for j: int in int$from_to(1, i-1) do
arr[idx(i,j)] := arr[idx(i,j-1)] + arr[idx(i-1,j-1)]
end
end
return(arr)
end make
end bell
start_up = proc ()
rows = 15
po: stream := stream$primary_output()
belltri: bell := bell$make(rows)
stream$putl(po, "The first 15 Bell numbers are:")
for i: int in int$from_to(1, rows) do
stream$putl(po, int$unparse(i)
|| ": " || int$unparse(bell$get(belltri, i, 0)))
end
stream$putl(po, "\nThe first 10 rows of the Bell triangle:")
for row: int in int$from_to(1, 10) do
for col: int in int$from_to(0, row-1) do
stream$putright(po, int$unparse(bell$get(belltri, row, col)), 7)
end
stream$putc(po, '\n')
end
end start_up

22
Task/Bell-numbers/Chipmunk-Basic/bell-numbers.basic Normal file
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100 cls
110 dim a(13)
120 for i = 0 to ubound(a) : a(i) = 0 : next i
130 n = 0
140 a(0) = 1
150 displayrow()
160 while n <= ubound(a)
170 a(n) = a(0)
180 j = n
190 while j >= 1
200 jm1 = j-1
210 a(jm1) = a(jm1)+a(j)
220 j = j-1
230 wend
240 n = n+1
250 displayrow()
260 wend
270 end
280 sub displayrow()
290 print "B(";
300 print right$(str$(n),2)") = " a(0)
310 return

61
Task/Bell-numbers/Common-Lisp/bell-numbers-1.lisp Normal file
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;; The triangle is a list of arrays; each array is a
;; triangle's row; the last row is at the head of the list.
(defun grow-triangle (triangle)
(if (null triangle)
'(#(1))
(let* ((last-array (car triangle))
(last-length (length last-array))
(new-array (make-array (1+ last-length)
:element-type 'integer)))
;; copy over the last element of the last array
(setf (aref new-array 0) (aref last-array (1- last-length)))
;; fill in the rest of the array
(loop for i from 0
;; the last index of the new array is the length
;; of the last array, which is 1 unit shorter
for j from 1 upto last-length
for sum = (+ (aref last-array i) (aref new-array i))
do (setf (aref new-array j) sum))
;; return the grown list
(cons new-array triangle))))
(defun make-triangle (num)
(if (<= num 1)
(grow-triangle nil)
(grow-triangle (make-triangle (1- num)))))
(defun bell (num)
(cond ((< num 0) nil)
((= num 0) 1)
(t (aref (first (make-triangle num)) (1- num)))))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Printing section
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defparameter *numbers-to-print*
(append
(loop for i upto 19 collect i)
'(49 50)))
(defun array->list (array)
(loop for i upto (1- (length array))
collect (aref array i)))
(defun print-bell-number (index bell-number)
(format t "B_~d (~:r Bell number) = ~:d~%"
index (1+ index) bell-number))
(defun print-bell-triangle (triangle)
(loop for row in (reverse triangle)
do (format t "~{~d~^, ~}~%" (array->list row))))
;; Final invocation
(loop for n in *numbers-to-print* do
(print-bell-number n (bell n)))
(princ #\newline)
(format t "The first 10 rows of Bell triangle:~%")
(print-bell-triangle (make-triangle 10))

43
Task/Bell-numbers/Common-Lisp/bell-numbers-2.lisp Normal file
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;;; Compute bell numbers analytically
;; Compute the factorial
(defun fact (n)
(cond ((< n 0) nil)
((< n 2) 1)
(t (* n (fact (1- n))))))
;; Compute the binomial coefficient (n choose k)
(defun binomial (n k)
(loop for i from 1 upto k
collect (/ (- (1+ n) i) i) into lst
finally (return (reduce #'* lst))))
;; Compute the Stirling number of the second kind
(defun stirling (n k)
(/
(loop for i upto k summing
(* (expt -1 i) (binomial k i) (expt (- k i) n)))
(fact k)))
;; Compute the Bell number
(defun bell (n)
(loop for k upto n summing (stirling n k)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Printing section
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defparameter *numbers-to-print*
(append
(loop for i upto 19 collect i)
'(49 50)))
(defun print-bell-number (index bell-number)
(format t "B_~d (~:r Bell number) = ~:d~%"
index (1+ index) bell-number))
;; Final invocation
(loop for n in *numbers-to-print* do
(print-bell-number n (bell n)))

68
Task/Bell-numbers/Cowgol/bell-numbers.cowgol Normal file
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include "cowgol.coh";
typedef B is uint32;
typedef I is intptr;
sub bellIndex(row: I, col: I): (addr: I) is
addr := (row * (row - 1) / 2 + col) * @bytesof B;
end sub;
sub getBell(row: I, col: I): (bell: B) is
bell := [LOMEM as [B] + bellIndex(row, col)];
end sub;
sub setBell(row: I, col: I, bell: B) is
[LOMEM as [B] + bellIndex(row, col)] := bell;
end sub;
sub bellTriangle(n: I) is
var length := n * (n + 1) / 2;
var bytes := length * @bytesof B;
if HIMEM - LOMEM < bytes then
print("not enough memory\n");
ExitWithError();
end if;
MemZero(LOMEM, bytes);
setBell(1, 0, 1);
var i: I := 2;
while i <= n loop
setBell(i, 0, getBell(i-1, i-2));
var j: I := 1;
while j < i loop
var value := getBell(i, j-1) + getBell(i-1, j-1);
setBell(i, j, value);
j := j + 1;
end loop;
i := i + 1;
end loop;
end sub;
const ROWS := 15;
bellTriangle(ROWS);
print("First fifteen Bell numbers:\n");
var i: I := 1;
while i <= ROWS loop
print_i32(i as uint32);
print(": ");
print_i32(getBell(i, 0) as uint32);
print_nl();
i := i + 1;
end loop;
print("\nThe first ten rows of Bell's triangle:\n");
i := 1;
while i <= 10 loop
var j: I := 0;
loop
print_i32(getBell(i, j) as uint32);
j := j + 1;
if j == i then break;
else print(", ");
end if;
end loop;
i := i + 1;
print_nl();
end loop;

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Task/Bell-numbers/D/bell-numbers.d Normal file
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import std.array : uninitializedArray;
import std.bigint;
import std.stdio : writeln, writefln;
auto bellTriangle(int n) {
auto tri = uninitializedArray!(BigInt[][])(n);
foreach (i; 0..n) {
tri[i] = uninitializedArray!(BigInt[])(i);
tri[i][] = BigInt(0);
}
tri[1][0] = 1;
foreach (i; 2..n) {
tri[i][0] = tri[i - 1][i - 2];
foreach (j; 1..i) {
tri[i][j] = tri[i][j - 1] + tri[i - 1][j - 1];
}
}
return tri;
}
void main() {
auto bt = bellTriangle(51);
writeln("First fifteen and fiftieth Bell numbers:");
foreach (i; 1..16) {
writefln("%2d: %d", i, bt[i][0]);
}
writeln("50: ", bt[50][0]);
writeln;
writeln("The first ten rows of Bell's triangle:");
foreach (i; 1..11) {
writeln(bt[i]);
}
}

35
Task/Bell-numbers/Delphi/bell-numbers.delphi Normal file
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program BellNumbers;
// For Rosetta Code.
// Delphi console application to display the Bell numbers B_0, ..., B_25.
// Uses signed 64-bit integers, the largest integer type available in Delphi.
{$APPTYPE CONSOLE}
uses SysUtils; // only for the display
const
MAX_INDEX = 25; // maximum index within the limits of int64
var
n : integer; // index of Bell number
j : integer; // loop variable
a : array [0..MAX_INDEX - 1] of int64; // working array to build up B_n
{ Subroutine to display that a[0] is the Bell number B_n }
procedure Display();
begin
WriteLn( SysUtils.Format( 'B_%-2d = %d', [n, a[0]]));
end;
(* Main program *)
begin
n := 0;
a[0] := 1;
Display(); // some programmers would prefer Display;
while (n < MAX_INDEX) do begin // and give begin a line to itself
a[n] := a[0];
for j := n downto 1 do inc( a[j - 1], a[j]);
inc(n);
Display();
end;
end.

