There are two essential factors that you should pay attention to when you are going to design a hash table.
1. Hash Function
The hash function is the most important component of a hash table which is used to map the key to a specific bucket. In the example in the previous article, we use y = x % 5 as a hash function, where x is the key value and y is the index of the assigned bucket.
The hash function will depend on the range of key values and the number of buckets.
Here are some examples of hash functions:
It is an open problem to design a hash function. The idea is to try to assign the key to the bucket as uniformly as you can. Ideally, a perfect hash function will be a one-one mapping between the key and the bucket. However, in most cases, a hash function is not perfect and it is a tradeoff between the amount of buckets and the capacity of a bucket.
2. Collision Resolution
Ideally, if our hash function is a perfect one-one mapping, we will not need to handle collisions. Unfortunately, in most cases, collisions are almost inevitable. For instance, in our previous hash function (y = x % 5), both 1987 and 2 are assigned to bucket 2. That is a collision.
A collision resolution algorithm should solve the following questions:
- How to organize the values in the same bucket?
- What if too many values are assigned to the same bucket?
- How to search for a target value in a specific bucket?
These questions are related to the capacity of the bucket and the number of keys which might be mapped into the same bucket according to our hash function.
Let's assume that the bucket, which holds the maximum number of keys, has N keys.
Typically, if N is constant and small, we can simply use an array to store keys in the same bucket. If N is variable or large, we might need to use height-balanced binary search tree instead.
Reference: https://leetcode.com/explore/learn/card/hash-table/182/practical-applications/1110/
ns13.59.167.61da2
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