binary tree

Find height or depth of a binary tree

Length of the longest path from the root node to a leaf node is the height of the binary tree. We find it in linear time using a recursive algorithm

Algorithms

Copy a binary tree where each node has a random pointer

We explored an algorithm to copy a binary tree with an additional pointer which points to any random node in the tree. We explored two techniques Naive solution using 2 traversals and Efficient solution using hashing.

Algorithms

Learn how to traverse a Binary Tree (Inorder , Preorder , Postorder)

In this article we will learn three Depth first traversals namely inorder, preorder and postorder and their use. These three types of traversals generally used in different types of binary tree. In summary, Inorder: left, root, right; Preorder: root, left, right and Postorder: left, right, root

Algorithms

Algorithm for finding the minimum number of swaps required to convert a binary tree to binary search tree

We developed an algorithm for finding the minimum number of swaps required to convert a binary tree to binary search tree. The Idea is do the inorder traversal of binary tree and store it in an array.Then find the minimum number of swaps require to sort an array which is the output we want.

Data Structures

A binary tree is a tree data structure in which each node has upto two children (that is a maximum of two children nodes), which are referred to as the left child and the right child. Implementation and applications of binary tree

Sorting Algorithms

Heap Sort

Heapsort is an efficient in-place comparison based sorting algorithm with O(N log N) time complexity and uses a data structure to achieve it. It uses a complete Binary Heap data structure to sort the elements depending on whether the heap is Min Heap (ascending) or Max heap (descending).

Data Structures

Treap / Randomized cartesian tree

A treap is a height balanced binary tree with heap properties. It is used to store a sequence in a tree, which allows for various applications like searching. It takes O(log N) time complexity for search, insert and delete operations and takes O(N) space complexity

Data Structures

Cartesian Tree

A Cartesian tree is a binary rooted tree data structure that can answer range queries can be answered by finding least common ancestors in the tree. An inorder traversal of the tree would give the original sequence used to form the tree. It is used as binary search tree for an ordered sequence

Data Structures

How many labeled and unlabeled binary tree can be there with N nodes?

In this article, we see how many labeled and unlabeled binary trees we can have with N nodes. This is related to the Catalan Numbers. Binary Tree : A tree whose elements have 0 or 1 or 2 children is called a binary tree.

binary tree

Properties of a Binary Tree

properties of Binary Tree are as follows: The maximum number of nodes at level ‘L’ of a binary tree is 2L-1, Maximum number of nodes in a binary tree of height ‘H’ is 2H – 1, In a Binary Tree with N nodes, minimum possible height or minimum number of levels is ⌈ Log2(N+1) ⌉