16
Task/Bell-numbers/Elixir/bell-numbers.elixir Normal file
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defmodule Bell do
def triangle(), do: Stream.iterate([1], fn l -> bell_row l, [List.last l] end)
def numbers(), do: triangle() |> Stream.map(&List.first/1)
defp bell_row([], r), do: Enum.reverse r
defp bell_row([a|a_s], r = [r0|_]), do: bell_row(a_s, [a + r0|r])
end
:io.format "The first 15 bell numbers are ~p~n~n",
[Bell.numbers() |> Enum.take(15)]
IO.puts "The 50th Bell number is #{Bell.numbers() |> Enum.take(50) |> List.last}"
IO.puts ""
IO.puts "THe first 10 rows of Bell's triangle:"
IO.inspect(Bell.triangle() |> Enum.take(10))

2
Task/Bell-numbers/F-Sharp/bell-numbers-1.fs Normal file
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// Generate bell triangle. Nigel Galloway: July 6th., 2019
let bell=Seq.unfold(fun g->Some(g,List.scan(+) (List.last g) g))[1I]

1
Task/Bell-numbers/F-Sharp/bell-numbers-2.fs Normal file
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bell|>Seq.take 10|>Seq.iter(printfn "%A")

1
Task/Bell-numbers/F-Sharp/bell-numbers-3.fs Normal file
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bell|>Seq.take 15|>Seq.iter(fun n->printf "%A " (List.head n));printfn ""

1
Task/Bell-numbers/F-Sharp/bell-numbers-4.fs Normal file
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printfn "%A" (Seq.head (Seq.item 49 bell))

13
Task/Bell-numbers/Factor/bell-numbers-1.factor Normal file
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USING: formatting io kernel math math.matrices sequences vectors ;
: next-row ( prev -- next )
[ 1 1vector ]
[ dup last [ + ] accumulate swap suffix! ] if-empty ;
: aitken ( n -- seq )
V{ } clone swap [ next-row dup ] replicate nip ;
0 50 aitken col [ 15 head ] [ last ] bi
"First 15 Bell numbers:\n%[%d, %]\n\n50th: %d\n\n" printf
"First 10 rows of the Bell triangle:" print
10 aitken [ "%[%d, %]\n" printf ] each

10
Task/Bell-numbers/Factor/bell-numbers-2.factor Normal file
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USING: formatting kernel math math.combinatorics sequences ;
: next-bell ( seq -- n )
dup length 1 - [ swap nCk * ] curry map-index sum ;
: bells ( n -- seq )
V{ 1 } clone swap 1 - [ dup next-bell suffix! ] times ;
50 bells [ 15 head ] [ last ] bi
"First 15 Bell numbers:\n%[%d, %]\n\n50th: %d\n" printf

7
Task/Bell-numbers/Factor/bell-numbers-3.factor Normal file
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USING: formatting kernel math math.extras math.ranges sequences ;
: bell ( m -- n )
[ 1 ] [ dup [1,b] [ stirling ] with map-sum ] if-zero ;
50 [ bell ] { } map-integers [ 15 head ] [ last ] bi
"First 15 Bell numbers:\n%[%d, %]\n\n50th: %d\n" printf

22
Task/Bell-numbers/FreeBASIC/bell-numbers.basic Normal file
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#define MAX 21
#macro ncp(n, p)
(fact(n)/(fact(p))/(fact(n-p)))
#endmacro
dim as ulongint fact(0 to MAX), bell(0 to MAX)
dim as uinteger n=0, k
fact(0) = 1
for k=1 to MAX
fact(k) = k*fact(k-1)
next k
bell(n) = 1
print n, bell(n)
for n=0 to MAX-1
for k=0 to n
bell(n+1) += ncp(n, k)*bell(k)
next k
print n+1, bell(n+1)
next n

22
Task/Bell-numbers/GW-BASIC/bell-numbers.basic Normal file
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100 CLS
110 DIM A#(13)
120 FOR I = 0 TO UBOUND(A#) : A#(I) = 0 : NEXT I
130 N = 0
140 A#(0) = 1
150 GOSUB 280
160 WHILE N <= 13
170 A#(N) = A#(0)
180 J = N
190 WHILE J >= 1
200 JM1 = J-1
210 A#(JM1) = A#(JM1)+A#(J)
220 J = J-1
230 WEND
240 N = N+1
250 GOSUB 280
260 WEND
270 END
280 REM Display Row
290 PRINT "B(";
300 PRINT RIGHT$(STR$(N),2)") = " A#(0)
310 RETURN

37
Task/Bell-numbers/Go/bell-numbers.go Normal file
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package main
import (
"fmt"
"math/big"
)
func bellTriangle(n int) [][]*big.Int {
tri := make([][]*big.Int, n)
for i := 0; i < n; i++ {
tri[i] = make([]*big.Int, i)
for j := 0; j < i; j++ {
tri[i][j] = new(big.Int)
}
}
tri[1][0].SetUint64(1)
for i := 2; i < n; i++ {
tri[i][0].Set(tri[i-1][i-2])
for j := 1; j < i; j++ {
tri[i][j].Add(tri[i][j-1], tri[i-1][j-1])
}
}
return tri
}
func main() {
bt := bellTriangle(51)
fmt.Println("First fifteen and fiftieth Bell numbers:")
for i := 1; i <= 15; i++ {
fmt.Printf("%2d: %d\n", i, bt[i][0])
}
fmt.Println("50:", bt[50][0])
fmt.Println("\nThe first ten rows of Bell's triangle:")
for i := 1; i <= 10; i++ {
fmt.Println(bt[i])
}
}

58
Task/Bell-numbers/Groovy/bell-numbers.groovy Normal file
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class Bell {
private static class BellTriangle {
private List<Integer> arr
BellTriangle(int n) {
int length = (int) (n * (n + 1) / 2)
arr = new ArrayList<>(length)
for (int i = 0; i < length; ++i) {
arr.add(0)
}
set(1, 0, 1)
for (int i = 2; i <= n; ++i) {
set(i, 0, get(i - 1, i - 2))
for (int j = 1; j < i; ++j) {
int value = get(i, j - 1) + get(i - 1, j - 1)
set(i, j, value)
}
}
}
private static int index(int row, int col) {
if (row > 0 && col >= 0 && col < row) {
return row * (row - 1) / 2 + col
} else {
throw new IllegalArgumentException()
}
}
int get(int row, int col) {
int i = index(row, col)
return arr.get(i)
}
void set(int row, int col, int value) {
int i = index(row, col)
arr.set(i, value)
}
}
static void main(String[] args) {
final int rows = 15
BellTriangle bt = new BellTriangle(rows)
System.out.println("First fifteen Bell numbers:")
for (int i = 0; i < rows; ++i) {
System.out.printf("%2d: %d\n", i + 1, bt.get(i + 1, 0))
}
for (int i = 1; i <= 10; ++i) {
System.out.print(bt.get(i, 0))
for (int j = 1; j < i; ++j) {
System.out.printf(", %d", bt.get(i, j))
}
System.out.println()
}
}
}

16
Task/Bell-numbers/Haskell/bell-numbers-1.hs Normal file
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bellTri :: [[Integer]]
bellTri =
let f xs = (last xs, xs)
in map snd (iterate (f . uncurry (scanl (+))) (1, [1]))
bell :: [Integer]
bell = map head bellTri
main :: IO ()
main = do
putStrLn "First 10 rows of Bell's Triangle:"
mapM_ print (take 10 bellTri)
putStrLn "\nFirst 15 Bell numbers:"
mapM_ print (take 15 bell)
putStrLn "\n50th Bell number:"
print (bell !! 49)

4
Task/Bell-numbers/Haskell/bell-numbers-2.hs Normal file
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import Control.Arrow
bellTri :: [[Integer]]
bellTri = map snd (iterate ((last &&& id) . uncurry (scanl (+))) (1,[1]))

