Multifactorial: Difference between revisions
m (→{{header|REXX}}: added/changed comments and whitespace, changed indentations.) |
m (added whitespace to the task's preamble, used a larger font to show the formulas.) |
||
| Line 1: | Line 1: | ||
{{task}} |
{{task}} |
||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
: <math>n! = n(n-1)(n-2)...(2)(1)</math> |
::: <math> n! = n(n-1)(n-2)...(2)(1) </math> |
||
</big></big> |
|||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
::: <math> n! = n(n-1)(n-2)...(2)(1) </math> |
|||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
</big></big> |
|||
<br> |
|||
In all cases, the terms in the products are positive integers. |
In all cases, the terms in the products are positive integers. |
||
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold: |
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold: |
||
# Write a function that given n and the degree, calculates the multifactorial. |
# Write a function that given '''n''' and the degree, calculates the multifactorial. |
||
# Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial. |
# Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial. |
||
<br> |
|||
<small>'''Note:''' The [[wp:Factorial#Multifactorials|wikipedia entry on multifactorials]] gives a different formula. This task uses the [http://mathworld.wolfram.com/Multifactorial.html Wolfram mathworld definition].</small> |
<small>'''Note:''' The [[wp:Factorial#Multifactorials|wikipedia entry on multifactorials]] gives a different formula. This task uses the [http://mathworld.wolfram.com/Multifactorial.html Wolfram mathworld definition].</small> |
||
<br><br> |
|||
=={{header|Ada}}== |
=={{header|Ada}}== |
||
Revision as of 08:59, 9 May 2016
You are encouraged to solve this task according to the task description, using any language you may know.
The factorial of a number (written as ), is defined as:
Multifactorials generalize factorials as follows:
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
- Write a function that given n and the degree, calculates the multifactorial.
- Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.
Ada
<lang Ada>with Ada.Text_IO; use Ada.Text_IO; procedure Mfact is
function MultiFact (num : Natural; deg : Positive) return Natural is
Result, N : Integer := num;
begin
if N = 0 then return 1; end if;
loop
N := N - deg; exit when N <= 0; Result := Result * N;
end loop; return Result;
end MultiFact;
begin
for deg in 1..5 loop
Put("Degree"& Integer'Image(deg) &":");
for num in 1..10 loop Put(Integer'Image(MultiFact(num,deg))); end loop;
New_line;
end loop;
end Mfact;</lang>
- Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
ALGOL 68
Translation of C. <lang Algol68>BEGIN
INT highest degree = 5; INT largest number = 10;
CO Recursive implementation of multifactorial function CO
PROC multi fact = (INT n, deg) INT : (n <= deg | n | n * multi fact(n - deg, deg));
CO Iterative implementation of multifactorial function CO
PROC multi fact i = (INT n, deg) INT :
BEGIN
INT result := n, nn := n;
WHILE (nn >= deg + 1) DO
result TIMESAB nn - deg; nn MINUSAB deg
OD;
result
END;
CO Print out multifactorials CO
FOR i TO highest degree DO
printf (($l, "Degree ", g(0), ":"$, i));
FOR j TO largest number DO
printf (($xg(0)$, multi fact (j, i)))
OD OD
END </lang>
- Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
AutoHotkey
<lang AutoHotkey>Loop, 5 {
Output .= "Degree " (i := A_Index) ": "
Loop, 10
Output .= MultiFact(A_Index, i) (A_Index = 10 ? "`n" : ", ")
} MsgBox, % Output
MultiFact(n, d) {
Result := n
while 1 < n -= d
Result *= n
return, Result
}</lang> Output:
Degree 1: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800 Degree 2: 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840 Degree 3: 1, 2, 3, 4, 10, 18, 28, 80, 162, 280 Degree 4: 1, 2, 3, 4, 5, 12, 21, 32, 45, 120 Degree 5: 1, 2, 3, 4, 5, 6, 14, 24, 36, 50
C
<lang c> /* Include statements and constant definitions */
- include <stdio.h>
- define HIGHEST_DEGREE 5
- define LARGEST_NUMBER 10
/* Recursive implementation of multifactorial function */ int multifact(int n, int deg){
return n <= deg ? n : n * multifact(n - deg, deg);
}
/* Iterative implementation of multifactorial function */ int multifact_i(int n, int deg){
int result = n;
while (n >= deg + 1){
result *= (n - deg);
n -= deg;
}
return result;
}
/* Test function to print out multifactorials */ int main(void){
int i, j;
for (i = 1; i <= HIGHEST_DEGREE; i++){
printf("\nDegree %d: ", i);
for (j = 1; j <= LARGEST_NUMBER; j++){
printf("%d ", multifact(j, i));
}
}
} </lang>
- Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
C#
<lang csharp>namespace RosettaCode.Multifactorial {
using System; using System.Linq;
internal static class Program
{
private static void Main()
{
Console.WriteLine(string.Join(Environment.NewLine,
Enumerable.Range(1, 5)
.Select(
degree =>
string.Join(" ",
Enumerable.Range(1, 10)
.Select(
number =>
Multifactorial(number, degree))))));
}
private static int Multifactorial(int number, int degree)
{
if (degree < 1)
{
throw new ArgumentOutOfRangeException("degree");
}
var count = 1 + (number - 1) / degree;
if (count < 1)
{
throw new ArgumentOutOfRangeException("number");
}
return Enumerable.Range(0, count)
.Aggregate(1, (accumulator, index) => accumulator * (number - degree * index));
}
}
}</lang> Output:
1 2 6 24 120 720 5040 40320 362880 3628800 1 2 3 8 15 48 105 384 945 3840 1 2 3 4 10 18 28 80 162 280 1 2 3 4 5 12 21 32 45 120 1 2 3 4 5 6 14 24 36 50
C++
<lang cpp>
- include <algorithm>
- include <iostream>
- include <iterator>
/*Generate multifactorials to 9
Nigel_Galloway November 14th., 2012.
