If the hiring managers really want to see some code, a take home problem seems like a good compromise to me. I can implement any arbitrary algorithm if I am allowed a little time and some reference material. In my day to day work, it's a pretty rare event where I need to implement an algorithm from scratch (I do mostly Java and Clojure). The longer I go without having to code one of these algorithms up, the harder they are for me to remember.
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If the hiring managers really want to see some code, a take home problem seems like a good compromise to me. I can implement any arbitrary algorithm if I am allowed a little time and some reference material. In my day to day work, it's a pretty rare event where I need to implement an algorithm from scratch (I do mostly Java and Clojure). The longer I go without having to code one of these algorithms up, the harder they are for me to remember.