Suppose a binary search tree has been constructed from the following sequence of numbers in the order in which they arrive : 6, 2, 10, 1, 5, 7, 11, 3, 9, 4, 8. Consider the following piece of code :

Show(root) { if (root !=NULL)

{ printf(“% d”, root → key);

show (root → right);

show (root → left);

}

else

return ; 

}

The sequence printed will be : 

The correct answer is Option 1.

Key Points

• The given code performs a traversal on a binary search tree (BST).
• This traversal is a variant of the pre-order traversal, but it visits the right subtree before the left subtree.
• In a pre-order traversal, the nodes are visited in the following order: Root, Right, Left.
• Given the sequence of numbers: 6, 2, 10, 1, 5, 7, 11, 3, 9, 4, 8, the BST is constructed as follows:
  • 6 is the root node.
  • 2 is inserted to the left of 6.
  • 10 is inserted to the right of 6.
  • 1 is inserted to the left of 2.
  • 5 is inserted to the right of 2.
  • 7 is inserted to the left of 10.
  • 11 is inserted to the right of 10.
  • 3 is inserted to the left of 5.
  • 9 is inserted to the right of 7.
  • 4 is inserted to the right of 3.
  • 8 is inserted to the left of 9.
• The traversal in the order: Root, Right, Left results in the sequence: 6, 10, 11, 7, 9, 8, 2, 5, 3, 4, 1.

Additional Information

• In a standard pre-order traversal (Root, Left, Right), the sequence would be different.
• This traversal is useful when you need to process the nodes in a specific order that prioritizes the right subtree over the left subtree.
• Binary search trees provide efficient searching, insertion, and deletion operations with an average time complexity of O(log n).
• Understanding different tree traversal techniques is crucial for various applications in computer science, including parsing expressions and optimizing search algorithms.