Heap extraction (bubble down) in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main purpose of the bubble down process in heap extraction?

The bubble down process restores the heap property after removing the root by moving the new root element down the tree until it is in the correct position.

beginner

In a max-heap, after extracting the root, which element replaces the root before bubbling down?

The last element in the heap replaces the root before the bubble down process begins.

intermediate

Describe the condition that determines when to stop the bubble down process.

Bubble down stops when the current node is greater than or equal to its children (in a max-heap) or when it has no children to compare with.

intermediate

Why is bubble down important for maintaining heap structure?

Bubble down ensures the heap property is maintained by repositioning the root element after extraction, keeping the heap organized for efficient operations.

intermediate

What is the time complexity of the bubble down operation in a heap?

The time complexity of bubble down is O(log n), where n is the number of elements in the heap, because it moves down at most the height of the heap.

What element replaces the root in a heap during extraction before bubble down?

A The smallest element in the heap

B The last element in the heap

C A new random element

D The second element in the heap

The last element in the heap replaces the root to maintain the complete tree structure before bubble down.

When does the bubble down process stop in a max-heap?

A When the current node is smaller than its children

B When the heap is empty

C When the current node is larger than or equal to its children

D After one swap only

Bubble down stops when the current node is larger than or equal to its children, maintaining the max-heap property.

What is the main goal of the bubble down operation?

A To restore heap property after extraction

B To insert a new element

C To sort the heap

D To delete the last element

Bubble down restores the heap property after the root is removed during extraction.

What is the time complexity of bubble down in a heap with n elements?

A O(n log n)

B O(n)

C O(1)

D O(log n)

Bubble down takes O(log n) time because it moves down the height of the heap, which is logarithmic in the number of elements.

Which heap property does bubble down help maintain?

A Heap order property (max or min)

B Balanced tree height

C Complete binary tree structure

D Sorted order of elements

Bubble down maintains the heap order property by repositioning elements after extraction.

Explain the steps involved in the heap extraction process using bubble down.

Think about what happens after removing the top element in a heap.

Why is bubble down necessary after extracting the root from a heap?

Consider what happens to the heap structure after root removal.