Min-heap and max-heap properties in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Min-Heap Property

Which of the following best describes the min-heap property for a binary heap?

A Every parent node is less than or equal to its children nodes.

B Every parent node is greater than or equal to its children nodes.

C All leaf nodes have smaller values than internal nodes.

D The root node has the largest value in the heap.

💡 Hint

Think about which node should have the smallest value in a min-heap.

In a min-heap, the parent node is always smaller than or equal to its children, ensuring the smallest element is at the root.

🧠 Conceptual

intermediate

Max-Heap Root Value

In a max-heap, what can be said about the value of the root node compared to other nodes?

A It is the smallest value in the heap.

B It is always equal to one of the leaf nodes.

C It is the largest value in the heap.

D It is equal to the average of all node values.

💡 Hint

Consider the heap property that defines max-heaps.

The max-heap property ensures the root node has the largest value, as every parent is greater than or equal to its children.

🔍 Analysis

advanced

Heap Property Violation Detection

Given the following array representing a binary heap: [10, 15, 20, 17, 25], which heap property does it violate if any?

Data Structures Theory

Array representation: [10, 15, 20, 17, 25]

A Does not violate min-heap or max-heap properties.

B Violates max-heap property because 15 is less than 10.

C Violates min-heap property because 17 is less than 15.

D Violates min-heap property because 15 is greater than 10.

💡 Hint

Check if parents are smaller or larger than their children according to min-heap or max-heap rules.

In this array, each parent node is less than or equal to its children, so it satisfies the min-heap property and does not violate min-heap or max-heap properties.

❓ Comparison

advanced

Comparing Min-Heap and Max-Heap Structures

Which statement correctly compares min-heaps and max-heaps?

A Max-heaps store elements in descending order in their array representation.

B Both min-heaps and max-heaps are complete binary trees but differ in parent-child value relationships.

C Min-heaps always have smaller height than max-heaps for the same number of elements.

D Min-heaps allow duplicate values but max-heaps do not.

💡 Hint

Think about the shape and ordering rules of heaps.

Both min-heaps and max-heaps are complete binary trees. The difference lies in whether parents are smaller (min-heap) or larger (max-heap) than their children.

❓ Reasoning

expert

Effect of Inserting an Element in a Min-Heap

When inserting a new element into a min-heap, which of the following best describes the process to maintain the min-heap property?

A Insert the element at the root and swap downwards until the property is restored.

B Insert the element at the root and swap upwards until the property is restored.

C Insert the element at the last position and swap downwards until the property is restored.

D Insert the element at the last position and swap upwards until the property is restored.

💡 Hint

Consider where new elements are added and how to restore heap order.

New elements are added at the last position (bottom-right) and then swapped upwards (heapify up) to maintain the min-heap property.