- /
int main(void) {
for (int g = 1; g < 10; g++) {
int v[11], n=0;
generate_n(std::ostream_iterator<int>(std::cout, " "), 10, [&]{n++; return v[n]=(g<n)? v[n-g]*n : n;});
std::cout << std::endl;
}
return 0;
} </lang>
- Output:
1 2 6 24 120 720 5040 40320 362880 3628800 1 2 3 8 15 48 105 384 945 3840 1 2 3 4 10 18 28 80 162 280 1 2 3 4 5 12 21 32 45 120 1 2 3 4 5 6 14 24 36 50 1 2 3 4 5 6 7 16 27 40 1 2 3 4 5 6 7 8 18 30 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 10
Clojure
<lang Clojure>(defn !! [m n]
(->> (iterate #(- % m) n) (take-while pos?) (apply *)))
(doseq [m (range 1 6)]
(prn m (map #(!! m %) (range 1 11))))</lang>
- Output:
1 (1 2 6 24 120 720 5040 40320 362880 3628800) 2 (1 2 3 8 15 48 105 384 945 3840) 3 (1 2 3 4 10 18 28 80 162 280) 4 (1 2 3 4 5 12 21 32 45 120) 5 (1 2 3 4 5 6 14 24 36 50)
Common Lisp
<lang lisp> (defun mfac (n m)
(reduce #'* (loop for i from n downto 1 by m collect i)))
(loop for i from 1 to 10
do (format t "~2@a: ~{~a~^ ~}~%"
i (loop for j from 1 to 10
collect (mfac j i))))
</lang>
- Output:
1: 1 2 6 24 120 720 5040 40320 362880 3628800 2: 1 2 3 8 15 48 105 384 945 3840 3: 1 2 3 4 10 18 28 80 162 280 4: 1 2 3 4 5 12 21 32 45 120 5: 1 2 3 4 5 6 14 24 36 50 6: 1 2 3 4 5 6 7 16 27 40 7: 1 2 3 4 5 6 7 8 18 30 8: 1 2 3 4 5 6 7 8 9 20 9: 1 2 3 4 5 6 7 8 9 10 10: 1 2 3 4 5 6 7 8 9 10
D
<lang d>import std.stdio, std.algorithm, std.range;
T multifactorial(T=long)(in int n, in int m) pure /*nothrow*/ {
T one = 1;
return reduce!q{a * b}(one, iota(n, 0, -m));
}
void main() {
foreach (immutable m; 1 .. 11)
writefln("%2d: %s", m, iota(1, 11)
.map!(n => multifactorial(n, m)));
}</lang>
- Output:
1: 1 2 6 24 120 720 5040 40320 362880 3628800 2: 1 2 3 8 15 48 105 384 945 3840 3: 1 2 3 4 10 18 28 80 162 280 4: 1 2 3 4 5 12 21 32 45 120 5: 1 2 3 4 5 6 14 24 36 50 6: 1 2 3 4 5 6 7 16 27 40 7: 1 2 3 4 5 6 7 8 18 30 8: 1 2 3 4 5 6 7 8 9 20 9: 1 2 3 4 5 6 7 8 9 10 10: 1 2 3 4 5 6 7 8 9 10
Elixir
<lang elixir>defmodule RC do
def multifactorial(n,d) do List.foldl(:lists.seq(n,1,-d), 1, fn x,p -> x*p end) end
end
Enum.each(1..5, fn d ->
multifac = Enum.map(1..10, fn n -> RC.multifactorial(n,d) end)
IO.puts "Degree #{d}: #{inspect multifac}"
end)</lang>
- Output:
Degree 1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800] Degree 2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840] Degree 3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280] Degree 4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120] Degree 5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
Erlang
<lang erlang>-module(multifac). -compile(export_all).
