Build Heap from Array Heapify in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of the heapify process when building a heap from an array?

Heapify rearranges elements to satisfy the heap property, ensuring each parent node is greater (max-heap) or smaller (min-heap) than its children.

beginner

In a zero-based array representation of a heap, what are the indices of the left and right children of the node at index i?

Left child index = 2 * i + 1, Right child index = 2 * i + 2.

intermediate

Why do we start heapifying from the last non-leaf node when building a heap from an array?

Because leaf nodes already satisfy the heap property, starting from the last non-leaf node ensures all subtrees become heaps efficiently.

intermediate

What is the time complexity of building a heap from an unsorted array using heapify?

The time complexity is O(n), where n is the number of elements in the array.

beginner

Explain the difference between max-heap and min-heap in the context of heapify.

Max-heap ensures each parent node is greater than its children; min-heap ensures each parent node is smaller than its children. Heapify adjusts nodes accordingly.

What is the index of the last non-leaf node in a heap stored as an array of size n?

A n/3

B n - 1

C n/2

D n/2 - 1

The last non-leaf node is at index n/2 - 1 in zero-based indexing.

Which of the following best describes the heapify operation?

A Swapping elements to maintain heap property starting from a node downwards

B Sorting the entire array

C Inserting a new element into the heap

D Removing the root element

Heapify fixes the heap property by moving a node downwards if needed.

What is the time complexity of heapify operation on a single node in a heap of size n?

A O(n)

B O(1)

C O(log n)

D O(n log n)

Heapify on a single node takes O(log n) time because it may move down the height of the heap.

When building a max-heap from an array, which property must be true after heapify is applied to a node?

A Node is greater than or equal to its children

B Node is less than its children

C Node is equal to its children

D Node is the smallest element in the heap

In a max-heap, each parent node must be greater than or equal to its children.

Which of these is NOT a step in building a heap from an array using heapify?

A Heapify each node to maintain heap property

B Sort the array in ascending order

C Start heapifying from the last non-leaf node to the root

D Use array indices to find children nodes

Sorting the array is not part of building a heap; heapify rearranges elements to satisfy heap property.

Describe the process of building a heap from an unsorted array using heapify.

Think about fixing subtrees from bottom to top.

Explain why the build heap operation using heapify is more efficient than inserting elements one by one into an empty heap.

Compare total time complexities and approach.