Data Structures and Algorithms The Complete Masterclass - Heaps

The video tutorial introduces heaps, focusing on binary heaps, and explains their structure and properties. It covers the concept of complete binary trees and how they relate to heaps, including the calculation of tree height. The tutorial discusses heap operations such as insertion and deletion, highlighting their complexities. It concludes with a brief mention of heapsort and priority queues, setting the stage for future lessons.

What is a key characteristic of a Max Heap?

• The root node is the largest element.

• The root node is the smallest element.

• All nodes have exactly two children.

• The tree is always perfectly balanced.

In a complete binary tree, where is a new element added?

• At the root node.

• At the rightmost position of the last level.

• At the leftmost position of the last level.

• At any random position.

Why is it important for a heap to maintain a balanced binary tree structure?

• To ensure the tree is always full.

• To maintain the logarithmic height of the tree.

• To ensure all nodes have two children.

• To allow for efficient searching.

What is the main disadvantage of searching in a heap?

• It can only be done in a Max Heap.

• It can only be done in a Min Heap.

• It requires O(N) time complexity.

• It requires O(log N) time complexity.

How is the left child of a node at index 'i' in a heap represented in an array?

• i - 1

• i / 2

• 2 * i + 2

• 2 * i + 1

How is a heap typically implemented in programming?

• Using a queue.

• Using a stack.

• Using a linked list.

• Using an array.

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

• O(N)

• O(1)

• O(log N)

• O(N log N)

During deletion in a heap, which element is typically removed?

• Any random node.

• The root node.

• The rightmost leaf node.

• The leftmost leaf node.

What happens if a new element is larger than its parent in a Max Heap during insertion?

• The element is ignored.

• The element is removed.

• The element is swapped with its parent.

• The element is placed at the root.

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

• O(1)

• O(N log N)

• O(log N)

• O(N)