Heaps

The video tutorial introduces heaps, focusing on binary heaps, including max and min heaps. It explains the structure of complete binary trees and balanced binary trees, essential for understanding heaps. The tutorial covers heap implementation using arrays and discusses key operations like search, insert, and delete, highlighting their complexities. The video concludes with a brief mention of heap sort and priority queues, setting the stage for further exploration in subsequent lectures.

What is a key characteristic of a max heap?

• The root node is the smallest element.

• The root node is the largest element.

• The tree is always perfectly balanced.

• All nodes have exactly two children.

In a complete binary tree, how are new elements added?

• From left to right at each level.

• From right to left at each level.

• At any random position.

• Only at the root node.

What is the height of a heap with 7 nodes?

• Approximately 2

• Approximately 3

• Approximately 4

• Approximately 5

Why is searching in a heap not recommended?

• Heaps are not sorted.

• Heaps have a high search complexity.

• Heaps only allow searching for the root node.

• Heaps do not store elements.

What is the time complexity of searching for an element in a heap?

• O(log n)

• O(n log n)

• O(n)

• O(1)

What is the primary reason for using arrays to implement heaps?

• Arrays automatically sort elements.

• Arrays allow easy calculation of parent and child indices.

• Arrays are faster than trees.

• Arrays are more memory efficient.

What happens when a new element is inserted into a heap?

• It is added randomly.

• It replaces the largest element.

• It is added at the last position and then heapified.

• It is added at the root.

What is the time complexity of inserting an element into a heap?

• O(n log n)

• O(n)

• O(log n)

• O(1)

Which element is typically removed during a deletion operation in a heap?

• The smallest element

• A random node

• The largest element

• The root node

What is the time complexity of deleting the root node in a heap?

• O(n)

• O(log n)

• O(n log n)

• O(1)