Hash Tables

Problem with Direct Addressing: U may be too large.

For example, consider a compiler symbol table. Symbols here are up to 30 alphabetic characters.

$\mid$U$\mid$ = 26 . 26 . 26 . ... . 26 = 26³⁰ = 2x10⁴² bits.
Note that 1 gigabyte is only 10⁹ bits.

Let K = set of actual keys occurring.
For large $\mid$U$\mid$, $\mid$K$\mid$ is typically $<<\mid$U$\mid$.

Define Table T of size $\mid$K$\mid$
(T is a hash table, where we have chopped up U).