Heapify operation in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the heapify operation in a heap data structure?

Heapify is the process of rearranging elements in a binary tree to satisfy the heap property, where each parent node is either greater than or equal to (max-heap) or less than or equal to (min-heap) its children.

beginner

Why is heapify important in building a heap?

Heapify ensures that the tree maintains the heap property after insertion or deletion, which is essential for efficient operations like finding the maximum or minimum element quickly.

intermediate

What is the time complexity of the heapify operation on a node?

The time complexity of heapify on a single node is O(log n), where n is the number of nodes in the heap, because it may need to move down the tree height to restore the heap property.

intermediate

How does heapify differ when building a heap from an unordered array versus after inserting a single element?

When building a heap from an unordered array, heapify is applied bottom-up starting from the last non-leaf node, while after inserting a single element, heapify is applied bottom-up (also called 'sift-up') to restore the heap property only along the path of the inserted element.

beginner

What is the difference between max-heapify and min-heapify?

Max-heapify ensures each parent node is greater than or equal to its children, while min-heapify ensures each parent node is less than or equal to its children. Both maintain the heap property but for different heap types.

What does the heapify operation do in a heap?

A Deletes the root node

B Restores the heap property by rearranging nodes

C Searches for an element

D Sorts the entire array

Heapify rearranges nodes to maintain the heap property after changes.

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

A O(1)

B O(n)

C O(log n)

D O(n log n)

Heapify may move down the height of the tree, which is log n.

When building a heap from an unordered array, heapify is applied starting from:

A The last non-leaf node upwards

B The last leaf node

C The root node

D Random nodes

Heapify starts from the last non-leaf node and moves upward to build the heap.

In a max-heap, heapify ensures that:

A Parent nodes are smaller than children

B The heap is sorted

C All nodes have equal values

D Parent nodes are greater than or equal to children

Max-heap property requires parents to be greater than or equal to their children.

Which of the following is NOT a use of heapify?

A Searching for an element in the heap

B Building a heap from an array

C Maintaining heap property after insertion

D Restoring heap after deletion

Heapify does not perform search operations.

Explain the heapify operation and why it is important in maintaining a heap.

Think about how heapify keeps the heap organized after changes.

Describe the difference between max-heapify and min-heapify.

Consider how parent and child nodes compare in each heap type.