Everything you need to know about Binary tree data structure

Everything you need to know about Binary tree data structure

Binary tree data structure is a very useful data structure. It is a common topic in coding interviews. In this blog, you will learn everything you need to know about Binary tree data structure.

Why does Binary tree data structure exist?

  • Stores the data in sorted order.
  • Easy to find nodes with binary search algorithm with O(logN) complexity.

If you don't know anything about trees, please read the following blog: Alt Text

Everything you need to know about Binary tree data structure

So,

What is a Binary tree?

A Binary tree is a tree where a parent node can have at most 2 children. It can have 0 children but it will never have 3 children or more. Let's see a picture.

Alt Text

You can see that none of the parent nodes have more than 2 children. They have 0-2 children.

Invalid tree: Alt Text

That is condition 1.

Condition 2 is:

  • Every left child value will be less than the parent value.
  • Every right child value will be greater than the parent value.

Alt Text

You can see that every parent and their children are maintaining the above condition.

What about duplicate values?

Now, it is up to you. You can allow duplicate values in the tree. If so, then you will add them to your left or right side.

What should a node contain?

A node will contain 3 data.

  • Left child node reference.
  • Right child node reference.
  • Actual value.

If a parent has no child or has only one child then the reference value will be null.

Properties of Binary tree

  • The maximum number of nodes at level 'l' of a binary tree is 2^l.

If you don't know about the levels of the height of a tree please read the blog about trees.

Alt Text

  • The maximum number of nodes in a binary tree of height 'h' is 2^h – 1.

Alt Text

  • The minimum number of nodes in a binary tree of height 'h' is h+1

Alt Text

There are some variations of binary trees. They are :

  • Full binary tree.
  • Perfect binary tree.
  • Complete binary tree.
  • Balanced binary tree.

I will talk about them on other blogs.

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