Heap Insert Operation Bubble Up in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of the bubble up operation in a heap insert?

The bubble up operation moves the newly inserted element up the heap to restore the heap property, ensuring the parent node is always smaller (min-heap) or larger (max-heap) than its children.

beginner

In a min-heap, when does the bubble up operation stop during insertion?

The bubble up stops when the inserted element is no longer smaller than its parent or it reaches the root of the heap.

beginner

How do you find the parent index of a node at index i in a heap stored as an array?

The parent index is calculated as (i - 1) / 2 using integer division.

beginner

What happens if the newly inserted element is larger than its parent in a min-heap during bubble up?

No swap occurs, and the bubble up operation stops because the heap property is maintained.

beginner

Why is the bubble up operation important for heap insert?

It ensures the heap remains a valid min-heap or max-heap after insertion, maintaining efficient access to the smallest or largest element.

What is the first step after inserting a new element at the end of a heap array?

A Remove the root element

B Sort the entire array

C Perform bubble up to restore heap property

D Do nothing

After insertion at the end, bubble up moves the element up to maintain the heap property.

In a min-heap, if the inserted element is smaller than its parent, what should happen?

A Swap with parent and continue bubble up

B Stop bubble up

C Swap with child

D Remove the element

If the inserted element is smaller, it swaps with the parent to maintain min-heap order.

How do you calculate the parent index of a node at index 5 in a heap array?

A 1

B 3

C 4

D 2

Parent index = (5 - 1) / 2 = 2.

When does the bubble up operation stop?

A When the element is at root or heap property is restored

B When the element reaches the last index

C After one swap only

D When the heap is empty

Bubble up stops when the element is at root or no longer violates heap property.

What data structure is commonly used to implement a heap?

A Linked list

B Array

C Stack

D Queue

Heaps are efficiently implemented using arrays.

Explain the bubble up operation during heap insertion step-by-step.

Think about how the new element moves up the tree.

Describe how to find the parent index of a node in a heap stored as an array and why this is important for bubble up.

Focus on array indexing and heap structure.

Practice

1. What is the main purpose of the bubble up operation during a heap insert?

easy

A. To swap the root with the last element

B. To restore the heap property by moving the inserted element up

C. To sort all elements in ascending order

D. To remove the smallest element from the heap

Solution

1. Step 1: Understand heap property

   A heap must maintain a specific order, usually parent nodes are greater (max-heap) or smaller (min-heap) than their children.

2. Step 2: Role of bubble up

   When a new element is inserted at the end, bubble up moves it up to restore the heap property if violated.

3. Final Answer:

   To restore the heap property by moving the inserted element up -> Option B

4. Quick Check:

   Bubble up fixes heap order after insert [OK]

Hint: Bubble up fixes heap order by moving new element up [OK]

Common Mistakes:

• Confusing bubble up with removing elements
• Thinking bubble up sorts the entire heap
• Believing bubble up swaps root with last element

2. Which Rust code snippet correctly swaps a child and its parent during bubble up in a max-heap?

easy

A. heap.swap(child_index, parent_index);

B. heap.insert(child_index, parent_index);

C. heap.remove(child_index);

D. heap.push(parent_index);

Solution

1. Step 1: Identify swap method usage

   To exchange two elements in a vector, Rust's Vec has a swap method taking two indices.

2. Step 2: Confirm correct parameters

   Swapping child and parent indices restores heap order during bubble up.

3. Final Answer:

   heap.swap(child_index, parent_index); -> Option A

4. Quick Check:

   swap() exchanges elements by index [OK]

Hint: Use Vec.swap(child, parent) to exchange elements [OK]

Common Mistakes:

• Using insert instead of swap
• Calling remove which deletes elements
• Using push which adds elements

3. Given the max-heap represented by the array [50, 30, 40, 10, 20], what will be the heap array after inserting 45 and performing bubble up?

medium

A. [50, 45, 40, 10, 20, 30]

B. [50, 30, 40, 10, 20, 45]

C. [50, 30, 45, 10, 20, 40]

D. [45, 30, 50, 10, 20, 40]

Solution

1. Step 1: Insert 45 at the end

   Array becomes [50, 30, 40, 10, 20, 45].

2. Step 2: Bubble up 45

   Parent of index 5 is index 2 (value 40). Since 45 > 40, swap them. New array: [50, 30, 45, 10, 20, 40].

3. Step 3: Check next parent

   Parent of index 2 is index 0 (value 50). 45 < 50, stop bubbling up.

4. Final Answer:

   [50, 30, 45, 10, 20, 40] -> Option C

5. Quick Check:

   Insert then bubble up swaps with parent if bigger [OK]

Hint: Insert at end, swap up while bigger than parent [OK]

Common Mistakes:

• Not swapping 45 with 40
• Swapping 45 with 30 incorrectly
• Stopping bubble up too early

4. In the following Rust code for bubble up, what is the bug?

fn bubble_up(heap: &mut Vec<i32>, mut index: usize) {
    while index > 0 {
        let parent = (index - 1) / 2;
        if heap[index] > heap[parent] {
            heap.swap(index, parent);
            index = parent;
        }
    }
}

medium

A. Loop condition should be index >= 0

B. Incorrect parent calculation formula

C. Using swap instead of insert

D. Missing update of index when no swap occurs, causing infinite loop

Solution

1. Step 1: Analyze loop behavior

   Loop runs while index > 0. Inside, swap and update index if heap[index] > heap[parent].

2. Step 2: Identify missing else case

   If heap[index] <= heap[parent], index is not updated, so loop never ends causing infinite loop.

3. Final Answer:

   Missing update of index when no swap occurs, causing infinite loop -> Option D

4. Quick Check:

   Loop must update index or break to avoid infinite loop [OK]

Hint: Always update index or break in bubble up loop [OK]

Common Mistakes:

• Ignoring infinite loop possibility
• Wrong parent index formula
• Confusing swap with insert
• Using invalid loop condition

5. You have a min-heap represented by [5, 10, 15, 20, 25]. You insert 12. After bubble up, what is the correct heap array?

hard

A. [5, 10, 12, 20, 25, 15]

B. [5, 10, 15, 20, 25, 12]

C. [5, 12, 10, 20, 25, 15]

D. [5, 10, 15, 12, 25, 20]

Solution

1. Step 1: Insert 12 at the end

   Array becomes [5, 10, 15, 20, 25, 12].

2. Step 2: Bubble up 12 in min-heap

   Parent of index 5 is index 2 (value 15). Since 12 < 15, swap them. New array: [5, 10, 12, 20, 25, 15].

3. Step 3: Check next parent

   Parent of index 2 is index 0 (value 5). 12 > 5, stop bubbling up.

4. Final Answer:

   [5, 10, 12, 20, 25, 15] -> Option A

5. Quick Check:

   Min-heap bubble up swaps if child smaller than parent [OK]

Hint: In min-heap, bubble up swaps smaller child with parent [OK]

Common Mistakes:

• Not swapping 12 with 15
• Stopping bubble up too early
• Confusing min-heap with max-heap rules