Which of the following traversal methods can be used to obtain a sorted sequence of elements in a binary search tree?PreorderPostorderLevel orderInorder
Question
Which of the following traversal methods can be used to obtain a sorted sequence of elements in a binary search tree?PreorderPostorderLevel orderInorder
Solution
The traversal method that can be used to obtain a sorted sequence of elements in a binary search tree is the Inorder traversal.
Here's why:
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Preorder Traversal: In this method, the order of traversal is Root, Left, Right. This does not guarantee a sorted sequence in a binary search tree.
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Postorder Traversal: In this method, the order of traversal is Left, Right, Root. This also does not guarantee a sorted sequence in a binary search tree.
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Level Order Traversal: This method traverses the tree level by level. This also does not guarantee a sorted sequence in a binary search tree.
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Inorder Traversal: In this method, the order of traversal is Left, Root, Right. When used on a binary search tree, this method will give a sorted sequence of elements. This is because for every node, all the elements in the left subtree are less, and all the elements in the right subtree are more than the node. So, traversing first through the left (smaller elements), then the root (middle element), and finally the right (larger elements) will give a sorted sequence.
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Say that we have a binary search tree with the keys 1, 2, 3, 4, 5, 6, 7. A preorder traversal of the tree prints the keys in the sequence 4, 1, 3, 2, 6, 5, 7. What sequence would be printed by a postorder traversal of the tree?
Implement Inorder, preorder and postorder tree traversal techniques.Unlike linear data structures (Array, Linked List, Queues, Stacks, etc) which have only one logical way to traverse them, trees can be traversed in different ways. The following are the generally used methods for traversing trees:INORDER TRAVERSAL:Traverse the left subtree, i.e., call Inorder(left->subtree)Visit the root.Traverse the right subtree, i.e., call Inorder(right->subtree)PREORDER TRAVERSAL:Visit the root.Traverse the left subtree, i.e., call Preorder(left->subtree)Traverse the right subtree, i.e., call Preorder(right->subtree)Postorder Traversal:Traverse the left subtree, i.e., call Postorder(left->subtree)Traverse the right subtree, i.e., call Postorder(right->subtree)Visit the rootInput Format:The input consists of two lines:The first line contains the number of nodes in the binary tree.The second line contains the values of the nodes, separated by spaces, representing the binary tree.Output Format:First Line contains the Inorder TraversalSecod Line contains the Preorder TravesalThird Line contains th Postorder Traversal Sample input6 5 3 8 1 4 10Sample output1 3 4 5 8 10 5 3 1 4 8 10 1 4 3 10 8 5
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