# Chaining

At every location (hash index) in your hash table store a linked list of items. This is better than bucketing as you only use as many nodes as necessary. Some space will still be wasted for the pointers but not nearly as much as bucketing. Table will also not overflow (ie no pre-defined number of buckets to exceed). You will still need to conduct a short linear search of the linked list but if your hash function uniformly distributes the items, the list should not be very long

For chaining, the runtimes depends on $\lambda$. The average length of each chain is $\lambda$. $\lambda$ is the number of expected probes needed for either an insertion or an unsuccessful search. For a successful search it is $1 + {\lambda \over 2}$ probes.