#include "big_int/big_integer.bi"

Type JugglerResult
    length As Integer     ' Sequence length
    maxVal As BigInt      ' Maximum value
    maxIdx As Integer     ' Index where maximum occurs
End Type

Function BigIntSqrt(Byref n As BigInt) As BigInt
    If n = 0 Then Return 0

    Dim As BigInt x = n
    Dim As BigInt y = (x + 1) \ 2
    While y < x
        x = y
        y = (x + n \ x) \ 2
    Wend

    Return x
End Function

Function BigIntToStr(Byref n As BigInt) As String
    If n = 0 Then Return "0"

    Dim As String result
    Dim As BigInt tmp = n
    Dim As BigInt ten = 10
    Dim As BigInt digit

    While tmp <> 0
        digit = tmp Mod 10
        result = Chr(Cint(digit) + Asc("0")) & result
        tmp \= 10
    Wend

    Return result
End Function

Function Juggler(n As Uinteger) As JugglerResult
    Dim As JugglerResult result
    Dim As BigInt a = n

    result.length = 0
    result.maxVal = a
    result.maxIdx = 0

    While a <> 1
        If (a Mod 2) = 0 Then
            ' Even: floor(sqrt(a))
            a = BigIntSqrt(a)
        Else
            ' Odd: floor(a^(3/2)) = floor(sqrt(a³))
            Dim As BigInt a_cubed = a * a * a
            a = BigIntSqrt(a_cubed)
        End If

        result.length += 1

        If a > result.maxVal Then
            result.maxVal = a
            result.maxIdx = result.length
        End If
    Wend

    Return result
End Function

' Main program
Print "n   l[n]            h[n]  i[n]"
Print String(31, "-")

For n As Integer = 20 To 39
    Dim As JugglerResult result = Juggler(n)
    Dim As String maxValStr = BigIntToStr(result.maxVal)

    Print Using "##   ##  "; n; result.length;

    If Len(maxValStr) < 14 Then
        Print Space(14 - Len(maxValStr)); maxValStr;
    Else
        Print maxValStr;
    End If

    Print Using "    ##"; result.maxIdx
Next

Sleep