multifac(N,D) ->
lists:foldl(fun (X,P) -> X * P end, 1, lists:seq(N,1,-D)).
main() ->
Ds = lists:seq(1,5),
Ns = lists:seq(1,10),
lists:foreach(fun (D) ->
io:format("Degree ~b: ~p~n",[D, [ multifac(N,D) || N <- Ns]])
end, Ds).</lang>
- Output:
<lang erlang>5> multifac:main(). Degree 1: [1,2,6,24,120,720,5040,40320,362880,3628800] Degree 2: [1,2,3,8,15,48,105,384,945,3840] Degree 3: [1,2,3,4,10,18,28,80,162,280] Degree 4: [1,2,3,4,5,12,21,32,45,120] Degree 5: [1,2,3,4,5,6,14,24,36,50] ok</lang>
ERRE
<lang ERRE> PROGRAM MULTIFACTORIAL
PROCEDURE MULTI_FACT(NUM,DEG->MF)
RESULT=NUM
N=NUM
IF N=0 THEN
MF=1
EXIT PROCEDURE
END IF
LOOP
N-=DEG
EXIT IF N<=0
RESULT*=N
END LOOP
MF=RESULT
END PROCEDURE
BEGIN
PRINT(CHR$(12);)
FOR DEG=1 TO 10 DO
PRINT("Degree";DEG;":";)
FOR NUM=1 TO 10 DO
MULTI_FACT(NUM,DEG->MF)
PRINT(MF;)
END FOR
PRINT
END FOR
END PROGRAM </lang>
Degree 1 : 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2 : 1 2 3 8 15 48 105 384 945 3840 Degree 3 : 1 2 3 4 10 18 28 80 162 280 Degree 4 : 1 2 3 4 5 12 21 32 45 120 Degree 5 : 1 2 3 4 5 6 14 24 36 50 Degree 6 : 1 2 3 4 5 6 7 16 27 40 Degree 7 : 1 2 3 4 5 6 7 8 18 30 Degree 8 : 1 2 3 4 5 6 7 8 9 20 Degree 9 : 1 2 3 4 5 6 7 8 9 10 Degree 10 : 1 2 3 4 5 6 7 8 9 10
F#
<lang fsharp>let rec mfact d = function
| n when n <= d -> n | n -> n * mfact d (n-d)
[<EntryPoint>] let main argv =
let (|UInt|_|) = System.UInt32.TryParse >> function | true, v -> Some v | false, _ -> None
let (maxDegree, maxN) =
match argv with
| [| UInt d; UInt n |] -> (int d, int n)
| [| UInt d |] -> (int d, 10)
| _ -> (5, 10)
let showFor d = List.init maxN (fun i -> mfact d (i+1)) |> printfn "%i: %A" d
ignore (List.init maxDegree (fun i -> showFor (i+1)))
0
</lang>
1: [1; 2; 6; 24; 120; 720; 5040; 40320; 362880; 3628800] 2: [1; 2; 3; 8; 15; 48; 105; 384; 945; 3840] 3: [1; 2; 3; 4; 10; 18; 28; 80; 162; 280] 4: [1; 2; 3; 4; 5; 12; 21; 32; 45; 120] 5: [1; 2; 3; 4; 5; 6; 14; 24; 36; 50]
Forth
<lang>: !n negate swap 1 dup rot do i * over +loop nip ;
- test cr 6 1 ?do 11 1 ?do i j !n . loop cr loop ;</lang>
- Output:
test 1 2 6 24 120 720 5040 40320 362880 3628800 1 2 3 8 15 48 105 384 945 3840 1 2 3 4 10 18 28 80 162 280 1 2 3 4 5 12 21 32 45 120 1 2 3 4 5 6 14 24 36 50 ok
FunL
<lang funl>def multifactorial( n, d ) = product( n..1 by -d )
for d <- 1..5
println( d, [multifactorial(i, d) | i <- 1..10] ))</lang>
- Output:
1, [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800] 2, [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840] 3, [1, 2, 3, 4, 10, 18, 28, 80, 162, 280] 4, [1, 2, 3, 4, 5, 12, 21, 32, 45, 120] 5, [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
GAP
<lang gap>MultiFactorial := function(n, k)
local r;
r := 1;
while n > 1 do
r := r*n;
n := n - k;
od;
return r;
end;
PrintArray(List([1 .. 10], n -> List([1 .. 5], k -> MultiFactorial(n, k)))); [ [ 1, 1, 1, 1, 1 ],
[ 2, 2, 2, 2, 2 ], [ 6, 3, 3, 3, 3 ], [ 24, 8, 4, 4, 4 ], [ 120, 15, 10, 5, 5 ], [ 720, 48, 18, 12, 6 ], [ 5040, 105, 28, 21, 14 ], [ 40320, 384, 80, 32, 24 ], [ 362880, 945, 162, 45, 36 ], [ 3628800, 3840, 280, 120, 50 ] ]</lang>
Go
<lang go>package main
import "fmt"
func multiFactorial(n, k int) int {
r := 1
for ; n > 1; n -= k {
r *= n
}
return r
}
func main() {
for k := 1; k <= 5; k++ {
fmt.Print("degree ", k, ":")
for n := 1; n <= 10; n++ {
fmt.Print(" ", multiFactorial(n, k))
}
fmt.Println()
}
}</lang>
- Output:
degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 degree 2: 1 2 3 8 15 48 105 384 945 3840 degree 3: 1 2 3 4 10 18 28 80 162 280 degree 4: 1 2 3 4 5 12 21 32 45 120 degree 5: 1 2 3 4 5 6 14 24 36 50
Haskell
<lang haskell>mulfac k = 1:s where s = [1 .. k] ++ zipWith (*) s [k+1..]
