Binary Search Tree


Binary Search Tree

Binary Search Tree is one the data structures that features fast searching, sorting, easy insertion and deletion. Its also a sorted version of the binary tree. The tree works by appointing one node and the data following the node is separated by their amount. If the data is bigger than the node then the data goes to the right subtree and on the other hand, the smaller data goes to the left sub tree. The system works recursively so the sub-subbranch of the BST also sorts the data, which makes it easier to search.

Operations

In BST there is 3 operations which is find(x), insert(x), remove(x).
Find = finding the key (x) in the BST
Insert = inserting a new key (x) into the BST
Remove = removing key (x) from BST
·       Find
Because the BST sorts the data adequately, finding a key (x) is very easy. When we commence a search, we will begin at the root and the program will compare the key to the root. If the data is bigger than it will continue to the right subbranch after that it will also compare the key to the data on the right subbranch if the key is smaller than it will go to the left sub subbranch and so on.

·       Insert
When inserting data, the first data begin at the root if key is bigger than the root, insert to the right subbranch, repeat it until an empty node to put the key. Remember that the key will always be a new leaf.


·       Remove
In removing a node, there are three cases which needs to be considered. First, if the key is a leaf, the node can be deleted directly. Second, else if the key is a node with one child delete the node containing the key and connect the child with the new parents. Third, if the key is in a node which has two children, find the right most child of its left subbranch (z) and replace it the value (z) or alternately you can choose the left most child of its right sub tree.



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