4
Task/Bell-numbers/Haskell/bell-numbers-3.hs Normal file
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import Control.Applicative
bellTri :: [[Integer]]
bellTri = map snd (iterate ((liftA2 (,) last id) . uncurry (scanl (+))) (1,[1]))

2
Task/Bell-numbers/Haskell/bell-numbers-4.hs Normal file
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bellTri :: [[Integer]]
bellTri = map snd (iterate (((,) . last <*> id) . uncurry (scanl (+))) (1, [1]))

20
Task/Bell-numbers/J/bell-numbers.j Normal file
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bell=: ([: +/\ (,~ {:))&.>@:{:
,. bell^:(<5) <1
+--------------+
|1 |
+--------------+
|1 2 |
+--------------+
|2 3 5 |
+--------------+
|5 7 10 15 |
+--------------+
|15 20 27 37 52|
+--------------+
{.&> bell^:(<15) <1
1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322
{:>bell^:49<1x
185724268771078270438257767181908917499221852770

61
Task/Bell-numbers/Java/bell-numbers.java Normal file
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import java.util.ArrayList;
import java.util.List;
public class Bell {
private static class BellTriangle {
private List<Integer> arr;
BellTriangle(int n) {
int length = n * (n + 1) / 2;
arr = new ArrayList<>(length);
for (int i = 0; i < length; ++i) {
arr.add(0);
}
set(1, 0, 1);
for (int i = 2; i <= n; ++i) {
set(i, 0, get(i - 1, i - 2));
for (int j = 1; j < i; ++j) {
int value = get(i, j - 1) + get(i - 1, j - 1);
set(i, j, value);
}
}
}
private int index(int row, int col) {
if (row > 0 && col >= 0 && col < row) {
return row * (row - 1) / 2 + col;
} else {
throw new IllegalArgumentException();
}
}
public int get(int row, int col) {
int i = index(row, col);
return arr.get(i);
}
public void set(int row, int col, int value) {
int i = index(row, col);
arr.set(i, value);
}
}
public static void main(String[] args) {
final int rows = 15;
BellTriangle bt = new BellTriangle(rows);
System.out.println("First fifteen Bell numbers:");
for (int i = 0; i < rows; ++i) {
System.out.printf("%2d: %d\n", i + 1, bt.get(i + 1, 0));
}
for (int i = 1; i <= 10; ++i) {
System.out.print(bt.get(i, 0));
for (int j = 1; j < i; ++j) {
System.out.printf(", %d", bt.get(i, j));
}
System.out.println();
}
}
}

16
Task/Bell-numbers/Jq/bell-numbers.jq Normal file
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# nth Bell number
def bell:
. as $n
| if $n < 0 then "non-negative integer expected"
elif $n < 2 then 1
else
reduce range(1; $n) as $i ([1];
reduce range(1; $i) as $j (.;
.[$i - $j] as $x
| .[$i - $j - 1] += $x )
| .[$i] = .[0] + .[$i - 1] )
| .[$n - 1]
end;
# The task
range(1;51) | bell

24
Task/Bell-numbers/Julia/bell-numbers.julia Normal file
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"""
bellnum(n)
Compute the ``n``th Bell number.
"""
function bellnum(n::Integer)
if n < 0
throw(DomainError(n))
elseif n < 2
return 1
end
list = Vector{BigInt}(undef, n)
list[1] = 1
for i = 2:n
for j = 1:i - 2
list[i - j - 1] += list[i - j]
end
list[i] = list[1] + list[i - 1]
end
return list[n]
end
for i in 1:50
println(bellnum(i))
end

52
Task/Bell-numbers/Kotlin/bell-numbers.kotlin Normal file
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class BellTriangle(n: Int) {
private val arr: Array<Int>
init {
val length = n * (n + 1) / 2
arr = Array(length) { 0 }
set(1, 0, 1)
for (i in 2..n) {
set(i, 0, get(i - 1, i - 2))
for (j in 1 until i) {
val value = get(i, j - 1) + get(i - 1, j - 1)
set(i, j, value)
}
}
}
private fun index(row: Int, col: Int): Int {
require(row > 0)
require(col >= 0)
require(col < row)
return row * (row - 1) / 2 + col
}
operator fun get(row: Int, col: Int): Int {
val i = index(row, col)
return arr[i]
}
private operator fun set(row: Int, col: Int, value: Int) {
val i = index(row, col)
arr[i] = value
}
}
fun main() {
val rows = 15
val bt = BellTriangle(rows)
println("First fifteen Bell numbers:")
for (i in 1..rows) {
println("%2d: %d".format(i, bt[i, 0]))
}
for (i in 1..10) {
print("${bt[i, 0]}")
for (j in 1 until i) {
print(", ${bt[i, j]}")
}
println()
}
}

73
Task/Bell-numbers/Little-Man-Computer/bell-numbers.lmc Normal file
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// Little Man Computer, for Rosetta Code.
// Calculate Bell numbers, using a 1-dimensional array and addition.
//
// After the calculation of B_n (n > 0), the array contains n elements,
// of which B_n is the first. Example to show calculation of B_(n+1):
// After calc. of B_3 = 5, array holds: 5, 3, 2
// Extend array by copying B_3 to high end: 5, 3, 2, 5
// Replace 2 by 5 + 2 = 7: 5, 3, 7, 5
// Replace 3 by 7 + 3 = 10: 5, 10, 7, 5
// Replace first 5 by 10 + 5 = 15: 15, 10, 7, 5
// First element of array is now B_4 = 15.
// Initialize; B_0 := 1
LDA c1
STA Bell
LDA c0
STA index
BRA print // skip increment of index
// Increment index of Bell number
inc_ix LDA index
ADD c1
STA index
// Here acc = index; print index and Bell number
print OUT
LDA colon
OTC // non-standard instruction; cosmetic only
LDA Bell
OUT
LDA index
BRZ inc_ix // if index = 0, skip rest and loop back
SUB c7 // reached maximum index yet?
BRZ done // if so, jump to exit
// Manufacture some instructions
LDA lda_0
ADD index
STA lda_ix
SUB c200 // convert LDA to STA with same address
STA sta_ix
// Copy latest Bell number to end of array
lda_0 LDA Bell // load Bell number
sta_ix STA 0 // address was filled in above
// Manufacture more instructions
LDA lda_ix // load LDA instruction
loop SUB c401 // convert to ADD with address 1 less
STA add_ix_1
ADD c200 // convert to STA
STA sta_ix_1
// Execute instructions; zero addresses were filled in above
lda_ix LDA 0 // load element of array
add_ix_1 ADD 0 // add to element below
sta_ix_1 STA 0 // update element below
LDA sta_ix_1 // load previous STA instruction
SUB sta_Bell // does it refer to first element of array?
BRZ inc_ix // yes, loop to inc index and print
LDA lda_ix // no, repeat with addresses 1 less
SUB c1
STA lda_ix
BRA loop
// Here when done
done HLT
// Constants
colon DAT 58
c0 DAT 0
c1 DAT 1
c7 DAT 7 // maximum index
c200 DAT 200
c401 DAT 401
sta_Bell STA Bell // not executed; used for comparison
// Variables
index DAT
Bell DAT
// Rest of array goes here
// end

29
Task/Bell-numbers/Lua/bell-numbers.lua Normal file
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-- Bell numbers in Lua
-- db 6/11/2020 (to replace missing original)
local function bellTriangle(n)
local tri = { {1} }
for i = 2, n do
tri[i] = { tri[i-1][i-1] }
for j = 2, i do
tri[i][j] = tri[i][j-1] + tri[i-1][j-1]
end
end
return tri
end
local N = 25 -- in lieu of 50, practical limit with double precision floats
local tri = bellTriangle(N)
print("First 15 and "..N.."th Bell numbers:")
for i = 1, 15 do
print(i, tri[i][1])
end
print(N, tri[N][1])
print()
print("First 10 rows of Bell triangle:")
for i = 1, 10 do
print("[ " .. table.concat(tri[i],", ") .. " ]")
end

