Next-word predictor from bigram counts

You get training sentences as lists of words, for example [["a", "b", "c"], ["a", "s", "d"]].

1. Count, for every word, which words follow it and how often.
2. predict(word) returns the word that most often follows it.
3. Change predict to sample the next word at random, weighted by those counts.
4. The vocabulary is huge. How do you keep memory and prediction time under control?