Hash Table and Binary Tree


Hash Table

Hash table is a data structure which stores data in an associative manner. Data is stored in an array format in a hash table, where each data has a unique index value. Thus, the insertion and search of a data can be done in a very short period of time, provided we know the index beforehand. These indexes can be found using a technique dubbed Hashing.

Hashing

           Hashing is a technique to convert certain key values from a data to a range of indexes for an array. There are many ways to hash, the simplest ones include taking the value of key then divide them by the number of available addresses, and take the remainder.



            The above code does exactly what the example did. However, one can clearly see a problem with it. If 2 keys result in the same hash, then the first hash will be replaced by the second and so on. This phenomena is called Collisions. Collision resolution can be done in 2 ways: Open Addressing and Closed Addressing

            In an open addressing technique, a hash collision will be resolved by probing, or searching through alternate indexes of the array until a free address is found. The most well-known probe sequence include: Linear Probing (probe interval is fixed – often set to 1), Quadratic Probing (probe interval increases quadratically), and Double Hashing (another hash is performed to determine the interval).

            In a closed addressing technique, instead of directly putting the hash result into an index in the array, it puts it into a linked list pointed by the index of the array. This way, collisions will be handled by adding a new node to a linked list and to look up the key, you only need to do a standard linked list traversal.


Binary Tree
            Binary Tree is a data structure in a form of a tree with only 2 branches/children. Since there are only 2 of them, they are typically called the left child and the right child depending on where the child is to its parent. The end of a branch in a binary tree is called a leaf A binary tree node only contains 3 parts: Data, a pointer to left child, and a pointer to right child.
            Common example of binary trees include:

1.    Full Binary Tree

A binary tree is called full only if all of its nodes have either 0 or 2 children. Binary trees with only 1 node or a node with only 1 child can not be called a full binary tree.

2.    Complete Binary Tree

A binary tree is completed only if all levels, with exception to the last possible, has its nodes completely filled. If the last level is not completely filled, the elements should be as left as possible.

3.    Perfect Binary Tree

A perfect binary tree is one in which all nodes have 2 children and all leaves are at the same level.

4.    Degenerate/Pathological Binary Tree

A tree where each parent node only has 1 child. Identical in behavior to a linked list.

Source:

- https://www.youtube.com/watch?v=KyUTuwz_b7Q
- https://en.wikipedia.org/wiki/Open_addressing
- https://www.geeksforgeeks.org/binary-tree-set-3-types-of-binary-tree/
- https://en.wikipedia.org/wiki/Binary_tree

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