Exploring Trees in Data Structures

What is a binary tree?

• A binary tree is a linear data structure with only one child per node.

• A binary tree is a type of graph that can have cycles.

• A binary tree is a tree where each node can have any number of children.

• A binary tree is a tree data structure where each node has at most two children.

How does a binary search tree differ from a binary tree?

• A binary tree can have duplicate nodes, while a binary search tree cannot.

• A binary tree allows for any arrangement of nodes, while a binary search tree follows a strict hierarchy.

• A binary search tree has ordered nodes, while a binary tree does not.

• A binary search tree is always balanced, whereas a binary tree can be unbalanced.

What is the balancing property of an AVL tree?

• The heights of the two child subtrees of any node differ by at most one.

• The heights of the child subtrees can differ by any amount.

• An AVL tree must have at least two child nodes for every parent node.

• The sum of the heights of the two child subtrees must be equal.

Describe the in-order traversal method of a binary tree.

• In-order traversal visits nodes in the order: left subtree, right subtree, root.

• In-order traversal visits nodes in the order: root, left subtree, right subtree.

• In-order traversal visits nodes in the order: left subtree, root, right subtree.

• In-order traversal visits nodes in the order: right subtree, root, left subtree.

What is the time complexity of searching in a binary search tree?

• O(log n) for unbalanced trees, O(n) for balanced trees.

• O(log n) for balanced trees, O(n) for unbalanced trees.

• O(1) for balanced trees, O(log n) for unbalanced trees.

• O(n log n) for both balanced and unbalanced trees.

Explain the concept of a heap in data structures.

• A heap is a type of graph that represents relationships between nodes.

• A heap is a linear data structure that stores elements in a sequential manner.

• A heap is a tree-based data structure that maintains a specific order among its elements, either as a max heap or a min heap.

• A heap is a collection of unordered elements that allows for random access.

What is the difference between a max heap and a min heap?

• A max heap is used for sorting in ascending order, while a min heap is used for sorting in descending order.

• Both max heaps and min heaps allow access to the maximum element only.

• A max heap allows access to the minimum element, while a min heap allows access to the maximum element.

• A max heap allows access to the maximum element, while a min heap allows access to the minimum element.

How do priority queues utilize heaps?

• Priority queues rely on linked lists for efficient element retrieval.

• Heaps are used in priority queues to maintain a fixed size of elements.

• Priority queues use arrays to store elements in sorted order.

• Priority queues utilize heaps to efficiently manage and retrieve elements based on their priority.

What are the three main types of tree traversal methods?

• Level-order, Depth-first, Breadth-first

• In-order, Pre-order, Level-order

• Post-order, Depth-first, Breadth-first

• Pre-order, In-order, Post-order

What is the purpose of balancing trees like AVL trees?

• To increase the overall size of the tree.

• To maintain efficient operations by keeping the tree height balanced.

• To ensure all nodes have two children.

• To allow for faster data retrieval without balancing.