Interviewing leaves me depressed. I just spent most of an hour proving I can't verify whether a tree is binary. Mostly, we didn't focus on anything relating d

Interviewing leaves me depressed. I just spent most of an hour proving I can't verify whether a tree is binary. Mostly, we didn't focus on anything relating directly to the position or talk about my experience in any way. We proved that there are holes in my education pertaining to basic CS, that I never encounter on a daily basis as a web developer. I guess the rest of the stuff was taken for granted. I understand that these tests can be important, but I can't help but feel that I will fail to qualify for any position that requires me to hold a host of basic CS algorithms in my head, but that I could still do a good job in the position - because I'm very good at learn as you go, and have learned lots of higher level stuff while building elegant, complex systems - without knowing how to verify a tree's binary nature.