How to resolve the algorithm Iterated digits squaring step by step in the PureBasic programming language

Published on 12 May 2024 09:40 PM
#Purebasic

How to resolve the algorithm Iterated digits squaring step by step in the PureBasic programming language

Table of Contents

Problem Statement

If you add the square of the digits of a Natural number (an integer bigger than zero), you always end with either 1 or 89: An example in Python:

Or, for much less credit - (showing that your algorithm and/or language is slow): This problem derives from the Project Euler problem 92. For a quick algorithm for this task see the talk page

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Iterated digits squaring step by step in the PureBasic programming language

Source code in the purebasic programming language

OpenConsole()
Procedure is89(x)
  Repeat
    s=0
    While x : s+ x%10*x%10 : x/10 : Wend
    If s=89 : ProcedureReturn 1 : EndIf
    If s=1  : ProcedureReturn 0 : EndIf
    x=s
  ForEver
EndProcedure

Procedure main()
  Dim sums(32*81+1) : sums(0)=1 : sums(1)=0
  
  For n=1 To n+1
    For i=n*81 To 1 Step -1
      For j=1 To 9
        s=j*j : If s>i : Break : EndIf
        sums(i)+sums(i-s)
      Next
    Next
    count89=0
    For i=1 To n*81+1
      If Not is89(i) : Continue : EndIf
      If sums(i)>9223372036854775807-count89
        PrintN("counter overflow for 10^"+Str(n))
        ProcedureReturn 0
      EndIf
      count89+sums(i)
    Next
    PrintN("1->10^"+LSet(Str(n),2,Chr(32))+": "+Str(count89))
  Next  
EndProcedure

start=ElapsedMilliseconds()
main()
Print("elapsed milliseconds= "+Str(ElapsedMilliseconds()-start))
Input()

OpenConsole()
Procedure sum_square_digits(n)
  num=n : sum=0
  While num>0
    digit=num%10
    num=(num-digit)/10
    sum+ digit*digit
  Wend
  ProcedureReturn sum
EndProcedure

Procedure main()
  i=0 : result=0 : count=0
  For i=1 To 1e8
    If Not i=1 Or Not i=89
      result=sum_square_digits(i)
    Else
      result=i
    EndIf
    While Not result=1 And Not result=89
      result=sum_square_digits(result)
    Wend
    If result=89 : count+1 : EndIf
  Next
  PrintN(Str(count))
EndProcedure

start=ElapsedMilliseconds()
main()
Print("elapsed milliseconds: "+Str(ElapsedMilliseconds()-start))
Input()

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