-- for single n mulfac1 k n = product [n, n-k .. 1]
main = mapM_ (print . take 10 . tail . mulfac) [1..5]</lang>
- Output:
[1,2,6,24,120,720,5040,40320,362880,3628800] [1,2,3,8,15,48,105,384,945,3840] [1,2,3,4,10,18,28,80,162,280] [1,2,3,4,5,12,21,32,45,120] [1,2,3,4,5,6,14,24,36,50]
Icon and Unicon
The following is Unicon specific but can be readily translated into Icon: <lang unicon>procedure main(A)
l := integer(A[1]) | 10 every writeRow(n := !l, [: mf(!10,n) :])
end
procedure writeRow(n, r)
writes(right(n,3),": ") every writes(right(!r,8)|"\n")
end
procedure mf(n, m)
if n <= 0 then return 1 return n*mf(n-m, m)
end</lang>
Sample run:
->mf 5 1: 1 2 6 24 120 720 5040 40320 362880 3628800 2: 1 2 3 8 15 48 105 384 945 3840 3: 1 2 3 4 10 18 28 80 162 280 4: 1 2 3 4 5 12 21 32 45 120 5: 1 2 3 4 5 6 14 24 36 50 ->
J
<lang J>
NB. tacit implementation of the recursive c function
NB. int multifact(int n,int deg){return n<=deg?n:n*multifact(n-deg,deg);}
multifact=: [`([ * - $: ])@.(<~) (a:,<' degree'),multifact table >:i.10
┌─────────┬──────────────────────────────────────┐ │ │ degree │ ├─────────┼──────────────────────────────────────┤ │multifact│ 1 2 3 4 5 6 7 8 9 10│ ├─────────┼──────────────────────────────────────┤ │ 1 │ 1 1 1 1 1 1 1 1 1 1│ │ 2 │ 2 2 2 2 2 2 2 2 2 2│ │ 3 │ 6 3 3 3 3 3 3 3 3 3│ │ 4 │ 24 8 4 4 4 4 4 4 4 4│ │ 5 │ 120 15 10 5 5 5 5 5 5 5│ │ 6 │ 720 48 18 12 6 6 6 6 6 6│ │ 7 │ 5040 105 28 21 14 7 7 7 7 7│ │ 8 │ 40320 384 80 32 24 16 8 8 8 8│ │ 9 │ 362880 945 162 45 36 27 18 9 9 9│ │10 │3628800 3840 280 120 50 40 30 20 10 10│ └─────────┴──────────────────────────────────────┘ </lang>
Java
<lang java>public class MultiFact { private static long multiFact(long n, int deg){ long ans = 1; for(long i = n; i > 0; i -= deg){ ans *= i; } return ans; }
public static void main(String[] args){ for(int deg = 1; deg <= 5; deg++){ System.out.print("degree " + deg + ":"); for(long n = 1; n <= 10; n++){ System.out.print(" " + multiFact(n, deg)); } System.out.println(); } } }</lang>
- Output:
degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 degree 2: 1 2 3 8 15 48 105 384 945 3840 degree 3: 1 2 3 4 10 18 28 80 162 280 degree 4: 1 2 3 4 5 12 21 32 45 120 degree 5: 1 2 3 4 5 6 14 24 36 50
JavaScript
Iterative
<lang JavaScript> function multifact(n, deg){ var result = n; while (n >= deg + 1){ result *= (n - deg); n -= deg; } return result; } </lang>
<lang JavaScript> function test (n, deg) { for (var i = 1; i <= deg; i ++) { var results = ; for (var j = 1; j <= n; j ++) { results += multifact(j, i) + ' '; } console.log('Degree ' + i + ': ' + results); } } </lang>
- Output:
<lang JavaScript> test(10, 5) Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50 </lang>
Recursive
<lang JavaScript> function multifact(n, deg){ return n <= deg ? n : n * multifact(n - deg, deg); } </lang>
Template:Test <lang JavaScript> function test (n, deg) { for (var i = 1; i <= deg; i ++) { var results = ; for (var j = 1; j <= n; j ++) { results += multifact(j, i) + ' '; } console.log('Degree ' + i + ': ' + results); } } </lang>
- Output:
<lang JavaScript> test(10, 5) Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50 </lang>
jq
<lang jq># Input: n
- Output: n * (n - d) * (n - 2d) ...
