Basic Binary Tree

> A javascript implementation of a Binary Tree data structure.

Description

A tree is a data structure that stores elements in a hierarchy these element are referred to as nodes and the lines that connect them as edges. Each node contains a value or data. We can have trees full of intergers or object. We can have personal objects in a tree these objects would be a part of an organization or a family. The top node in the tree is called the root. The root has 2 children and the root is the parent of these nodes. These nodes also have 2 children each if the nodes on the bottom of of the tree these are known as leaf nodes.

In binary trees a root can have up to 2 children. A node with out any children is called a leaf. the height of a leaf node is 0 as we go up in the tree the height increases. The height of a tree is the height of the root node which is the longest path to the leaf. The depth of a root node is 0 as we go down this number increases. The depth of a node is more accurately the number of edges from the root to the node.

A binary search tree is a special kind of binary tree in which all the values in the left subtree is less than the root and the right subtree is greater than the root. The left and right subtree each must also be a binary search tree.

We have a couple of different algorithms for travesing binary trees this algorithm falls into 2 catergories. Breadth First which is also known as level order traversal. Then we have Depth first we have 3 depth first algorithms Pre-order, In-order, and Post-order. The different between these algorithms is in the order in which we visit the root node along with the right and left subtrees.

---

Basic Usage

Install using npm:

``bash
npm install basic-binarytree --save
`

`javascript
const Tree = require('basic-binarytree');
const tree = new Tree();

tree.insert(7);
// --> Inserts 7 as the main root of the Tree

tree.insert(4);
// --> Inserts 4 as a child on the left side of the main root because is is less than the main root. This creates the left subtree.

tree.insert(9);
// --> Inserts 9 as a child on the right side of the main root because is is greater than the main root. This creates the right subtree.

tree.find(4);
// --> true

tree.traversePreOrder();
// --> prints 7, 4, 9

tree.traverseInOrder();
// --> prints 4, 7, 9

tree.traversePostOrder();
// --> prints 4, 9, 7

tree.height();
// --> returns 1

tree.min();
// --> returns 4

tree.max();
// --> returns 9

tree.minBinSearch();
// --> returns 4

tree.maxBinSearch();
// --> returns 9

tree.equals(tree2)
// --> returns false

tree.isBinary();
// --> returns false

tree.kDistance(1);
// --> returns [4, 9]

tree.traverseLevelOrder();
// --> returns 7, 4, 9

tree.getSize();
// --> returns 3

tree.countLeaves();
// --> returns 2

tree.contains(5);
// --> returns false

tree.areSiblings(4, 9);
// --> returns true

tree.getAncestors(9);
// --> returns 7

tree.findInOrderSuccesor(7);
// --> returns 9

``

API

All of the methods Avaliable for a Binary Tree instance:

- ### insert():
Inserts a new node into the tree. If tree is empty this will become the main root of the tree. If not if it is less than the main root it will go on to be the left child or if greater than it will be the right child.

- ### find(value):
This looks to see if the value inserted is in the tree.

- ### traversePreOrder():
In preorder all we did was print the root and moved on to the left subtree and printed its root. We went to the left again and printed that node then made our way to the right. After this subtree is done we went to the main root and repeated the same process for the right subtree.

- ### traverseInOrder():
This is the same concept as the method above expect this one prints in this order left, root, right. So with this algorithm we are going to start from the farest left node and traverse from that left node it's root then to the right node.

- ### traversePostOrder():
This is the same concept as the method above expect this one prints in this order left, right, root.

- ### tree.height();
This returns the height of the tree.

- ### tree.min();
This returns the smallest value in the tree using recursion.

- ### tree.max();
This returns the largest value in a tree using recursion.

- ### tree.minBinSearch();
This returns the smallest value in the tree using a faster algorithm this
is for if the tree is a binary search tree.

- ### tree.maxBinSearch();
This returns the largest value in the tree using a faster algorithm this
is for if the tree is a binary search tree.

- ### tree.equals(other)
This compares another tree object to see if the nodes matches.

- ### tree.isBinary():
this checks to see if the tree is a binary tree or binary search tree.
this is a good tool for interviews because at times we need to find out if a tree is one or the other options.

- ### tree.kDistance(value):
This returns all of the nodes that are a certian distance away from the main root.

- ### tree.traverseLevelOrder():
This prints all of the nodes level by level.

- ### tree.getSize():
This returns the amount of nodes in the tree.

- ### tree.countLeaves():
This counts all of the leafs or all of the nodes at the bottom of the tree.

- ### tree.contains(value):
Checks to see the value inserted is in the tree this is done by using recursion.

- ### tree.areSiblings(first, second):
This check to see if a root has these 2 values as children

- ### tree.getAncestors(value):
This returns all of the roots that are before this node

- ### tree.findInOrderSuccesor(value):
This method returns the next node of the given value in a in-order traversal