Insertion in Binary Tree

What is Binary Tree?

Binary tree is a tree data structure(non-linear) in which each node can have at most two children which are referred to as the left child and the right child....

Representation of Binary Tree

Each node in a Binary Tree has three parts:...

Types of Binary Tree

Binary Tree can be classified into multiples types based on multiple factors:...

Operations On Binary Tree

1. Insertion in Binary Tree...

1. Insertion in Binary Tree

We can insert a node anywhere in a binary tree by inserting the node as the left or right child of any node or by making the node as root of the tree....

2. Traversal of Binary Tree

Traversal of Binary Tree involves visiting all the nodes of the binary tree. Tree Traversal algorithms can be classified broadly into two categories:...

3. Deletion in Binary Tree

We can delete any node in the binary tree and rearrange the nodes after deletion to again form a valid binary tree....

4. Searching in Binary Tree

We can search for an element in the node by using any of the traversal techniques....

Auxiliary Operations On Binary Tree

Finding the height of the treeFind level of a node in a Binary treeFinding the size of the entire tree...

Implementation of Binary Tree

Below is the code for insertion, deletion and traversal of the binary tree:...

Complexity Analysis of Binary Tree Operations

Operations Time Complexity Space Complexity Insertion O(N)O(N) Preorder TraversalO(N)O(N) Inorder Traversal O(N) O(N) Postorder TraversalO(N) O(N) Level Order TraversalO(N) O(N) Deletion O(N) O(N) Searching O(N) O(N)...

Advantages of Binary Tree

Efficient Search: Binary trees are efficient when searching for a specific element, as each node has at most two child nodes, allowing for binary search algorithms to be used.Memory Efficient: Binary trees require lesser memory as compared to other tree data structures, therefore they are memory-efficient.Binary trees are relatively easy to implement and understand as each node has at most two children, left child and right child....

Disadvantages of Binary Tree

Limited structure: Binary trees are limited to two child nodes per node, which can limit their usefulness in certain applications. For example, if a tree requires more than two child nodes per node, a different tree structure may be more suitable.Unbalanced trees: Unbalanced binary trees, where one subtree is significantly larger than the other, can lead to inefficient search operations. This can occur if the tree is not properly balanced or if data is inserted in a non-random order.Space inefficiency: Binary trees can be space inefficient when compared to other data structures. This is because each node requires two child pointers, which can be a significant amount of memory overhead for large trees.Slow performance in worst-case scenarios: In the worst-case scenario, a binary tree can become degenerate or skewed, meaning that each node has only one child. In this case, search operations can degrade to O(n) time complexity, where n is the number of nodes in the tree....

Applications of Binary Tree

Binary Tree can be used to represent hierarchical data.Huffman Coding trees are used in data compression algorithms.Priority Queue is another application of binary tree that is used for searching maximum or minimum in O(1) time complexity.Useful for indexing segmented at the database is useful in storing cache in the system,Binary trees can be used to implement decision trees, a type of machine learning algorithm used for classification and regression analysis....

Frequently Asked Questions on Binary Tree

1. What is a binary tree?...

Conclusion:

Tree is a hierarchical data structure. Main uses of trees include maintaining hierarchical data, providing moderate access and insert/delete operations. Binary trees are special cases of tree where every node has at most two children....