# Bucketing

Bucketing makes the hash table a 2D array instead of a single dimensional array. Every entry in the array is big enough to hold N items (N is not amount of data. Just a constant).

Problems:

* Lots of wasted space.
* If N is exceeded, another strategy will need to be used
* Not good for memory based implementations but doable if buckets are disk-based)

For bucketing it is alright to have $$\lambda > 1$$. However, the higher $$\lambda$$ is the higher a chance of collision. $$\lambda > 1$$ guarantees there will be at least 1 collision (pigeon hole principle). That will increase both the run time and the possibility of running out of buckets.

For a hash table of N locations and X buckets at each location:

* Successful Search - O(X) worst case
* Unsuccessful Search - O(X) worst case
* Insertion - O(X) - assuming success, bucketing does not have good way to handle non-successful insertions.
* Deletion - O(X)
* Storage:  O(N \* X)