How many hash buckets

Question

If I notice that a hash table (or any other data structure built on a hash table) is filling up, at what point should you build a new table with more buckets. And given n items

Answer 1

Generally, you look out for the load factor (informally, you already said that) which is formally defined as α = n / N, i.e. the ratio of used to total buckets. In order for a hash table to function properly (or at least to reason about its performance in mathematical terms), it should be α < 1.

Everything else is really up to empirical tests: If you see that your hash table doesn't perform good starting at α > 0.5, then be sure to stay under that value. This value also depends on your collision resolution techique. Hashing with chaining may require other load factors than hashing with open addressing. Yet another factor is cache locality. If your table gets too big, it won't fit into the main memory. Since your access into the array is random, loading from cache may become a bottleneck.