37
Task/Bell-numbers/MSX-Basic/bell-numbers.basic Normal file
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100 ROWS = 15
110 M$ = CHR$(13)
120 N = ROWS: GOSUB 500
130 PRINT "FIRST FIFTEEN BELL NUMBERS:"
140 FOR I = 1 TO ROWS
150 BR = I: BC = 0: GOSUB 350
160 PRINT RIGHT$(" " + STR$(I),2); ": "; BV; MID$(M$,1,2)
170 T = T + 1 - (T = 2) * 3
180 NEXT I
190 PRINT
200 PRINT "THE FIRST 10 ROWS OF BELL'S TRIANGLE:";
210 FOR I = 1 TO 10
220 BR = I: BC = 0: GOSUB 350
230 PRINT M$: PRINT BV;
240 FOR J = 1 TO I - 1
250 IF I - 1 >= J THEN BR = I: BC = J: GOSUB 350: PRINT BV;
260 NEXT J, I
270 END
300 BI = BR * (BR-1) / 2 + BC
310 RETURN
350 GOSUB 300
360 BV = TRI(BI)
370 RETURN
400 GOSUB 300
410 TRI(BI) = BV
420 RETURN
500 DIM TRI(N * (N+1) / 2)
510 BR = 1: BC = 0: BV = 1: GOSUB 400
520 FOR I = 2 TO N
530 BR = I - 1: BC = I - 2: GOSUB 350
540 BR = I: BC = 0: GOSUB 400
550 FOR J = 1 TO I - 1
560 BR = I: BC = J - 1: GOSUB 350: V = BV
570 BR = I - 1: BC = J - 1: GOSUB 350
580 BR = I: BC = J: BV = V + BV: GOSUB 400
590 NEXT J, I
600 RETURN

16
Task/Bell-numbers/Maple/bell-numbers.maple Normal file
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bell1:=proc(n)
option remember;
add(binomial(n-1,k)*bell1(k),k=0..n-1)
end:
bell1(0):=1:
bell1(50);
# 185724268771078270438257767181908917499221852770
combinat[bell](50);
# 185724268771078270438257767181908917499221852770
bell1~([$0..20]);
# [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570,
# 4213597, 27644437, 190899322, 1382958545, 10480142147,
# 82864869804, 682076806159, 5832742205057, 51724158235372]

2
Task/Bell-numbers/Mathematica/bell-numbers-1.math Normal file
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BellTriangle[n_Integer?Positive] := NestList[Accumulate[# /. {a___, b_} :> {b, a, b}] &, {1}, n - 1];
BellNumber[n_Integer] := BellTriangle[n][[n, 1]];

14
Task/Bell-numbers/Mathematica/bell-numbers-2.math Normal file
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@ -0,0 +1,14 @@
In[51]:= Array[BellNumber, 25]
Out[51]= {1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, \
4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, \
682076806159, 5832742205057, 51724158235372, 474869816156751, \
4506715738447323, 44152005855084346, 445958869294805289}
In[52]:= BellTriangle[10]
Out[52]= {{1}, {1, 2}, {2, 3, 5}, {5, 7, 10, 15}, {15, 20, 27, 37,
52}, {52, 67, 87, 114, 151, 203}, {203, 255, 322, 409, 523, 674,
877}, {877, 1080, 1335, 1657, 2066, 2589, 3263, 4140}, {4140, 5017,
6097, 7432, 9089, 11155, 13744, 17007, 21147}, {21147, 25287, 30304,
36401, 43833, 52922, 64077, 77821, 94828, 115975}}

28
Task/Bell-numbers/Nim/bell-numbers-1.nim Normal file
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import math
iterator b(): int =
## Iterator yielding the bell numbers.
var numbers = @[1]
yield 1
var n = 0
while true:
var next = 0
for k in 0..n:
next += binom(n, k) * numbers[k]
numbers.add(next)
yield next
inc n
when isMainModule:
import strformat
const Limit = 25 # Maximum index beyond which an overflow occurs.
echo "Bell numbers from B0 to B25:"
var i = 0
for n in b():
echo fmt"{i:2d}: {n:>20d}"
inc i
if i > Limit:
break

51
Task/Bell-numbers/Nim/bell-numbers-2.nim Normal file
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iterator b(): int =
## Iterator yielding the bell numbers.
var row = @[1]
yield 1
yield 1
while true:
var newRow = newSeq[int](row.len + 1)
newRow[0] = row[^1]
for i in 1..newRow.high:
newRow[i] = newRow[i - 1] + row[i - 1]
row = move(newRow)
yield row[^1] # The last value of the row is one step ahead of the first one.
iterator bellTriangle(): seq[int] =
## Iterator yielding the rows of the Bell triangle.
var row = @[1]
yield row
while true:
var newRow = newSeq[int](row.len + 1)
newRow[0] = row[^1]
for i in 1..newRow.high:
newRow[i] = newRow[i - 1] + row[i - 1]
row = move(newRow)
yield row
when isMainModule:
import strformat
import strutils
const Limit = 25 # Maximum index beyond which an overflow occurs.
echo "Bell numbers from B0 to B25:"
var i = 0
for n in b():
echo fmt"{i:2d}: {n:>20d}"
inc i
if i > Limit:
break
echo "\nFirst ten rows of Bell triangle:"
i = 0
for row in bellTriangle():
inc i
var line = ""
for val in row:
line.addSep(" ", 0)
line.add(fmt"{val:6d}")
echo line
if i == 10:
break

121
Task/Bell-numbers/Pascal/bell-numbers.pas Normal file
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program BellNumbers;
{$Ifdef FPC}
{$optimization on,all}
{$ElseIf}
{Apptype console}
{$EndIf}
uses
sysutils,gmp;
var
T0 :TDateTime;
procedure BellNumbersUint64(OnlyBellNumbers:Boolean);
var
BList : array[0..24] of Uint64;
BellNum : Uint64;
BListLenght,i :nativeUInt;
begin
IF OnlyBellNUmbers then
Begin
writeln('Bell triangles ');
writeln(' 1 = 1');
end
else
Begin
writeln('Bell numbers');
writeln(' 1 = 1');
writeln(' 2 = 1');
end;
BList[0]:= 1;
BListLenght := 1;
BellNum := 1;
repeat
// For i := BListLenght downto 1 do BList[i] := BList[i-1]; or
move(Blist[0],Blist[1],BListLenght*SizeOf(Blist[0]));
BList[0] := BellNum;
For i := 1 to BListLenght do
Begin
BellNum += BList[i];
BList[i] := BellNum;
end;
// Output
IF OnlyBellNUmbers then
Begin
IF BListLenght<=9 then
Begin
write(BListLenght+1:3,' = ');
For i := 0 to BListLenght do
write(BList[i]:7);
writeln;
end
ELSE
BREAK;
end
else
writeln(BListLenght+2:3,' = ',BellNum);
inc(BListLenght);
until BListLenght >= 25;
writeln;
end;
procedure BellNumbersMPInteger;
const
MaxIndex = 5000;//must be > 0
var
//MPInteger as alternative to mpz_t -> selfcleaning
BList : array[0..MaxIndex] of MPInteger;
BellNum : MPInteger;
BListLenght,i :nativeUInt;
BellNumStr : AnsiString;
Begin
BellNumStr := '';
z_init(BellNum);
z_ui_pow_ui(BellNum,10,32767);
BListLenght := z_size(BellNum);
writeln('init length ',BListLenght);
For i := 0 to MaxIndex do
Begin
// z_init2_set(BList[i],BListLenght);
z_add_ui( BList[i],i);
end;
writeln('init length ',z_size(BList[0]));
T0 := now;
BListLenght := 1;
z_set_ui(BList[0],1);
z_set_ui(BellNum,1);
repeat
//Move does not fit moving interfaces // call fpc_intf_assign
For i := BListLenght downto 1 do BList[i] := BList[i-1];
z_set(BList[0],BellNum);
For i := 1 to BListLenght do
Begin
BellNum := z_add(BellNum,BList[i]);
z_set(BList[i],BellNum);
end;
inc(BListLenght);
if (BListLenght+1) MOD 100 = 0 then
Begin
BellNumStr:= z_get_str(10,BellNum);
//z_sizeinbase (BellNum, 10) is not exact :-(
write('Bell(',(IntToStr(BListLenght)):6,') has ',
(IntToStr(Length(BellNumStr))):6,' decimal digits');
writeln(FormatDateTime(' NN:SS.ZZZ',now-T0),'s');
end;
until BListLenght>=MaxIndex;
BellNumStr:= z_get_str(10,BellNum);
writeln(BListLenght:6,'.th ',Length(BellNumStr):8);
//clean up ;-)
BellNumStr := '';
z_clear(BellNum);
For i := MaxIndex downto 0 do
z_clear(BList[i]);
end;
BEGIN
BellNumbersUint64(True);BellNumbersUint64(False);
BellNumbersMPInteger;
END.

