Data Structures and Algorithms

# How to Perform Perfect Hashing?

## What is Perfect Hashing?

Perfect hashing is a technique for creating a hash table with no collisions, meaning that each key is uniquely mapped to a single slot in the table. The following steps show how to perform perfect hashing.

## Performing Perfect Hashing

1. Choose a hash function: A hash function is a function that maps a key to an index in the hash table. In perfect hashing, a two-level hash function is used, consisting of an initial hash function that maps the keys to a smaller range of values, followed by a second hash function that maps the reduced range of values to an index in the hash table. The initial hash function should be designed to distribute the keys evenly across the reduced range of values.
2. Build a hash table for the initial hash function: Create a hash table for the initial hash function that uses chaining to handle collisions. The size of the hash table should be proportional to the number of keys that need to be hashed. Each slot in the hash table should store a list of keys that map to the same value under the initial hash function.
3. Find a second hash function: For each slot in the hash table, find a second hash function that maps the keys in that slot to a unique index in the final hash table. This can be done by constructing a smaller hash table for the keys in that slot and using a perfect hashing algorithm to build a hash function that maps the keys to unique indices. There are several perfect hashing algorithms that can be used for this purpose, such as the GPERF algorithm or the CHD algorithm.
4. Build the final hash table: Using the second hash function for each slot in the initial hash table, build the final hash table by assigning each key to the unique index in the table that is obtained by applying the two-level hash function.
5. Lookup key-value pairs: To lookup a key in the perfect hash table, compute the two-level hash function for the key to obtain the index in the final hash table. If the slot at the computed index contains the key, return the associated value. If the slot is empty or contains a different key, the key is not present in the hash table.

## Conclusion

In conclusion, Perfect hashing can be used to achieve O(1) lookup performance for a set of keys, with no collisions. However, the process of building the perfect hash table can be complex and may require significant computational resources, especially for large sets of keys.

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