continued_fraction_to_fraction.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 15 July 2017
# https://github.com/trizen

# Convert a finite continued fraction to a fraction.

#
## Straightforward solution
#
func cfrac2num(f) {
    func (i) {
        (i < f.end) ? (f[i] + 1/__FUNC__(i+1)) : f[i]
    }(0)
}

#
## Computing the numerator and the denominator separately
#
func contfrac2num(f) {

    f = [f[-1], f...]

    func kd((0)) { 1 }
    func kd((1)) { 0 }
    func kd (n) is cached {
        f[n-1]*kd(n - 1) + kd(n - 2)
    }

    func kn((0)) { 0 }
    func kn((1)) { 1 }
    func kn (n) is cached {
        f[n-1]*kn(n - 1) + kn(n - 2)
    }

    kn(f.len) / kd(f.len)
}


var b = [2,3,4,7,8,12,13,4]
say cfrac2num(b).as_frac            # 1141741/494582
say contfrac2num(b).as_frac         # =//=

say ''

var d = [19,2,3,19,42,13,9,66,7]
say cfrac2num(d).as_frac            #=> 6047225352/311237315
say contfrac2num(d).as_frac         # =//=