How to resolve the algorithm First perfect square in base n with n unique digits step by step in the Quackery programming language

Published on 12 May 2024 09:40 PM
#Quackery

How to resolve the algorithm First perfect square in base n with n unique digits step by step in the Quackery programming language

Table of Contents

Problem Statement

Find the first perfect square in a given base N that has at least N digits and exactly N significant unique digits when expressed in base N. E.G. In base 10, the first perfect square with at least 10 unique digits is 1026753849 (32043²). You may use analytical methods to reduce the search space, but the code must do a search. Do not use magic numbers or just feed the code the answer to verify it is correct.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm First perfect square in base n with n unique digits step by step in the Quackery programming language

Source code in the quackery programming language

 [ dup 1
    [ 2dup > while
      + 1 >>
      2dup / again ]
    drop nip ]            is sqrt       ( n --> n )

  [ base share bit 1 -
    0 rot
    [ dup while
      base share /mod bit
      rot | swap again ]
    drop = ]              is pandigital ( n --> b )

  [ base share
    dup 2 - times
      [ base share *
       i^ 2 + + ] ]       is firstpan   (   --> n )

  [ dup * ]               is squared    ( n --> n )

  11 times
    [ i^ 2 + base put
      firstpan sqrt from
        [ index squared
          pandigital if
            [ index end ] ]
      base share
      say "Base " decimal echo
      base release
      say ": " dup echo
      say "^" 2 echo say " = " 
      squared echo
      cr base release ]

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