Binary Search Tree Basics

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Questions and Answers

What is the first step when inserting a new key in a binary search tree (BST)?

Insert the new node at the root node.

Start searching from the root until a leaf node is found. (correct)

Always add the new node as a right child.

Start searching from the rightmost node.

When removing a node with two children from a BST, what is the appropriate action according to the algorithm?

Link the child directly to the surrounding nodes.

Remove the node and shift the remaining nodes to the left.

Copy the contents of the inorder successor to the node being removed. (correct)

Delete the node and replace it with the maximum value in the left subtree.

Which case scenario describes a situation where a node to be removed has no children?

Transfer the children to an external queue.

The parent's link should be set to NULL. (correct)

A new child must be added.

The node can be replanted.

What indicates the next node in an inorder traversal of a binary search tree?

The successor node. Signup and view all the answers

In the context of deletion in a BST, what must be ensured when removing a node with one child?

The single child must be linked directly to the parent of the removed node. Signup and view all the answers

Which of the following statements about binary search trees (BST) is true?

All left descendants of a node are smaller than the node. Signup and view all the answers

What does the 'TREE-MINIMUM' function return in the context of BST?

The node with the minimum value in the entire tree. Signup and view all the answers

Which traversal method is used to find the successor in a binary search tree?

Inorder traversal Signup and view all the answers

What is the expected time complexity for lookup, insertion, or deletion operations in a balanced binary search tree?

O(log n) Signup and view all the answers

Which traversal method processes the nodes in the order of parent node first, then left child, and finally right child?

Preorder traversal Signup and view all the answers

In a binary search tree, where would you insert a new node with a value less than the root's key?

In the left subtree Signup and view all the answers

What should be done when deleting a node from a BST that has two children?

Replace it with its in-order predecessor or successor Signup and view all the answers

What property of a binary search tree ensures that each subtree must also be a binary search tree?

There are no duplicate nodes Signup and view all the answers

Which of the following statements about the height of a binary search tree is true?

Average height is O(log n) but worst case can be O(n) Signup and view all the answers

During postorder traversal of a binary search tree, which node is visited last?

The root node Signup and view all the answers

What is a key characteristic of a binary search tree that differentiates it from a regular binary tree?

All nodes are organized by a specific value order Signup and view all the answers

If a binary search tree has a height of O(n), what is likely true about its structure?

It is a linked list Signup and view all the answers

Which function accurately represents the process of deleting a node in a binary search tree?

Replace the node correctly based on its children Signup and view all the answers

What is the primary purpose of the TREE-DELETE-WITHOUT-PARENT function in a BST?

To delete a node while maintaining the tree structure Signup and view all the answers

Which sequence of nodes is traversed first in an inorder traversal of a BST?

Left, Root, Right Signup and view all the answers

After deleting a node with two children from a BST, what is usually the next step?

Replace it with the inorder predecessor or successor Signup and view all the answers

What is the output of a preorder traversal of the sequence 15, 18, 6, 7, 17, 3, 4, 13, 9, 20?

15, 18, 7, 6, 3, 4, 13, 9, 17, 20 Signup and view all the answers

When traversing a BST in postorder, which node is visited last?

The root node Signup and view all the answers

After deleting node 4 from the given BST, what key will replace it if node 4 has a right child?

The leftmost node in the right subtree Signup and view all the answers

Which traversal method first processes the root node?

Preorder traversal Signup and view all the answers

What is a key characteristic of a binary search tree (BST)?

All left descendants are less than the node and all right descendants are greater Signup and view all the answers

What will be the inorder traversal of a BST after sequentially deleting nodes 4, 7, and 15 from it?

A, B, C, D, E, G, H, I Signup and view all the answers

What represents the minimum key during deletion in a BST?

The leftmost leaf node Signup and view all the answers

If a BST node has no children, what occurs during its deletion?

It is simply removed with no further changes Signup and view all the answers

When finding the inorder predecessor of a node in a BST, what must be looked at?

The largest node in its left subtree Signup and view all the answers

In a BST, which traversal method yields nodes in sorted order?

Inorder Signup and view all the answers

In the procedural algorithm for deleting a node, which condition is checked first?

If the current node is NULL Signup and view all the answers

Which of the following is a characteristic of a postorder traversal?

It processes child nodes before the parent Signup and view all the answers

Study Notes

Binary Search Tree (BST)

BSTs, sometimes called ordered or sorted binary trees, store keys in sorted order.
Properties:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- The left and right subtrees each must also be a binary search tree.
- There must be no duplicate nodes.
Operations (lookup, addition, deletion) can be executed efficiently.
Operations traverse the tree from root to leaf, making comparisons to keys, and deciding whether to continue searching in left or right subtrees.
On average, each comparison allows operations to skip about half of the tree, making the time proportional to the logarithm of the number of items stored.
Average height of a BST with n nodes is O(log n).
Worst case height of a BST with n nodes is O(n).
A tree node has:
- data: Data element
- left: Pointer to left node
- right: Pointer to right node
- root: Pointer to root node (initially NULL)
newnode(int element) creates a new node in the tree.

Traversals

Preorder: (parent, left, right)
Inorder: (left, parent, right)
Postorder: (left, right, parent)
Example Preorder traversal: 60, 41, 16, 25, 53, 46, 42, 55, 74 …
Example Inorder traversal: 16, 25, 41, 42, 46, 53, 55, 60 …
Example Postorder traversal: 25, 16, 42, 46, 55, 53, 41, 62…

Searching

TREE-SEARCH(x, k):
- If x is nil or k equals x.key, return x.
- If k < x.key, return TREE-SEARCH(x.left, k).
- Otherwise, return TREE-SEARCH(x.right, k).
ITERATIVE-TREE-SEARCH(x, k):
- While x is not nil and k is not equal to x.key:
 - If k < x.key, x = x.left.
 - Otherwise, x = x.right.
- Return x.
Running time (both iterative and recursive) is O(h), where h is the height of the tree.

Minimum and Maximum

TREE-MINIMUM(x):
- While x.left is not nil, x = x.left.
- Return x.
TREE-MAXIMUM(x):
- While x.right is not nil, x = x.right.
- Return x.

Successor and Predecessor

Successor: next node in inorder traversal.
Predecessor: previous node in inorder traversal.

Insertion

New key is inserted at a leaf node.
Search from root to leaf to find insertion point.
Add the new node as a child of the leaf node.
Duplicate keys are not allowed.
If a key already exists, return the existing node.

Deletion

Search for the node to remove.
Execute the removal algorithm.
- Case 1: No children: Set parent's corresponding link to nil and dispose of the node.
- Case 2: One child: Link the single child directly to the parent of the removed node.
- Case 3: Two children: Find the inorder successor (minimum in the right subtree), copy its contents to the node being removed, and delete the inorder successor from the right subtree.

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Description

This quiz explores the fundamentals of Binary Search Trees (BSTs), including their properties, operations, and efficiency. Learn how BSTs organize data and the implications for searching, adding, and deleting nodes. Test your understanding of these essential data structures in computer science.