def multifactorial(d):
. as $n | ($n / d | floor) as $k | reduce ($n - (d * range(0; $k))) as $i (1; . * $i);</lang>
<lang jq># Print out a d-by-n table of multifactorials neatly: def table(d; n):
def lpad(i): tostring | (i - length) * " " + .;
def pp(stream): reduce stream as $i (""; . + ($i | lpad(8)));
range(1; d+1) as $d | "Degree \($d): \( pp(range(1; n+1) | multifactorial($d)) )";</lang>
The specific task: <lang jq>table(5; 10)</lang>
- Output:
<lang sh>$ jq -n -r -f Multifactorial.jq Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 1 3 4 5 18 28 40 162 280 Degree 4: 1 1 1 4 5 6 7 32 45 60 Degree 5: 1 1 1 1 5 6 7 8 9 50</lang>
Julia
multifact calculates the mulitfactorial function iteratively. <lang Julia> function multifact{T<:Integer,U<:Integer}(n::T, k::U)
-1<n && 0<k || throw(DomainError())
1 < k || return factorial(n)
r = one(T)
for i in n:-k:2
r *= i
end
return r
end
khi = 5 nhi = 10 println("Showing multifactorial for n in [1,", nhi, "] and k in [1,", khi, "].") for k = 1:khi
a = Int64[multifact(i, k) for i in 1:nhi]
lab = "n"*"!"^k
println(@sprintf(" %-6s => ", lab), a)
end </lang>
- Output:
Showing multifactorial for n in [1,10] and k in [1,5]. n! => [1,2,6,24,120,720,5040,40320,362880,3628800] n!! => [1,2,3,8,15,48,105,384,945,3840] n!!! => [1,2,3,4,10,18,28,80,162,280] n!!!! => [1,2,3,4,5,12,21,32,45,120] n!!!!! => [1,2,3,4,5,6,14,24,36,50]
Lua
<lang Lua>function multiFact (n, degree)
local fact = 1
for i = n, 2, -degree do
fact = fact * i
end
return fact
end
print("Degree\t|\tMultifactorials 1 to 10") print(string.rep("-", 52)) for d = 1, 5 do
io.write(" " .. d, "\t| ")
for n = 1, 10 do
io.write(multiFact(n, d) .. " ")
end
print()
end</lang>
- Output:
Degree | Multifactorials 1 to 10 ---------------------------------------------------- 1 | 1 2 6 24 120 720 5040 40320 362880 3628800 2 | 1 2 3 8 15 48 105 384 945 3840 3 | 1 2 3 4 10 18 28 80 162 280 4 | 1 2 3 4 5 12 21 32 45 120 5 | 1 2 3 4 5 6 14 24 36 50
Mathematica
<lang mathematica>Multifactorial[n_, m_] := Abs[ Apply[ Times, Range[-n, -1, m]]] Table[ Multifactorial[j, i], {i, 5}, {j, 10}] // TableForm</lang>
- Output:
1: 1 2 6 24 120 720 5040 40320 362880 3628800 2: 1 2 3 8 15 48 105 384 945 3840 3: 1 2 3 4 10 18 28 80 162 280 4: 1 2 3 4 5 12 21 32 45 120 5: 1 2 3 4 5 6 14 24 36 50
МК-61/52
<lang>П1 <-> П0 П2 ИП0 ИП1 1 + - x>=0 23 ИП2 ИП0 ИП1 - * П2 ИП0 ИП1 - П1 БП 04 ИП2 С/П</lang>
Instruction: number ^ degree В/О С/П
Nim
<lang nim># Recursive proc multifact(n, deg): int =
result = (if n <= deg: n else: n * multifact(n - deg, deg))
- Iterative
proc multifactI(n, deg): int =
result = n var n = n while n >= deg + 1: result *= n - deg n -= deg
for i in 1..5:
stdout.write "\nDegree ", i, ": " for j in 1..10: stdout.write multifactI(j, i), " "</lang>
Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
Objeck
<lang objeck> class Multifact {
function : MultiFact(n : Int, deg : Int) ~ Int {
result := n;
while (n >= deg + 1){
result *= (n - deg);
n -= deg;
};
return result; }
function : Main(args : String[]) ~ Nil {
for (i := 1; i <= 5; i+=1;){
IO.Console->Print("Degree ")->Print(i)->Print(": ");
for (j := 1; j <= 10; j+=1;){
IO.Console->Print(' ')->Print(MultiFact(j, i));
};
IO.Console->PrintLine();
};
}
} </lang>
Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
Oforth
<lang Oforth>func: multifact(deg, n) { 1 while(n 0 > ) [ n * n deg - ->n ] }
func: printMulti { | i |
5 loop: i [ System.Out i << " : " << 10 seq map(#[ i multifact]) << cr ]