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Task/Bell-numbers/Perl/bell-numbers.pl Normal file
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use strict 'vars';
use warnings;
use feature 'say';
use bigint;
my @b = 1;
my @Aitkens = [1];
push @Aitkens, do {
my @c = $b[-1];
push @c, $b[$_] + $c[$_] for 0..$#b;
@b = @c;
[@c]
} until (@Aitkens == 50);
my @Bell_numbers = map { @$_[0] } @Aitkens;
say 'First fifteen and fiftieth Bell numbers:';
printf "%2d: %s\n", 1+$_, $Bell_numbers[$_] for 0..14, 49;
say "\nFirst ten rows of Aitken's array:";
printf '%-7d'x@{$Aitkens[$_]}."\n", @{$Aitkens[$_]} for 0..9;

31
Task/Bell-numbers/Phix/bell-numbers.phix Normal file
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(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">bellTriangle</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- nb: returns strings to simplify output</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">sz</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"1"</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">tri</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000000;">line</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">line</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">line</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">tri</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tri</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">sz</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">line</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">line</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span>
<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">line</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sz</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">tri</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tri</span><span style="color: #0000FF;">[$],</span><span style="color: #000000;">sz</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">line</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">line</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">tri</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">bt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bellTriangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">50</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First fifteen and fiftieth Bell numbers:\n%s\n50:%s\n\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">15</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)),</span><span style="color: #000000;">bt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">50</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"The first ten rows of Bell's triangle:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--

18
Task/Bell-numbers/Picat/bell-numbers-1.picat Normal file
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main =>
B50=b(50),
println(B50[1..18]),
println(b50=B50.last),
nl.
b(M) = R =>
A = new_array(M-1),
bind_vars(A,0),
A[1] := 1,
R = [1, 1],
foreach(N in 2..M-1)
A[N] := A[1],
foreach(K in N..-1..2)
A[K-1] := A[K-1] + A[K],
end,
R := R ++ [A[1]]
end.

23
Task/Bell-numbers/Picat/bell-numbers-2.picat Normal file
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main =>
Tri = tri(50),
foreach(I in 1..10)
println(Tri[I].to_list)
end,
nl,
println(tri50=Tri.last.first),
nl.
% Adjustments for base-1.
tri(N) = Tri[2..N+1] =>
Tri = new_array(N+1),
foreach(I in 1..N+1)
Tri[I] := new_array(I-1),
bind_vars(Tri[I],0)
end,
Tri[2,1] := 1,
foreach(I in 3..N+1)
Tri[I,1] := Tri[I-1,I-2],
foreach(J in 2..I-1)
Tri[I,J] := Tri[I,J-1] + Tri[I-1,J-1]
end
end.

45
Task/Bell-numbers/Picat/bell-numbers-3.picat Normal file
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main :-
bell(49, Bell),
printf("First 15 Bell numbers:\n"),
print_bell_numbers(Bell, 15),
Number=Bell.last.first,
printf("\n50th Bell number: %w\n", Number),
printf("\nFirst 10 rows of Bell triangle:\n"),
print_bell_rows(Bell, 10).
bell(N, Bell):-
bell(N, Bell, [], _).
bell(0, [[1]|T], T, [1]):-!.
bell(N, Bell, B, Row):-
N1 is N - 1,
bell(N1, Bell, [Row|B], Last),
next_row(Row, Last).
next_row([Last|Bell], Bell1):-
Last=last(Bell1),
next_row1(Last, Bell, Bell1).
next_row1(_, [], []):-!.
next_row1(X, [Y|Rest], [B|Bell]):-
Y is X + B,
next_row1(Y, Rest, Bell).
print_bell_numbers(_, 0):-!.
print_bell_numbers([[Number|_]|Bell], N):-
printf("%w\n", Number),
N1 is N - 1,
print_bell_numbers(Bell, N1).
print_bell_rows(_, 0):-!.
print_bell_rows([Row|Rows], N):-
print_bell_row(Row),
N1 is N - 1,
print_bell_rows(Rows, N1).
print_bell_row([Number]):-
!,
printf("%w\n", Number).
print_bell_row([Number|Numbers]):-
printf("%w ", Number),
print_bell_row(Numbers).

46
Task/Bell-numbers/Picat/bell-numbers-4.picat Normal file
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import cp.
main =>
member(N,1..10),
X = new_list(N),
X :: 1..N,
value_precede_chain(1..N,X),
solve_all($[ff,split],X)=All,
println(N=All.len),
if N <= 4 then
% convert to sets
Set = {},
foreach(Y in All)
L = new_array(N),
bind_vars(L,{}),
foreach(I in 1..N)
L[Y[I]] := L[Y[I]] ++ {I}
end,
Set := Set ++ { {E : E in L, E != {}} }
end,
println(Set)
end,
nl,
fail,
nl.
%
% Ensure that a value N+1 is placed in the list X not before
% all the value 1..N are placed in the list.
%
value_precede_chain(C, X) =>
foreach(I in 2..C.length)
value_precede(C[I-1], C[I], X)
end.
value_precede(S,T,X) =>
XLen = X.length,
B = new_list(XLen+1),
B :: 0..1,
foreach(I in 1..XLen)
Xis #= (X[I] #= S),
(Xis #=> (B[I+1] #= 1))
#/\ ((#~ Xis #= 1) #=> (B[I] #= B[I+1]))
#/\ ((#~ B[I] #= 1) #=> (X[I] #!= T))
end,
B[1] #= 0.

18
Task/Bell-numbers/PicoLisp/bell-numbers.l Normal file
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(de bell (N)
(make
(setq L (link (list 1)))
(do N
(setq L
(link
(make
(setq A (link (last L)))
(for B L
(setq A (link (+ A B))) ) ) ) ) ) ) )
(setq L (bell 51))
(for N 15
(tab (2 -2 -2) N ":" (get L N 1)) )
(prinl 50 ": " (get L 50 1))
(prinl)
(prinl "First ten rows:")
(for N 10
(println (get L N)) )

45
Task/Bell-numbers/Prolog/bell-numbers.pro Normal file
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bell(N, Bell):-
bell(N, Bell, [], _).
bell(0, [[1]|T], T, [1]):-!.
bell(N, Bell, B, Row):-
N1 is N - 1,
bell(N1, Bell, [Row|B], Last),
next_row(Row, Last).
next_row([Last|Bell], Bell1):-
last(Bell1, Last),
next_row1(Last, Bell, Bell1).
next_row1(_, [], []):-!.
next_row1(X, [Y|Rest], [B|Bell]):-
Y is X + B,
next_row1(Y, Rest, Bell).
print_bell_numbers(_, 0):-!.
print_bell_numbers([[Number|_]|Bell], N):-
writef('%w\n', [Number]),
N1 is N - 1,
print_bell_numbers(Bell, N1).
print_bell_rows(_, 0):-!.
print_bell_rows([Row|Rows], N):-
print_bell_row(Row),
N1 is N - 1,
print_bell_rows(Rows, N1).
print_bell_row([Number]):-
!,
writef('%w\n', [Number]).
print_bell_row([Number|Numbers]):-
writef('%w ', [Number]),
print_bell_row(Numbers).
main:-
bell(49, Bell),
writef('First 15 Bell numbers:\n'),
print_bell_numbers(Bell, 15),
last(Bell, [Number|_]),
writef('\n50th Bell number: %w\n', [Number]),
writef('\nFirst 10 rows of Bell triangle:\n'),
print_bell_rows(Bell, 10).

