Traversals | Data Structures
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The document discusses tree traversals, which involve systematically visiting each node of a tree. There are three common traversals: preorder, inorder, and postorder. Preorder visits the node, then left subtree, then right subtree. Inorder visits the left subtree, then the node, then the right subtree. Postorder visits the left subtree, then the right subtree, then the node. The document provides examples of these traversals on sample trees.
Traversals | Data Structures
- 1. The process of systematically visiting all the nodes in a tree and performing some computation at each node in the tree is called a tree traversal.
- 2. H D B N L F J A C E G I K M O H B F N E G O
- 3. Name for each Node: CODE public void displayTree(Node n){ if( n == null ) return; printf(n.data); displayTree(n.left); displayTree(n.right); } •Visit the node •Visit the left subtree, if any. •Visit the right subtree, if any. Preorder (N-L-R) public void displayTree(Node n){ if( n == null ) return; displayTree(n.left); printf(n.data); displayTree(n.right); } •Visit the left subtree, if any. Visit the node •Visit the right subtree, if any. Inorder (L-N-R) public void displayTree(Node n){ if( n == null ) return; displayTree(n.left); displayTree(n.right); printf(n.data); } •Visit the left subtree, if any. •Visit the right subtree, if any. •Visit the node Postorder (L-R-N)
- 4. N-L-R H D B N L F J A C E G I K M O H D A C E L J I K N O
- 5. L-N-R H D B N L F J A C E G I K M O A B C D E F G H I J K L M N O Note: An inorder traversal of a BST visits the keys sorted in increasing order.
- 6. L-R-N H D B N L F J A C E G I K M O A C B E G F D I K J M O N L H
- 7. The children of any node in a binary tree are ordered into a left child and a right child A node can have a left and a right child, a left child only, a right child only, or no children The tree made up of a left child (of a node x) and all its descendents is called the left subtree of x Right subtrees are defined similarly 7 8 9 10 1 3 11 5 4 6 7 12
- 8. Assume: visiting a node is printing its label Preorder: 1 3 5 4 6 7 8 9 10 11 12 Inorder: 4 5 6 3 1 8 7 9 11 10 12 Postorder: 4 6 5 3 8 11 12 10 9 7 1 8 1 3 8 9 11 5 4 6 7 10 12
- 9. Assume: visiting a node is printing its data Preorder: 15 8 2 6 3 7 11 10 12 14 20 27 22 30 Inorder: 2 3 6 7 8 10 11 12 14 15 20 22 27 30 Postorder: 3 7 6 2 10 14 12 11 8 22 30 27 20 15 9 6 15 8 2 3 7 11 10 14 12 20 27 22 30
- 10. Observe the output of the inorder traversal of the BST example two slides earlier It is sorted This is no coincidence As a general rule, if you output the keys (data) of the nodes of a BST using inorder traversal, the data comes out sorted in increasing order 10