How to resolve the algorithm Numbers which are not the sum of distinct squares step by step in the Quackery programming language

Published on 12 May 2024 09:40 PM
#Quackery

How to resolve the algorithm Numbers which are not the sum of distinct squares step by step in the Quackery programming language

Table of Contents

Problem Statement

Integer squares are the set of integers multiplied by themselves: 1 x 1 = 1, 2 × 2 = 4, 3 × 3 = 9, etc. ( 1, 4, 9, 16 ... ) Most positive integers can be generated as the sum of 1 or more distinct integer squares. Many can be generated in multiple ways: The number of positive integers that cannot be generated by any combination of distinct squares is in fact finite:

Find and show here, on this page, every positive integer than cannot be generated as the sum of distinct squares. Do not use magic numbers or pre-determined limits. Justify your answer mathematically.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Numbers which are not the sum of distinct squares step by step in the Quackery programming language

Source code in the quackery programming language

  [ [] swap
    behead swap
    witheach
      [ 2dup = iff
          drop done
        dip join ]
    join ]                          is unique  ( [ --> [   )

  [ stack ]                         is cut     (   --> s   )

  [ -1 cut put
    1 temp put
    1 swap
    behead swap
     witheach
      [ tuck - -1 = iff
          [ dip 1+
            over temp share
            > if 
              [ over temp replace
                 i^ cut replace ] ]
        else
          [ nip 1 swap ] ]
     2drop
     temp take cut take ]           is maxrun  ( [ --> n n )

  [ [] swap 0 over
    witheach [ bit | ]
    swap -1 peek times
      [ dup i^ bit & not if
          [ dip [ i^ join ] ] ]
    drop ]                          is missing ( [ --> [   )

  1 temp put
  ' [ 0 ]
  1 from
    [ dup witheach
        [ temp share +
          join ]
      sort unique
      dup maxrun drop
      index 2 + temp tally
      temp share > iff
        end done
      2 incr ]
  temp release
  dup maxrun
  nip split
  drop missing
  say "Numbers that are not the sum of distinct squares:"
  cr echo

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