Binary Tree Traversals Overview

Binary Tree Traversals

• A binary tree is a data structure that can be empty or consists of a root node with disjoint left and right subtrees.
• Different ways exist to visit or traverse the nodes in a binary tree. These are called traversals.
• Common traversals include preorder, inorder, and postorder.

Preorder Traversal

• Visit the root node first.
• Traverse the left subtree recursively.
• Traverse the right subtree recursively.
• The process is done in a top-down fashion.
• This traversal method lists nodes in the order of root, left-subtree, and right-subtree.

Inorder Traversal

• Traverse the left subtree recursively.
• Visit the root node.
• Traverse the right subtree recursively.
• This traversal method lists the nodes in the left-subtree, root, then the right-subtree.

Postorder Traversal

• Traverse the left subtree recursively.
• Traverse the right subtree recursively.
• Visit the root node.
• This traversal method lists the nodes in the left-subtree, right-subtree, and then root.

Recursive Implementation of Traversals

• Preorder, inorder, and postorder traversals can be implemented recursively.
• The recursive method typically operates on the root node and makes recursive calls to the left and right subtrees.

Binary Tree Class

• A binary tree class typically defines nodes and methods to handle root nodes and trees.
• A tree can be empty represented by a null root(e.g.:root = null) or has child nodes.
• Example: class BinaryTree<T> { Node<T> root; }

Reconstructing a Binary Tree

• It is not possible to reconstruct a binary tree from only one traversal.
• To reconstruct a binary tree, you need at least the inorder and preorder (or postorder) traversals.
• Inorder tells us how nodes are arranged in left-root-right order.
• Preorder (or postorder) reveals the root.

Exercises

• Binary trees can be built based on given traversals.
• You can find the minimum element(value) in a binary tree by using recursive postorder traversal method.
• Inorder traversal takes linear time complexity, O(n) in a binary tree with n nodes.