> The quality of junior engineers I've interviewed has been abysmal. Maybe because we don't have the name nor the high end salary, or maybe our recruiting firms and HR suck in general. My hire/no-hire ratio is literally 50:1.

I'm sorry but to me this part reads like a humorous phrase that's popular in some circles in my region which goes:

"Maybe <list of negative things, usually correct characterizations of the speaker>, but at least <something even worse>"

The companies I worked for used automated coding quizzes like Codility to weed out the worst applicants, but I suspect you're already doing that.

How is them knowing when binary search is useful relevant to what they'll be doing at work should they get hired?