}</lang>
- Output:
1 : [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800] 2 : [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840] 3 : [1, 2, 3, 4, 10, 18, 28, 80, 162, 280] 4 : [1, 2, 3, 4, 5, 12, 21, 32, 45, 120] 5 : [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
PARI/GP
<lang parigp>fac(n,d)=prod(k=0,(n-1)\d,n-k*d) for(k=1,5,for(n=1,10,print1(fac(n,k)" "));print)</lang>
1 2 6 24 120 720 5040 40320 362880 3628800 1 2 3 8 15 48 105 384 945 3840 1 2 3 4 10 18 28 80 162 280 1 2 3 4 5 12 21 32 45 120 1 2 3 4 5 6 14 24 36 50
Perl
<lang perl>{ # <-- scoping the cache and bigint clause my @cache; use bigint; sub mfact { my ($s, $n) = @_; return 1 if $n <= 0; $cache[$s][$n] //= $n * mfact($s, $n - $s); } }
for my $s (1 .. 10) { print "step=$s: "; print join(" ", map(mfact($s, $_), 1 .. 10)), "\n"; }</lang>
- Output:
step=1: 1 2 6 24 120 720 5040 40320 362880 3628800 step=2: 1 2 3 8 15 48 105 384 945 3840 step=3: 1 2 3 4 10 18 28 80 162 280 step=4: 1 2 3 4 5 12 21 32 45 120 step=5: 1 2 3 4 5 6 14 24 36 50 step=6: 1 2 3 4 5 6 7 16 27 40 step=7: 1 2 3 4 5 6 7 8 18 30 step=8: 1 2 3 4 5 6 7 8 9 20 step=9: 1 2 3 4 5 6 7 8 9 10 step=10: 1 2 3 4 5 6 7 8 9 10
Perl 6
<lang perl6>for 1 .. 5 -> $degree {
sub mfact($n) { [*] $n, *-$degree ...^ * <= 0 };
say "$degree: ", map &mfact, 1..10
}</lang>
- Output:
1: 1 2 6 24 120 720 5040 40320 362880 3628800 2: 1 2 3 8 15 48 105 384 945 3840 3: 1 2 3 4 10 18 28 80 162 280 4: 1 2 3 4 5 12 21 32 45 120 5: 1 2 3 4 5 6 14 24 36 50
PL/I
<lang> multi: procedure options (main); /* 29 October 2013 */
declare (i, j, n) fixed binary;
declare text character (6) static initial ('n!!!!!');
do i = 1 to 5;
put skip edit (substr(text, 1, i+1), '=' ) (A, COLUMN(8));
do n = 1 to 10;
put edit ( trim( multifactorial(n,i) ) ) (X(1), A);
end;
end;
multifactorial: procedure (n, j) returns (fixed(15));
declare (n, j) fixed binary; declare f fixed (15), m fixed(15);
f, m = n;
do while (m > j); f = f * (m-fixed(j)); m = m - j; end;
return (f);
end multifactorial;
end multi; </lang> Output:
n! = 1 2 6 24 120 720 5040 40320 362880 3628800 n!! = 1 2 3 8 15 48 105 384 945 3840 n!!! = 1 2 3 4 10 18 28 80 162 280 n!!!! = 1 2 3 4 5 12 21 32 45 120 n!!!!! = 1 2 3 4 5 6 14 24 36 50
Python
Python: Iterative
<lang python>>>> from functools import reduce >>> from operator import mul >>> def mfac(n, m): return reduce(mul, range(n, 0, -m))
>>> for m in range(1, 11): print("%2i: %r" % (m, [mfac(n, m) for n in range(1, 11)]))
1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800] 2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840] 3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280] 4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120] 5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50] 6: [1, 2, 3, 4, 5, 6, 7, 16, 27, 40] 7: [1, 2, 3, 4, 5, 6, 7, 8, 18, 30] 8: [1, 2, 3, 4, 5, 6, 7, 8, 9, 20] 9: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
10: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] >>> </lang>
Python: Recursive
<lang python>>>> def mfac2(n, m): return n if n <= (m + 1) else n * mfac2(n - m, m)
>>> for m in range(1, 6): print("%2i: %r" % (m, [mfac2(n, m) for n in range(1, 11)]))
1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800] 2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840] 3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280] 4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120] 5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
