project-euler/Sidef/751 Concatenation Coincidence.sf

#!/usr/bin/ruby

# Author: Trizen
# Date: 23 March 2022
# https://github.com/trizen

# Concatenation Coincidence
# https://projecteuler.net/problem=751

# Runtime: 0.454s

func b(n, t) is cached {
    return t if (n == 1)
    floor(b(n-1, t)) * (b(n-1, t) - floor(b(n-1, t)) + 1)
}

assert_eq(
    1..10 -> map {|n| b(n, 2.956938891377988).floor }
    3..12 -> map { .fib }
)

define PREC   = 24
define PREFIX = 2

func f(t) {
    var terms = []

    1..PREC -> lazy.while {|k|
        terms << b(k, t).floor
        terms.join.len <= PREC
    }

    var lead = terms.shift
    var dec = Num(terms.join)

    var x = lead+(dec / 10**(dec.ilog10+1))
    say "#{t} <=> #{x}"
    return x
}

var theta = bsearch_le(10**PREC, 10**(PREC+1), {|k|
    var t = PREFIX+(k / 10**(k.ilog10+1))
    t <=> f(t)
})

say ("Answer: ", Num("#{PREFIX}.#{theta}").round(-PREC))