Heaps And Priority Queues : MCQs & PYQs with Explanation

Option A

Option B

A Max-Heap must satisfy two conditions:

• Every parent node must have a value greater than or equal to its children.
• It must be a Complete Binary Tree. This means every level is completely filled except possibly the last level, and the last level must be filled from left to right.

In Option B, the root node is 100, which is greater than its children 80 and 60. Similarly, 80 is greater than its children 40 and 50, and 60 is greater than its children 20 and 30. Thus, every parent node has a value greater than its children.
The tree is also a complete binary tree because all levels before the last are completely filled, and the nodes at the last level are arranged from left to right.

Option B

A Max-Heap is a complete binary tree in which every parent node is greater than or equal to its children. When a heap is constructed from an array (Using Heapify), the largest element becomes the root, and smaller elements move toward the lower levels.
After inserting all the nodes in the max-heap there are total 3-level and right child of root node is 10.

Option B

A max-heap is a binary tree in which every parent node contains a value greater than or equal to its child nodes. In the given heap, the value 20 is first inserted at the next available position at the end of the heap.
After insertion, the heap becomes 23, 17, 14, 6, 13, 10, 1, 5, 20
Now 20 is compared with its parent node 6. Since 20 is greater than 6, both values are swapped. After swapping, 20 becomes the child of 17.
Next, 20 is compared with 17. Since 20 is greater than 17, they are swapped again.
Finally, the max-heap becomes 23, 20, 14, 17, 13, 10, 1, 5, 6
Thus, the heap property is maintained after insertion.

Option D

A max-heap is a complete binary tree in which every parent node is greater than or equal to its children. When a heap is constructed from an array (Using Heapify), the largest element becomes the root, and smaller elements move toward the lower levels.
After inserting all the nodes in the max-heap, the last element is 2.

Option D

A Priority Queue is a special type of queue in which each element is assigned a priority. Unlike a normal queue (FIFO), the element with the highest priority (lowest priority in a min-priority queue) is removed first, regardless of its insertion order.
The most efficient data structure for implementing a priority queue is a Heap Tree. A heap maintains the priority order while allowing insertion and deletion operations to be performed efficiently.
Heap Tree is best for implementing a Priority Queue because the highest priority element is always at the root. Hence, insertion and deletion are efficient O(log n), and accessing the priority element takes only O(1) time.

• The highest (Max Heap) or lowest (Min Heap) priority element is always at the root.
• No need to search the entire data structure to find the highest-priority element.
• Both insertion and deletion remain efficient even for large datasets.