How to resolve the algorithm Gapful numbers step by step in the Forth programming language

Published on 12 May 2024 09:40 PM
#Forth

How to resolve the algorithm Gapful numbers step by step in the Forth programming language

Table of Contents

Problem Statement

Numbers   (positive integers expressed in base ten)   that are (evenly) divisible by the number formed by the first and last digit are known as   gapful numbers.

Evenly divisible   means divisible with   no   remainder.

All   one─   and two─digit   numbers have this property and are trivially excluded.   Only numbers   ≥ 100   will be considered for this Rosetta Code task.

187   is a   gapful   number because it is evenly divisible by the number   17   which is formed by the first and last decimal digits of   187.

About   7.46%   of positive integers are   gapful.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Gapful numbers step by step in the Forth programming language

Source code in the forth programming language

variable                  cnt
: Int>Str                 s>d <# #s #>  ;
: firstDigit              C@  [char] 0 -   ;
: lastDigit               + 1- c@ [char] 0 - ;
: cnt++                   cnt dup  @ 1+ dup rot ! ;
: GapfulNumber?           dup dup Int>Str
                          2dup drop firstDigit 10 * 
                          -rot lastDigit +
                          /mod drop  0= ;
: main                    0 cnt ! 2dup  
                          cr ." First " . ." gapful numbers  >= " .
                          begin  dup cnt @ -
                          while swap GapfulNumber? 
                                if dup cr cnt++  . ." : " . then
                                1+ swap
                          repeat 2drop ;

100        30 main cr
1000000    15 main cr
1000000000 10 main cr

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