Binary Tree

Preview

1. What is a binary tree, and how is it different from other types of trees?
2. What are the common traversal algorithms used to traverse a binary tree?
3. How do you insert or delete nodes in a binary tree, and what are the associated time complexities?
4. What is the maximum and minimum height of a binary tree, and how is it calculated?
5. How do you determine if a binary tree is balanced, and what are the benefits of a balanced tree in terms of time complexity?

Explain

A binary tree is a tree-based data structure in which each node has at most two children, known as left child and right child. These children are ordered for a parent node, meaning one child precedes the other. The first node of the tree, known as the root, only has references to its two children, while the other nodes can have references to their parent, left child, and right child.

Here is an example of a binary tree:

       1
     /   \
    2     3
   / \   / \
  4   5 6   7

In the above example, 1 is the root node, and its left child is 2, and the right child is 3. The left subtree of 1 contains nodes 2, 4, and 5, while the right subtree contains nodes 3, 6, and 7. Every child node in the tree has, at most, two children. For instance, 4 and 5 have no children on their own, but are both children of 2. 6 and 7 have no children, and they are the children of 3.

Keypoint

1. A binary tree is a tree data structure in which each node has at most two children, referred to as left child and right child.

2. The nodes are arranged in a hierarchical order, with the topmost node being the root node.

3. Each node contains a value or data, and the values of the nodes on the left and right branches satisfy a specific ordering.

4. Binary trees can be of many types, such as balanced, unbalanced, complete, or perfect.

5. In a binary search tree, the left subtree of a node contains only nodes with values less than the node, while the right subtree contains nodes with values greater than the node.

6. Traversing a binary tree can be done in several ways, including pre-order, in-order, or post-order traversal.

7. Binary trees are frequently used in computer science and programming, for example, to construct efficient searching and sorting algorithms.

Review

1. What is the height of a binary tree with 7 nodes?
   Answer: The height of a binary tree with 7 nodes can range from 2 to 3 levels depending on the arrangement of nodes within the tree.

2. What is a binary search tree, and what is its purpose?
   Answer: A binary search tree is a type of binary tree where every node’s left child is less than the parent, and every right child is greater than the parent. It is used to implement searching algorithms efficiently.

3. How do you delete a node from a binary tree?
   Answer: To delete a node from a binary tree, you must first find the node to be deleted. Then, move its right subtree to the parent of the node, and find the leftmost node of the right subtree to attach to the end. Finally, remove the node.

4. What is the difference between a binary tree and a binary search tree?
   Answer: A binary tree is a tree where each node can have at most two children. A binary search tree is a binary tree where each node’s left child is less than the parent, and every right child is greater than the parent.

5. What is a height-balanced binary tree?
   Answer: A height-balanced binary tree is a binary tree where the difference in height between the left and right subtrees of every node is at most one.