>>> </lang>
Racket
<lang racket>#lang racket
(define (multi-factorial-fn m)
(lambda (n)
(let inner ((acc 1) (n n))
(if (<= n m) (* acc n)
(inner (* acc n) (- n m))))))
- using (multi-factorial-fn m) as a first-class function
(for*/list ([m (in-range 1 (add1 5))] [mf-m (in-value (multi-factorial-fn m))])
(for/list ([n (in-range 1 (add1 10))]) (mf-m n)))
(define (multi-factorial m n) ((multi-factorial-fn m) n))
(for/list ([m (in-range 1 (add1 5))])
(for/list ([n (in-range 1 (add1 10))]) (multi-factorial m n)))</lang>
Output:
'((1 2 6 24 120 720 5040 40320 362880 3628800) (1 2 3 8 15 48 105 384 945 3840) (1 2 3 4 10 18 28 80 162 280) (1 2 3 4 5 12 21 32 45 120) (1 2 3 4 5 6 14 24 36 50)) '((1 2 6 24 120 720 5040 40320 362880 3628800) (1 2 3 8 15 48 105 384 945 3840) (1 2 3 4 10 18 28 80 162 280) (1 2 3 4 5 12 21 32 45 120) (1 2 3 4 5 6 14 24 36 50))
REXX
This version also handles zero as well as positive integers. <lang rexx>/*REXX program calculates and displays K-fact (multifactorial) of non-negative integers.*/ numeric digits 1000 /*get ka-razy with the decimal digits. */ parse arg num deg . /*get optional arguments from the C.L. */ if num== | num=="," then num=15 /*Not specified? Then use the default.*/ if deg== | deg=="," then deg=10 /* " " " " " " */ say '═══showing multiple factorials (1 ──►' deg") for numbers 1 ──►" num say
do d=1 for deg /*the factorializing (degree) of !'s.*/
_= /*the list of factorials (so far). */
do f=1 for num /* ◄── perform a ! from 1 ───► number.*/
_=_ Kfact(f, d) /*build a list of factorial products.*/
end /*f*/ /* [↑] D can default to unity. */
say right('n'copies("!", d), 1+deg) right('['d"]", 2+length(num) )':' _
end /*d*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ Kfact: procedure; !=1; do j=arg(1) to 2 by -word(arg(2) 1,1); !=!*j; end; return !</lang> output when using the default input:
═══showing multiple factorials (1 ──► 10) for numbers 1 ──► 15
n! [1]: 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
n!! [2]: 1 2 3 8 15 48 105 384 945 3840 10395 46080 135135 645120 2027025
n!!! [3]: 1 2 3 4 10 18 28 80 162 280 880 1944 3640 12320 29160
n!!!! [4]: 1 2 3 4 5 12 21 32 45 120 231 384 585 1680 3465
n!!!!! [5]: 1 2 3 4 5 6 14 24 36 50 66 168 312 504 750
n!!!!!! [6]: 1 2 3 4 5 6 7 16 27 40 55 72 91 224 405
n!!!!!!! [7]: 1 2 3 4 5 6 7 8 18 30 44 60 78 98 120
n!!!!!!!! [8]: 1 2 3 4 5 6 7 8 9 20 33 48 65 84 105
n!!!!!!!!! [9]: 1 2 3 4 5 6 7 8 9 10 22 36 52 70 90
n!!!!!!!!!! [10]: 1 2 3 4 5 6 7 8 9 10 11 24 39 56 75
Ring
<lang ring> see "Degree " + "|" + " Multifactorials 1 to 10" + nl see copy("-", 52) + nl for d = 1 to 5
see "" + d + " " + "| "
for n = 1 to 10
see "" + multiFact(n, d) + " "
next
see nl
next
func multiFact n, degree
fact = 1
for i = n to 2 step -degree
fact = fact * i
next
return fact
</lang> Output:
Degree | Multifactorials 1 to 10 ---------------------------------------------------- 1 | 1 2 6 24 120 720 5040 40320 362880 3628800 2 | 1 2 3 8 15 48 105 384 945 3840 3 | 1 2 3 4 10 18 28 80 162 280 4 | 1 2 3 4 5 12 21 32 45 120 5 | 1 2 3 4 5 6 14 24 36 50
Ruby
<lang ruby> def multifact(n, d)
n.step(1, -d).inject( :* )
end
(1..5).each {|d| puts "Degree #{d}: #{(1..10).map{|n| multifact(n, d)}.join "\t"}"} </lang> output
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
Scala
<lang scala> def multiFact(n : BigInt, degree : BigInt) = (n to 1 by -degree).product
for{
degree <- 1 to 5
