project-euler/Sidef/800 Hybrid Integers.sf

#!/usr/bin/ruby

# Author: Trizen
# Date: 03 November 2022
# https://github.com/trizen

# Hybrid Integers
# https://projecteuler.net/problem=800

# Runtime: 26 seconds.

func C(a, b) {

    var limit = log(a)*b
    var count = 0

    for (var p = 2; true; p.next_prime!) {

        var p_log = p.log

        #~ var k = bsearch_inverse(p+1, limit/p_log, {|q|
            #~ (p_log*q + q.log*p) <~> limit
        #~ }) \\ break

        var k = bsearch_le(p+1, limit/p_log, {|q|
            (p_log*q + q.log*p) <=> limit
        })

        count += (prime_count(p+1, k) || break)
    }

    return count
}

say C(800, 1)           #=> 2
say C(163, 165)         #=> 1000
say C(800, 800)         #=> 10790
say C(800800, 800800)