How to resolve the algorithm Smith numbers step by step in the PureBasic programming language

Published on 12 May 2024 09:40 PM
#Purebasic

How to resolve the algorithm Smith numbers step by step in the PureBasic programming language

Table of Contents

Problem Statement

Smith numbers are numbers such that the sum of the decimal digits of the integers that make up that number is the same as the sum of the decimal digits of its prime factors excluding 1. By definition, all primes are excluded as they (naturally) satisfy this condition! Smith numbers are also known as   joke   numbers.

Using the number 166 Find the prime factors of 166 which are: 2 x 83 Then, take those two prime factors and sum all their decimal digits: 2 + 8 + 3 which is 13 Then, take the decimal digits of 166 and add their decimal digits: 1 + 6 + 6 which is 13 Therefore, the number 166 is a Smith number.

Write a program to find all Smith numbers below 10000.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Smith numbers step by step in the PureBasic programming language

Source code in the purebasic programming language

DisableDebugger
#ECHO=#True ; #True: Print all results
Global NewList f.i()

Procedure.i ePotenz(Wert.i)  
  Define.i var=Wert, i  
  While var
    i+1
    var/10    
  Wend  
  ProcedureReturn i  
EndProcedure

Procedure.i n_Element(Wert.i,Stelle.i=1)  
  If Stelle>0
    ProcedureReturn (Wert%Int(Pow(10,Stelle))-Wert%Int(Pow(10,Stelle-1)))/Int(Pow(10,Stelle-1))    
  Else
    ProcedureReturn 0    
  EndIf  
EndProcedure

Procedure.i qSumma(Wert.i)  
  Define.i sum, pos  
  For pos=1 To ePotenz(Wert)
    sum+ n_Element(Wert,pos)    
  Next pos  
  ProcedureReturn sum  
EndProcedure

Procedure.b IsPrime(n.i)
  Define.i i=5
  If n<2 : ProcedureReturn #False : EndIf
  If n%2=0 : ProcedureReturn Bool(n=2) : EndIf
  If n%3=0 : ProcedureReturn Bool(n=3) : EndIf
  While i*i<=n
    If n%i=0 : ProcedureReturn #False : EndIf
    i+2
    If n%i=0 : ProcedureReturn #False : EndIf
    i+4
  Wend  
  ProcedureReturn #True
EndProcedure

Procedure PFZ(n.i,pf.i=2)
  If n>1 And n<>pf
    If n%pf=0      
      AddElement(f()) : f()=pf
      PFZ(n/pf,pf)
    Else
      While Not IsPrime(pf+1) : pf+1 : Wend
      PFZ(n,pf+1)
    EndIf
  ElseIf n=pf
    AddElement(f()) : f()=pf
  EndIf   
EndProcedure

OpenConsole("Smith numbers")
;upto=100 : sn=0 : Gosub Smith_loop
;upto=1000 : sn=0 : Gosub Smith_loop
upto=10000 : sn=0 : Gosub Smith_loop
Input()
End

Smith_loop:
  For i=2 To upto
    ClearList(f()) : qs=0
    PFZ(i)
    CompilerIf #ECHO : Print(Str(i)+~": \t") : CompilerEndIf
    ForEach f()
      CompilerIf #ECHO : Print(Str(F())+~"\t") : CompilerEndIf
      qs+qSumma(f())
    Next
    If ListSize(f())>1 And qSumma(i)=qs 
      CompilerIf #ECHO : Print("SMITH-NUMBER") : CompilerEndIf
      sn+1
    EndIf
    CompilerIf #ECHO : PrintN("") : CompilerEndIf
  Next
  Print(~"\n"+Str(sn)+" Smith number up to "+Str(upto))
Return

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