How to resolve the algorithm Multifactorial step by step in the J programming language

Published on 12 May 2024 09:40 PM
#J

How to resolve the algorithm Multifactorial step by step in the J programming language

Table of Contents

Problem Statement

The factorial of a number, written as

n !

{\displaystyle n!}

, is defined as

n !

n ( n − 1 ) ( n − 2 ) . . . ( 2 ) ( 1 )

{\displaystyle n!=n(n-1)(n-2)...(2)(1)}

. 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:

Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Multifactorial step by step in the J programming language

Source code in the j programming language

   NB. n multifact degree
   multifact=: */@([ - ] * i.@>.@%)&>
   ('';'       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│
└─────────┴──────────────────────────────────────┘

You may also check:How to resolve the algorithm Shortest common supersequence step by step in the zkl programming language
You may also check:How to resolve the algorithm Bitmap/Write a PPM file step by step in the Python programming language
You may also check:How to resolve the algorithm Brace expansion step by step in the Phix programming language
You may also check:How to resolve the algorithm Palindrome dates step by step in the AppleScript programming language
You may also check:How to resolve the algorithm Hello world/Web server step by step in the Dylan.NET programming language