str = (1 to 10).map(n => multiFact(n, degree)).mkString(" ")
} println(s"Degree $degree: $str") </lang>
- Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
Seed7
<lang seed7>$ include "seed7_05.s7i";
const func integer: multiFact (in var integer: num, in integer: degree) is func
result
var integer: multiFact is 1;
begin
while num > 1 do
multiFact *:= num;
num -:= degree;
end while;
end func;
const proc: main is func
local
var integer: degree is 0;
var integer: num is 0;
begin
for degree range 1 to 5 do
write("Degree " <& degree <& ": ");
for num range 1 to 10 do
write(multiFact(num, degree) <& " ");
end for;
writeln;
end for;
end func;</lang>
- Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
Sidef
<lang ruby>func mfact(s, n) {
n > 0 ? (n * mfact(s, n-s)) : 1
} 10.times { |s|
say "step=#{s}: #{1..10 -> map {|n| mfact(s, n)}.join(' ')}"
}</lang>
- Output:
step=1: 1 2 6 24 120 720 5040 40320 362880 3628800 step=2: 1 2 3 8 15 48 105 384 945 3840 step=3: 1 2 3 4 10 18 28 80 162 280 step=4: 1 2 3 4 5 12 21 32 45 120 step=5: 1 2 3 4 5 6 14 24 36 50 step=6: 1 2 3 4 5 6 7 16 27 40 step=7: 1 2 3 4 5 6 7 8 18 30 step=8: 1 2 3 4 5 6 7 8 9 20 step=9: 1 2 3 4 5 6 7 8 9 10 step=10: 1 2 3 4 5 6 7 8 9 10
Tcl
<lang tcl>package require Tcl 8.6
proc mfact {n m} {
set mm [expr {-$m}]
for {set r $n} {[incr n $mm] > 1} {set r [expr {$r * $n}]} {}
return $r
}
foreach n {1 2 3 4 5 6 7 8 9 10} {
puts $n:[join [lmap m {1 2 3 4 5 6 7 8 9 10} {mfact $m $n}] ,]
}</lang>
- Output:
1:1,2,6,24,120,720,5040,40320,362880,3628800 2:1,2,3,8,15,48,105,384,945,3840 3:1,2,3,4,10,18,28,80,162,280 4:1,2,3,4,5,12,21,32,45,120 5:1,2,3,4,5,6,14,24,36,50 6:1,2,3,4,5,6,7,16,27,40 7:1,2,3,4,5,6,7,8,18,30 8:1,2,3,4,5,6,7,8,9,20 9:1,2,3,4,5,6,7,8,9,10 10:1,2,3,4,5,6,7,8,9,10
VBScript
<lang vb> Function multifactorial(n,d) If n = 0 Then multifactorial = 1 Else For i = n To 1 Step -d If i = n Then multifactorial = n Else multifactorial = multifactorial * i End If Next End If End Function
For j = 1 To 5 WScript.StdOut.Write "Degree " & j & ": " For k = 1 To 10 If k = 10 Then WScript.StdOut.Write multifactorial(k,j) Else WScript.StdOut.Write multifactorial(k,j) & " " End If Next WScript.StdOut.WriteLine Next </lang>
- Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
Wortel
<lang wortel>@let {
facd &[d n]?{<= n d n @prod@range[n 1 @-d]}
; tacit implementation
facdt ^(!?(/^> .1 ^(@prod @range ~1jdtShj &^!(@- @id))) @,)
; recursive
facdrec &[n d] ?{<= n d n *n !!facdrec -n d d}
; output
l @to 10
~@each @to 5 &n !console.log "Degree {n}: {@join @s !*\facd n l}"
}</lang> Output
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
XPL0
<lang XPL0>code ChOut=8, CrLf=9, IntOut=11;
func MultiFac(N, D); \Return multifactorial of N in degree D int N, D; int F; [F:= 1; repeat F:= F*N;
N:= N-D;
until N <= 1; return F; ];
int I, J; \generate table of multifactorials for J:= 1 to 5 do
[for I:= 1 to 10 do
[IntOut(0, MultiFac(I, J)); ChOut(0, 9\tab\)];
CrLf(0);
]</lang>
- Output:
1 2 6 24 120 720 5040 40320 362880 3628800 1 2 3 8 15 48 105 384 945 3840 1 2 3 4 10 18 28 80 162 280 1 2 3 4 5 12 21 32 45 120 1 2 3 4 5 6 14 24 36 50
zkl
<lang zkl>fcn mfact(n,m){ [n..1,-m].reduce('*,1) } foreach m in ([1..5]){ println("%d: %s".fmt(m,[1..10].apply(mfact.fp1(m)))) }</lang>
- Output:
1: L(1,2,6,24,120,720,5040,40320,362880,3628800) 2: L(1,2,3,8,15,48,105,384,945,3840) 3: L(1,2,3,4,10,18,28,80,162,280) 4: L(1,2,3,4,5,12,21,32,45,120) 5: L(1,2,3,4,5,6,14,24,36,50)