23
Task/Bell-numbers/Python/bell-numbers-1.py Normal file
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def bellTriangle(n):
tri = [None] * n
for i in xrange(n):
tri[i] = [0] * i
tri[1][0] = 1
for i in xrange(2, n):
tri[i][0] = tri[i - 1][i - 2]
for j in xrange(1, i):
tri[i][j] = tri[i][j - 1] + tri[i - 1][j - 1]
return tri
def main():
bt = bellTriangle(51)
print "First fifteen and fiftieth Bell numbers:"
for i in xrange(1, 16):
print "%2d: %d" % (i, bt[i][0])
print "50:", bt[50][0]
print
print "The first ten rows of Bell's triangle:"
for i in xrange(1, 11):
print bt[i]
main()

198
Task/Bell-numbers/Python/bell-numbers-2.py Normal file
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'''Bell numbers'''
from itertools import accumulate, chain, islice
from operator import add, itemgetter
from functools import reduce
# bellNumbers :: [Int]
def bellNumbers():
'''Bell or exponential numbers.
A000110
'''
return map(itemgetter(0), bellTriangle())
# bellTriangle :: [[Int]]
def bellTriangle():
'''Bell triangle.'''
return map(
itemgetter(1),
iterate(
compose(
bimap(last)(identity),
list, uncurry(scanl(add))
)
)((1, [1]))
)
# ------------------------- TEST --------------------------
# main :: IO ()
def main():
'''Tests'''
showIndex = compose(repr, succ, itemgetter(0))
showValue = compose(repr, itemgetter(1))
print(
fTable(
'First fifteen Bell numbers:'
)(showIndex)(showValue)(identity)(list(
enumerate(take(15)(bellNumbers()))
))
)
print('\nFiftieth Bell number:')
bells = bellNumbers()
drop(49)(bells)
print(
next(bells)
)
print(
fTable(
"\nFirst 10 rows of Bell's triangle:"
)(showIndex)(showValue)(identity)(list(
enumerate(take(10)(bellTriangle()))
))
)
# ------------------------ GENERIC ------------------------
# bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)
def bimap(f):
'''Tuple instance of bimap.
A tuple of the application of f and g to the
first and second values respectively.
'''
def go(g):
def gox(x):
return (f(x), g(x))
return gox
return go
# compose :: ((a -> a), ...) -> (a -> a)
def compose(*fs):
'''Composition, from right to left,
of a series of functions.
'''
def go(f, g):
def fg(x):
return f(g(x))
return fg
return reduce(go, fs, identity)
# drop :: Int -> [a] -> [a]
# drop :: Int -> String -> String
def drop(n):
'''The sublist of xs beginning at
(zero-based) index n.
'''
def go(xs):
if isinstance(xs, (list, tuple, str)):
return xs[n:]
else:
take(n)(xs)
return xs
return go
# fTable :: String -> (a -> String) ->
# (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
'''Heading -> x display function -> fx display function ->
f -> xs -> tabular string.
'''
def gox(xShow):
def gofx(fxShow):
def gof(f):
def goxs(xs):
ys = [xShow(x) for x in xs]
w = max(map(len, ys))
def arrowed(x, y):
return y.rjust(w, ' ') + ' -> ' + fxShow(f(x))
return s + '\n' + '\n'.join(
map(arrowed, xs, ys)
)
return goxs
return gof
return gofx
return gox
# identity :: a -> a
def identity(x):
'''The identity function.'''
return x
# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated
applications of f to x.
'''
def go(x):
v = x
while True:
yield v
v = f(v)
return go
# last :: [a] -> a
def last(xs):
'''The last element of a non-empty list.'''
return xs[-1]
# scanl :: (b -> a -> b) -> b -> [a] -> [b]
def scanl(f):
'''scanl is like reduce, but returns a succession of
intermediate values, building from the left.
'''
def go(a):
def g(xs):
return accumulate(chain([a], xs), f)
return g
return go
# succ :: Enum a => a -> a
def succ(x):
'''The successor of a value.
For numeric types, (1 +).
'''
return 1 + x
# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
def go(xs):
return (
xs[0:n]
if isinstance(xs, (list, tuple))
else list(islice(xs, n))
)
return go
# uncurry :: (a -> b -> c) -> ((a, b) -> c)
def uncurry(f):
'''A function over a tuple,
derived from a curried function.
'''
def go(tpl):
return f(tpl[0])(tpl[1])
return go
# MAIN ---
if __name__ == '__main__':
main()

19
Task/Bell-numbers/Quackery/bell-numbers.quackery Normal file
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[ ' [ [ 1 ] ] ' [ 1 ]
rot 1 - times
[ dup -1 peek nested
swap witheach
[ over -1 peek + join ]
tuck nested join swap ]
drop ] is bell's-triangle ( n --> [ )
[ bell's-triangle [] swap
witheach [ 0 peek join ] ] is bell-numbers ( n --> [ )
say "First fifteen Bell numbers:" cr
15 bell-numbers echo
cr cr
say "Fiftieth Bell number:" cr
50 bell-numbers -1 peek echo
cr cr
say "First ten rows of Bell's triangle:" cr
10 bell's-triangle witheach [ echo cr ]

26
Task/Bell-numbers/QuickBASIC/bell-numbers.basic Normal file
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' Bell numbers
DECLARE SUB DisplayRow (N%, BellNum&)
CONST MAXINDEX% = 14
DIM A&(MAXINDEX% - 1)
FOR I% = 0 TO MAXINDEX% - 1
A&(I%) = 0
NEXT I%
N% = 0
A&(0) = 1
DisplayRow N%, A&(0)
WHILE N% < MAXINDEX%
A&(N%) = A&(0)
FOR J% = N% TO 1 STEP -1
A&(J% - 1) = A&(J% - 1) + A&(J%)
NEXT J%
N% = N% + 1
DisplayRow N%, A&(0)
WEND
END
SUB DisplayRow (N%, BellNum&)
PRINT "B(";
PRINT USING "##"; N%;
PRINT ") = ";
PRINT USING "#########"; BellNum&
END SUB

24
Task/Bell-numbers/REXX/bell-numbers.rexx Normal file
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/*REXX program calculates and displays a range of Bell numbers (index starts at zero).*/
parse arg LO HI . /*obtain optional arguments from the CL*/
if LO=='' & HI=="" then do; LO=0; HI=14; end /*Not specified? Then use the default.*/
if LO=='' | LO=="," then LO= 0 /* " " " " " " */
if HI=='' | HI=="," then HI= 15 /* " " " " " " */
numeric digits max(9, HI*2) /*crudely calculate the # decimal digs.*/
!.=.; !.0= 1; !.1= 1; @.= 1 /*the FACT function uses memoization.*/
do j=0 for HI+1; $= j==0; jm= j-1 /*JM is used for a shortcut (below). */
do k=0 for j; _= jm - k /* [↓] calculate a Bell # the easy way*/
$= $ + comb(jm, k) * @._ /*COMB≡combination or binomial function*/
end /*k*/
@.j= $ /*assign the Jth Bell number to @ array*/
if j>=LO & j<=HI then say ' Bell('right(j, length(HI) )") = " commas($)
end /*j*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg _; do c=length(_)-3 to 1 by -3; _=insert(',', _, c); end; return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
comb: procedure expose !.; parse arg x,y; if x==y then return 1
if x-y<y then y= x - y; if !.x.y\==. then return !.x.y / fact(y)
_= 1; do j=x-y+1 to x; _= _*j; end; !.x.y= _; return _ / fact(y)
/*──────────────────────────────────────────────────────────────────────────────────────*/
fact: procedure expose !.; parse arg x; if !.x\==. then return !.x; != 1
do f=2 for x-1; != ! * f; end; !.x= !; return !

