Bell numbers: Difference between revisions
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→{{header|ALGOL W}}: fixed trans
m (→{{header|BASIC}}: MaxN instead of confusing MaxIndex. Printing shortened.) |
m (→{{header|ALGOL W}}: fixed trans) |
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Line 296:
4140.0 5017.0 6097.0 7432.0 9089.0 11155.0 13744.0 17007.0 21147.0
21147.0 25287.0 30304.0 36401.0 43833.0 52922.0 64077.0 77821.0 94828.0 115975.0</pre>
=={{header|ALGOL W}}==
{{Trans|ALGOL 68|First 15 numbers only}}
<syntaxhighlight lang="algolw">
begin % show some Bell numbers %
integer MAX_BELL;
MAX_BELL := 15;
begin
procedure showBell ( integer value n, bellNumber ) ;
write( i_w := 2, s_w := 0, n, ": ", i_w := 1, bellNumber );
integer array a ( 0 :: MAX_BELL - 2 );
for i := 1 until MAX_BELL - 2 do a( i ) := 0;
a( 0 ) := 1;
showBell( 1, a( 0 ) );
for n := 0 until MAX_BELL - 2 do begin
% replace a with the next line of the triangle %
a( n ) := a( 0 );
for j := n step -1 until 1 do a( j - 1 ) := a( j - 1 ) + a( j );
showBell( n + 2, a( 0 ) )
end for_n
end
end.
</syntaxhighlight>
{{out}}
<pre>
1: 1
2: 1
3: 2
4: 5
5: 15
6: 52
7: 203
8: 877
9: 4140
10: 21147
11: 115975
12: 678570
13: 4213597
14: 27644437
15: 190899322
</pre>
=={{header|APL}}==
Line 1,620 ⟶ 1,661:
B_25 = 4638590332229999353
</pre>
=={{header|EasyLang}}==
{{trans|Julia}}
<syntaxhighlight lang="easylang">
func bell n .
len list[] n
list[1] = 1
for i = 2 to n
for j = 1 to i - 2
list[i - j - 1] += list[i - j]
.
list[i] = list[1] + list[i - 1]
.
return list[n]
.
for i = 1 to 15
print bell i
.
</syntaxhighlight>
=={{header|Elixir}}==
Line 1,767 ⟶ 1,827:
{{out}}
As above.
=={{header|FutureBasic}}==
FB does not yet offer native support for Big Ints.
<syntaxhighlight lang="futurebasic">
local fn BellNumbers( limit as long )
long j, n = 1
mda(0) = 1
printf @"%2llu. %19llu", n, mda_integer(0)
while ( n < limit )
mda(n) = mda(0)
for j = n to 1 step -1
mda(j - 1) = mda_integer(j - 1) + mda_integer(j)
next
n++
printf @"%2llu. %19llu", n, mda_integer(0)
wend
end fn
fn BellNumbers( 25 )
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
1. 1
2. 2
3. 5
4. 15
5. 52
6. 203
7. 877
8. 4140
9. 21147
10. 115975
11. 678570
12. 4213597
13. 27644437
14. 190899322
15. 1382958545
16. 10480142147
17. 82864869804
18. 682076806159
19. 5832742205057
20. 51724158235372
21. 474869816156751
22. 4506715738447323
23. 44152005855084346
24. 445958869294805289
25. 4638590332229999353
</pre>
=={{header|Go}}==
Line 2,516 ⟶ 2,627:
36401, 43833, 52922, 64077, 77821, 94828, 115975}}
</syntaxhighlight>
=={{header|Maxima}}==
It exists in Maxima the belln built-in function.
Below is another way
<syntaxhighlight lang="maxima">
/* Subfactorial numbers */
subfactorial(n):=block(
subf[0]:1,
subf[n]:n*subf[n-1]+(-1)^n,
subf[n])$
/* Bell numbers implementation */
my_bell(n):=if n=0 then 1 else block(
makelist((1/((n-1)!))*subfactorial(j)*binomial(n-1,j)*(n-j)^(n-1),j,0,n-1),
apply("+",%%))$
/* First 50 */
block(
makelist(my_bell(u),u,0,49),
table_form(%%));
</syntaxhighlight>
{{out}}
<pre>
matrix(
[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],
[4638590332229999353],
[49631246523618756274],
[545717047936059989389],
[6160539404599934652455],
[71339801938860275191172],
[846749014511809332450147],
[10293358946226376485095653],
[128064670049908713818925644],
[1629595892846007606764728147],
[21195039388640360462388656799],
[281600203019560266563340426570],
[3819714729894818339975525681317],
[52868366208550447901945575624941],
[746289892095625330523099540639146],
[10738823330774692832768857986425209],
[157450588391204931289324344702531067],
[2351152507740617628200694077243788988],
[35742549198872617291353508656626642567],
[552950118797165484321714693280737767385],
[8701963427387055089023600531855797148876],
[139258505266263669602347053993654079693415],
[2265418219334494002928484444705392276158355],
[37450059502461511196505342096431510120174682],
[628919796303118415420210454071849537746015761],
[10726137154573358400342215518590002633917247281]
)
</pre>
=={{header|Modula-2}}==
Line 3,954 ⟶ 4,142:
Bell(49) = 10,726,137,154,573,358,400,342,215,518,590,002,633,917,247,281
</pre>
=={{header|RPL}}==
{{works with|HP|48}}
≪ → n
≪ { 1 }
'''WHILE''' 'n' DECR '''REPEAT'''
DUP DUP SIZE GET 1 →LIST
1 3 PICK SIZE '''FOR''' j
OVER j GET OVER j GET + +
'''NEXT''' SWAP DROP
'''END''' HEAD
≫ ≫ ‘<span style="color:blue">BELL</span>’ STO
'''Variant with a better use of the stack'''
Slightly faster then, although more wordy:
≪ → n
≪ { 1 } 1
'''WHILE''' 'n' DECR '''REPEAT'''
DUP 1 →LIST
1 4 PICK SIZE '''FOR''' j
3 PICK j GET ROT + SWAP OVER +
'''NEXT''' ROT DROP SWAP
'''END''' DROP HEAD
≫ ≫ ‘<span style="color:blue">BELL</span>’ STO
≪ {} 1 15 '''FOR''' n n <span style="color:blue">BELL</span> + '''NEXT''' ≫ EVAL
{{out}}
<pre>
1: { 1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 }
</pre>
It makes no sense to display 10 rows of the Bell triangle on a screen limited to 22 characters and 7 lines in the best case.
=={{header|Ruby}}==
Line 4,470 ⟶ 4,690:
{{trans|Go}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
var bellTriangle = Fn.new { |n|
| |||