Many candidates wrongly assume they failed to get a position because they got a question wrong. Unless the question was trivial (i.e. what is the height of a tree?), most of the time these questions are intended to see how well you can carefully think through, create, clarify, and debug your code.

For example, when I was reading your writeup as a former interviewer (lots and lots of college candidates for MSFT -- I was a dev manager and did both my own hiring and was flown to colleges for those "interview days" for several years), I was far more worried that you had trouble finding the bug in binary search than that you got it wrong. Everyone gets problems wrong the first time unless they have just implemented them recently. Superior candidates are good at rapidly trying good normal and edge cases, hammering out a good solution, and writing inspired code when given hints at how to improve their solutions.