26
Task/Bell-numbers/Racket/bell-numbers.rkt Normal file
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#lang racket
(define (build-bell-row previous-row)
(define seed (last previous-row))
(reverse
(let-values (((reversed _) (for/fold ((acc (list seed)) (prev seed))
((pprev previous-row))
(let ((n (+ prev pprev))) (values (cons n acc) n)))))
reversed)))
(define reverse-bell-triangle
(let ((memo (make-hash '((0 . ((1)))))))
(λ (rows) (hash-ref! memo
rows
(λ ()
(let ((prev (reverse-bell-triangle (sub1 rows))))
(cons (build-bell-row (car prev)) prev)))))))
(define bell-triangle (compose reverse reverse-bell-triangle))
(define bell-number (compose caar reverse-bell-triangle))
(module+ main
(map bell-number (range 15))
(bell-number 50)
(bell-triangle 10))

13
Task/Bell-numbers/Raku/bell-numbers-1.raku Normal file
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my @Aitkens-array = lazy [1], -> @b {
my @c = @b.tail;
@c.push: @b[$_] + @c[$_] for ^@b;
@c
} ... *;
my @Bell-numbers = @Aitkens-array.map: { .head };
say "First fifteen and fiftieth Bell numbers:";
printf "%2d: %s\n", 1+$_, @Bell-numbers[$_] for flat ^15, 49;
say "\nFirst ten rows of Aitken's array:";
.say for @Aitkens-array[^10];

5
Task/Bell-numbers/Raku/bell-numbers-2.raku Normal file
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sub binomial { [*] ($^n … 0) Z/ 1 .. $^p }
my @bell = 1, -> *@s { [+] @s »*« @s.keys.map: { binomial(@s-1, $_) } } … *;
.say for @bell[^15], @bell[50 - 1];

7
Task/Bell-numbers/Raku/bell-numbers-3.raku Normal file
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my @Stirling_numbers_of_the_second_kind =
(1,),
{ (0, |@^last) »+« (|(@^last »*« @^last.keys), 0) } … *
;
my @bell = @Stirling_numbers_of_the_second_kind.map: *.sum;
.say for @bell.head(15), @bell[50 - 1];

18
Task/Bell-numbers/RapidQ/bell-numbers.rapidq Normal file
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' Bell numbers
CONST MAXINDEX% = 14
DIM A&(MAXINDEX% - 1)
FOR I% = 0 TO MAXINDEX% - 1
A&(I%) = 0
NEXT I%
N% = 0
A&(0) = 1
PRINT FORMAT$("B(%2d) = %9d", N%, A&(0))
WHILE N% < MAXINDEX%
A&(N%) = A&(0)
FOR J% = N% TO 1 STEP -1
A&(J% - 1) = A&(J% - 1) + A&(J%)
NEXT J%
N% = N% + 1
PRINT FORMAT$("B(%2d) = %9d", N%, A&(0))
WEND
END

34
Task/Bell-numbers/Ruby/bell-numbers.rb Normal file
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def bellTriangle(n)
tri = Array.new(n)
for i in 0 .. n - 1 do
tri[i] = Array.new(i)
for j in 0 .. i - 1 do
tri[i][j] = 0
end
end
tri[1][0] = 1
for i in 2 .. n - 1 do
tri[i][0] = tri[i - 1][i - 2]
for j in 1 .. i - 1 do
tri[i][j] = tri[i][j - 1] + tri[i - 1][j - 1]
end
end
return tri
end
def main
bt = bellTriangle(51)
puts "First fifteen and fiftieth Bell numbers:"
for i in 1 .. 15 do
puts "%2d: %d" % [i, bt[i][0]]
end
puts "50: %d" % [bt[50][0]]
puts
puts "The first ten rows of Bell's triangle:"
for i in 1 .. 10 do
puts bt[i].inspect
end
end
main()

31
Task/Bell-numbers/Rust/bell-numbers.rust Normal file
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use num::BigUint;
fn main() {
let bt = bell_triangle(51);
// the fifteen first
for i in 1..=15 {
println!("{}: {}", i, bt[i][0]);
}
// the fiftieth
println!("50: {}", bt[50][0])
}
fn bell_triangle(n: usize) -> Vec<Vec<BigUint>> {
let mut tri: Vec<Vec<BigUint>> = Vec::with_capacity(n);
for i in 0..n {
let v = vec![BigUint::from(0u32); i];
tri.push(v);
}
tri[1][0] = BigUint::from(1u32);
for i in 2..n {
tri[i][0] = BigUint::from_bytes_be(&tri[i - 1][i - 2].to_bytes_be());
for j in 1..i {
let added_big_uint = &tri[i][j - 1] + &tri[i - 1][j - 1];
tri[i][j] = BigUint::from_bytes_be(&added_big_uint.to_bytes_be());
}
}
tri
}

60
Task/Bell-numbers/Scala/bell-numbers.scala Normal file
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import scala.collection.mutable.ListBuffer
object BellNumbers {
class BellTriangle {
val arr: ListBuffer[Int] = ListBuffer.empty[Int]
def this(n: Int) {
this()
val length = n * (n + 1) / 2
for (_ <- 0 until length) {
arr += 0
}
this (1, 0) = 1
for (i <- 2 to n) {
this (i, 0) = this (i - 1, i - 2)
for (j <- 1 until i) {
this (i, j) = this (i, j - 1) + this (i - 1, j - 1)
}
}
}
private def index(row: Int, col: Int): Int = {
require(row > 0, "row must be greater than zero")
require(col >= 0, "col must not be negative")
require(col < row, "col must be less than row")
row * (row - 1) / 2 + col
}
def apply(row: Int, col: Int): Int = {
val i = index(row, col)
arr(i)
}
def update(row: Int, col: Int, value: Int): Unit = {
val i = index(row, col)
arr(i) = value
}
}
def main(args: Array[String]): Unit = {
val rows = 15
val bt = new BellTriangle(rows)
println("First fifteen Bell numbers:")
for (i <- 0 until rows) {
printf("%2d: %d\n", i + 1, bt(i + 1, 0))
}
for (i <- 1 to 10) {
print(bt(i, 0))
for (j <- 1 until i) {
print(s", ${bt(i, j)}")
}
println()
}
}
}

48
Task/Bell-numbers/Scheme/bell-numbers.ss Normal file
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; Given the remainder of the previous row and the final cons of the current row,
; extend (in situ) the current row to be a complete row of the Bell triangle.
; Return the final value in the extended row (for use in computing the following row).
(define bell-triangle-row-extend
(lambda (prevrest thisend)
(cond
((null? prevrest)
(car thisend))
(else
(set-cdr! thisend (list (+ (car prevrest) (car thisend))))
(bell-triangle-row-extend (cdr prevrest) (cdr thisend))))))
; Return the Bell triangle of rows 0 through N (as a list of lists).
(define bell-triangle
(lambda (n)
(let* ((tri (list (list 1)))
(triend tri)
(rowendval (caar tri)))
(do ((index 0 (1+ index)))
((>= index n) tri)
(let ((nextrow (list rowendval)))
(set! rowendval (bell-triangle-row-extend (car triend) nextrow))
(set-cdr! triend (list nextrow))
(set! triend (cdr triend)))))))
; Print out the Bell numbers 0 through 19 and 49 thgough 51.
; (The Bell numbers are the first number on each row of the Bell triangle.)
(printf "~%The Bell numbers:~%")
(let loop ((triangle (bell-triangle 51)) (count 0))
(when (pair? triangle)
(when (or (<= count 19) (>= count 49))
(printf " ~2d: ~:d~%" count (caar triangle)))
(loop (cdr triangle) (1+ count))))
; Print out the Bell triangle of 10 rows.
(printf "~%First 10 rows of the Bell triangle:~%")
(let rowloop ((triangle (bell-triangle 9)))
(when (pair? triangle)
(let eleloop ((rowlist (car triangle)))
(when (pair? rowlist)
(printf " ~7:d" (car rowlist))
(eleloop (cdr rowlist))))
(newline)
(rowloop (cdr triangle))))

