Hashtable

Hashing

• Hashing is designed to solve the problem of needing to efficiently find or store an item in a collection. It is a technique to narrow down the search space.
• Hashing means using some function or algorithm to map object data to some representative integer value.
• One basic approach. Calculate a hash for each key and store the hash value in an array index of the same value. Store the key, value pair in the same index positions in other arrays.
• However, this approach suffers from wasted space in the array - for those array indexes for which corresponding hash values are never generated.
• Another problem is collisions - a single hash value can represent many keys.
• How to reduce the no. of collisions - increase the address space. Therefore, most hashing algorithms are a trade-off between space and time efficiency.
• To solve wasted space use : hashcode modulo arraysize.
• To solve collisions use linkedlists to store key->value pairs for each hash value.
• Also choosing prime numbers as the hash table size gives better results.

Hash function properties

• Be able to distribute the keys evenly over the range of positions in the array.
• Distribute the keys over a larger range of values.
• Combining the above two, Ideally a hash function should distribute hash codes evenly over the range of integers.

Collision Resolution

• Now when we calculate a hash for a key & find that there is a collision, we can resize the array & store all the keys separately.
• However, this is expensive & there will be lots of wasted space in the array.
• One solution to collision is called linear probing. i.e. Just place the item in the next available slot.
• Another solution is use buckets to store more than one item at each position.
• However the buckets can have large no. of items which makes searching through them also costly.
• We need to redistribute evenly between the greater no. of buckets, leading to a decrease in the size of each individual bucket.
• When to resize ? Monitor the load factor. No. of values/No. of buckets (No. of array indices). If it is too high, then some of the buckets are too large.
• A good load factor is 0.75 - 75% full.