How to resolve the algorithm Left factorials step by step in the J programming language

Published on 12 May 2024 09:40 PM
#J

How to resolve the algorithm Left factorials step by step in the J programming language

Table of Contents

Problem Statement

Left factorials,   !n,   may refer to either   subfactorials   or to   factorial sums; the same notation can be confusingly seen being used for the two different definitions. Sometimes,   subfactorials   (also known as derangements)   may use any of the notations:

(It may not be visually obvious, but the last example uses an upside-down exclamation mark.)

This Rosetta Code task will be using this formula   (factorial sums)   for   left factorial:

Display the left factorials for:

Display the length (in decimal digits) of the left factorials for:

Let's start with the solution:

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

Source code in the j programming language

leftFact=: +/@:!@i."0


   (,. leftFact) i.11
 0      0
 1      1
 2      2
 3      4
 4     10
 5     34
 6    154
 7    874
 8   5914
 9  46234
10 409114
   (,. leftFact) 10*2+i.10x
 20                                                                                                                                                                128425485935180314
 30                                                                                                                                                   9157958657951075573395300940314
 40                                                                                                                                   20935051082417771847631371547939998232420940314
 50                                                                                                                   620960027832821612639424806694551108812720525606160920420940314
 60                                                                                                 141074930726669571000530822087000522211656242116439949000980378746128920420940314
 70                                                                               173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
 80                                                             906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
 90                                         16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
100                      942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
110 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
   (,. #@":@leftFact) 1000*1+i.10x
 1000  2565
 2000  5733
 3000  9128
 4000 12670
 5000 16322
 6000 20062
 7000 23875
 8000 27749
 9000 31678
10000 35656

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