Heap sort algorithm in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the Heap Property

Which of the following best describes the max-heap property used in heap sort?

A All leaf nodes have the same value.

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

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

D The root node is the smallest element in the heap.

💡 Hint

Think about how the largest element is positioned in a max-heap.

In a max-heap, each parent node is greater than or equal to its children, ensuring the largest element is at the root.

📋 Factual

intermediate

Heap Sort Time Complexity

What is the average and worst-case time complexity of the heap sort algorithm?

A O(n) average and O(n^2) worst case.

B O(n log n) for both average and worst cases.

C O(n^2) average and O(n log n) worst case.

D O(log n) average and O(n log n) worst case.

💡 Hint

Consider the cost of building the heap and repeatedly extracting the max element.

Heap sort builds a heap in O(n) and performs n extract-max operations each costing O(log n), resulting in O(n log n) overall.

🔍 Analysis

advanced

Heap Sort Stability

Heap sort is known to be:

A Unstable, because it may change the relative order of equal elements.

B Stable, because it preserves the relative order of equal elements.

C Stable only when implemented with a max-heap.

D Stable only when implemented with a min-heap.

💡 Hint

Think about how heap sort swaps elements during the sorting process.

Heap sort is unstable because it swaps elements that may be equal, changing their original order.

🚀 Application

advanced

Heap Sort Step Output

Given the array [4, 10, 3, 5, 1], what is the array after building the max heap (heapify) step in heap sort?

A [10, 5, 3, 4, 1]

B [10, 4, 3, 5, 1]

C [5, 10, 3, 4, 1]

D [4, 10, 3, 5, 1]

💡 Hint

Build the max heap by ensuring each parent is larger than its children starting from the bottom.

After heapify, the largest element 10 moves to the root, and the array becomes [10, 5, 3, 4, 1].

❓ Reasoning

expert

Heap Sort Space Complexity Reasoning

Why does heap sort have a space complexity of O(1) compared to merge sort's O(n)?

A Heap sort copies the array multiple times but frees memory immediately.

B Heap sort uses a separate array to store sorted elements, but it is optimized to O(1) space.

C Heap sort requires additional recursive calls that use constant space.

D Heap sort sorts the array in place by rearranging elements within the original array without extra storage.

💡 Hint

Consider how heap sort manipulates the input array during sorting.

Heap sort rearranges elements inside the original array without needing extra arrays, so it uses constant extra space.