Lec 06 - Hash Table

Definition

A Hash Table is a data structure that uses a hash function to efficiently map keys to values, for efficient search/retrieval, insertion, and/or removals. It uses a hash function to map large or even non-Integer keys into a small range of Integer indices (typically [0..hash_table_size-1]).

Doing so, you may notice that the probability of two distinct keys colliding into the same index is relatively high and each of this potential collision needs to be resolved to maintain data integrity.

Hash Function

The ideas of hashing are:

1. Map (some) non-Integer keys (e.g., Strings) to Integers keys,

2. Map large Integers to smaller Integers.

Preliminaries

Suppose we have a hash table of size M where keys are used to identify the data and a specific hash function is used to compute a hash value.

A hash value/hash code of key v is computed from the key v with the use of a hash function to get an Integer in the range 0 to M-1. This hash value is used as the base/home index/address of the Hash Table entry for the data.

Hash Integer — Best Practice

The best practice is,

$$h(v)=v~\%~M$$

e.g., map v into Hash Table of size M slots.

The Hash Table size M is set to be a reasonably large prime not near a power of 2, about 2+ times larger than the expected number of keys N that will ever be used in the Hash Table. This way, the load factor $\alpha=N/M<0.5$ — this will improve Hash Table performance, we shall see later when we deal with the collision.

Hash String — Best Practice

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Collision

Collision happens when two (or more) keys have the same hash value. As we have seen above, the probability of having collision is very high in the Hash Table, thus we need to solve it. There are two major ideas: Closed Addressing versus Open Addressing method.

Closed Addressing

In Closed Addressing, the hash code of a key gives its fixed/closed base address. Collision is resolved by appending the collided keys inside an auxiliary data structure (usually any form of List ADT) identified by the base address.

Open Addressing

In Open Addressing, all hashed keys are located in a single array. The hash code of a key gives its base address. Collision is resolved by checking/probing multiple alternative addresses (hence the name open) in the table based on a certain rule.