1
Task/Bell-numbers/Sidef/bell-numbers-1.sidef Normal file
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say 15.of { .bell }

1
Task/Bell-numbers/Sidef/bell-numbers-2.sidef Normal file
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func bell(n) { sum(0..n, {|k| stirling2(n, k) }) }

17
Task/Bell-numbers/Sidef/bell-numbers-3.sidef Normal file
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func bell_numbers (n) {
var acc = []
var bell = [1]
(n-1).times {
acc.unshift(bell[-1])
acc.accumulate!
bell.push(acc[-1])
}
bell
}
var B = bell_numbers(50)
say "The first 15 Bell numbers: #{B.first(15).join(', ')}"
say "The fiftieth Bell number : #{B[50-1]}"

10
Task/Bell-numbers/Sidef/bell-numbers-4.sidef Normal file
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func aitken_array (n) {
var A = [1]
[[1]] + (n-1).of {
A = [A[-1], A...].accumulate
}
}
aitken_array(10).each { .say }

7
Task/Bell-numbers/Sidef/bell-numbers-5.sidef Normal file
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func A((0), (0)) { 1 }
func A(n, (0)) { A(n-1, n-1) }
func A(n, k) is cached { A(n, k-1) + A(n-1, k-1) }
for n in (^10) {
say (0..n -> map{|k| A(n, k) })
}

43
Task/Bell-numbers/Swift/bell-numbers.swift Normal file
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public struct BellTriangle<T: BinaryInteger> {
@usableFromInline
var arr: [T]
@inlinable
public internal(set) subscript(row row: Int, col col: Int) -> T {
get { arr[row * (row - 1) / 2 + col] }
set { arr[row * (row - 1) / 2 + col] = newValue }
}
@inlinable
public init(n: Int) {
arr = Array(repeating: 0, count: n * (n + 1) / 2)
self[row: 1, col: 0] = 1
for i in 2...n {
self[row: i, col: 0] = self[row: i - 1, col: i - 2]
for j in 1..<i {
self[row: i, col: j] = self[row: i, col: j - 1] + self[row: i - 1, col: j - 1]
}
}
}
}
let tri = BellTriangle<Int>(n: 15)
print("First 15 Bell numbers:")
for i in 1...15 {
print("\(i): \(tri[row: i, col: 0])")
}
for i in 1...10 {
print(tri[row: i, col: 0], terminator: "")
for j in 1..<i {
print(", \(tri[row: i, col: j])", terminator: "")
}
print()
}

32
Task/Bell-numbers/V-(Vlang)/bell-numbers.v Normal file
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import math.big
fn bell_triangle(n int) [][]big.Integer {
mut tri := [][]big.Integer{len: n}
for i in 0..n {
tri[i] = []big.Integer{len: i}
for j in 0..i {
tri[i][j] = big.zero_int
}
}
tri[1][0] = big.integer_from_u64(1)
for i in 2..n {
tri[i][0] = tri[i-1][i-2]
for j := 1; j < i; j++ {
tri[i][j] = tri[i][j-1] + tri[i-1][j-1]
}
}
return tri
}
fn main() {
bt := bell_triangle(51)
println("First fifteen and fiftieth Bell numbers:")
for i := 1; i <= 15; i++ {
println("${i:2}: ${bt[i][0]}")
}
println("50: ${bt[50][0]}")
println("\nThe first ten rows of Bell's triangle:")
for i := 1; i <= 10; i++ {
println(bt[i])
}
}

54
Task/Bell-numbers/Visual-Basic-.NET/bell-numbers.vb Normal file
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Imports System.Numerics
Imports System.Runtime.CompilerServices
Module Module1
<Extension()>
Sub Init(Of T)(array As T(), value As T)
If IsNothing(array) Then Return
For i = 0 To array.Length - 1
array(i) = value
Next
End Sub
Function BellTriangle(n As Integer) As BigInteger()()
Dim tri(n - 1)() As BigInteger
For i = 0 To n - 1
Dim temp(i - 1) As BigInteger
tri(i) = temp
tri(i).Init(0)
Next
tri(1)(0) = 1
For i = 2 To n - 1
tri(i)(0) = tri(i - 1)(i - 2)
For j = 1 To i - 1
tri(i)(j) = tri(i)(j - 1) + tri(i - 1)(j - 1)
Next
Next
Return tri
End Function
Sub Main()
Dim bt = BellTriangle(51)
Console.WriteLine("First fifteen Bell numbers:")
For i = 1 To 15
Console.WriteLine("{0,2}: {1}", i, bt(i)(0))
Next
Console.WriteLine("50: {0}", bt(50)(0))
Console.WriteLine()
Console.WriteLine("The first ten rows of Bell's triangle:")
For i = 1 To 10
Dim it = bt(i).GetEnumerator()
Console.Write("[")
If it.MoveNext() Then
Console.Write(it.Current)
End If
While it.MoveNext()
Console.Write(", ")
Console.Write(it.Current)
End While
Console.WriteLine("]")
Next
End Sub
End Module

25
Task/Bell-numbers/Wren/bell-numbers.wren Normal file
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import "/big" for BigInt
import "/fmt" for Fmt
var bellTriangle = Fn.new { |n|
var tri = List.filled(n, null)
for (i in 0...n) {
tri[i] = List.filled(i, null)
for (j in 0...i) tri[i][j] = BigInt.zero
}
tri[1][0] = BigInt.one
for (i in 2...n) {
tri[i][0] = tri[i-1][i-2]
for (j in 1...i) {
tri[i][j] = tri[i][j-1] + tri[i-1][j-1]
}
}
return tri
}
var bt = bellTriangle.call(51)
System.print("First fifteen and fiftieth Bell numbers:")
for (i in 1..15) Fmt.print("$2d: $,i", i, bt[i][0])
Fmt.print("$2d: $,i", 50, bt[50][0])
System.print("\nThe first ten rows of Bell's triangle:")
for (i in 1..10) Fmt.print("$,7i", bt[i])

17
Task/Bell-numbers/XPL0/bell-numbers.xpl0 Normal file
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\Bell numbers
code CrLf=9, IntOut=11, Text=12;
define MaxIndex = 14;
integer A(MaxIndex), I, J, N;
begin
for I:= 0 to MaxIndex - 1 do A(I):= 0;
N:= 0; A(0):= 1;
Text(0, "B("); IntOut(0, N); Text(0, ") = "); IntOut(0, A(0)); CrLf(0);
while N < MaxIndex do
begin
A(N):= A(0);
for J:= N downto 1 do A(J - 1):= A(J - 1) + A(J);
N:= N + 1;
Text(0, "B("); IntOut(0, N); Text(0, ") = "); IntOut(0, A(0)); CrLf(0)
end;
end

7
Task/Bell-numbers/Zkl/bell-numbers-1.zkl Normal file
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fcn bellTriangleW(start=1,wantRow=False){ // --> iterator
Walker.zero().tweak('wrap(row){
row.insert(0,row[-1]);
foreach i in ([1..row.len()-1]){ row[i]+=row[i-1] }
wantRow and row or row[-1]
}.fp(List(start))).push(start,start);
}

2
Task/Bell-numbers/Zkl/bell-numbers-2.zkl Normal file
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println("First fifteen Bell numbers:");
bellTriangleW().walk(15).println();

2
Task/Bell-numbers/Zkl/bell-numbers-3.zkl Normal file
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println("Rows of the Bell Triangle:");
bt:=bellTriangleW(1,True); do(11){ println(bt.next()) }

3
Task/Bell-numbers/Zkl/bell-numbers-4.zkl Normal file
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print("The fiftieth Bell number: ");
var [const] BI=Import("zklBigNum"); // libGMP
bellTriangleW(BI(1)).drop(50).value.println();