/*
     Fibonacci Numbers to the nth term, using the formula:

            (1 + sqrt(5))^n - (1 - sqrt(5))^n
     F[n] = =================================
                     2^n * sqrt(5)
*/

#include <vector>
#include <cmath>
#include <iostream>
#include <limits>
#include <iomanip>

static std::vector<double> fibonacci_sequence( unsigned int n )
{
    static const double root5 = std::sqrt(5.0) ;
    static const double root5_plus_1 = root5 + 1 ;
    static const double root5_minus_1 = root5 - 1 ;

    std::vector<double> result { 1, 1 } ;

    double a = root5_plus_1 * root5_plus_1 ;
    double b = root5_minus_1 * root5_minus_1 ;
    double denom = root5 * 4 ;

    for( unsigned int i = 2 ; i < n ; ++i )
    {
         a *= root5_plus_1 ;
         b *= root5_minus_1 ;
         denom *= 2 ;

         result.push_back( std::round( (a-b)/denom ) ) ;
    }

    return result ;
}

static unsigned int number_of_terms( unsigned int max, const char* prompt )
{
    std::cout << "please enter " << prompt << ": [2, " << max << "]: " ;
    unsigned int n ;
    if( std::cin >> n && n >= 2 && n <= max ) return n ;

    std::cin.clear() ;
    std::cin.ignore( std::numeric_limits<std::streamsize>::max(), '\n' ) ;
    return number_of_terms( max, prompt ) ;
}

static int ndigits( unsigned int n )
{
    if( n < 10 ) return 1 ;
    else return 1 + ndigits( n/10 ) ;
}

int main()
{
    constexpr unsigned int MAX_TERMS = 50 ;
    const char* const prompt = "number of terms in the fibonacci_sequence" ;

    const auto seq = fibonacci_sequence( number_of_terms( MAX_TERMS, prompt ) ) ;

    std::cout << std::fixed << std::setprecision(0) << '\n' ;
    const int width = ndigits( seq.back() ) + 2 ;

    int cols = 0 ;
    const int maxcols = 60 - width ;
    for( auto v : seq )
    {
        std::cout << std::setw(width) << v ;
        cols += width ;
        if( cols > maxcols ) { std::cout << '\n' ; cols = 0 ; }
    }
    std::cout << '\n' ;
}