Heap insertion (bubble up) in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to insert a new element at the end of the heap array.

Data Structures Theory

heap.append([1])

Drag options to blanks, or click blank then click option'

Aparent

Bindex

Cvalue

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'index' or 'parent' instead of the actual value to insert.

Trying to insert at the root directly.

The new element to insert is added at the end of the heap array using append with the value to insert.

2fill in blank

medium

Complete the code to find the parent index of the newly inserted element at index i.

Data Structures Theory

parent = ([1] - 1) // 2

Drag options to blanks, or click blank then click option'

Ai

Bvalue

Cheap

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Using the value instead of the index to calculate the parent.

Using addition instead of subtraction.

In a binary heap stored as an array, the parent index of a node at index i is calculated as (i - 1) // 2.

3fill in blank

hard

Fix the error in the condition to continue bubbling up while the current index is greater than 0.

Data Structures Theory

while [1] > 0:

Drag options to blanks, or click blank then click option'

Avalue

Bi

Cheap

Dparent

Attempts:

3 left

💡 Hint

Common Mistakes

Checking the value instead of the index in the loop condition.

Using 'parent' or 'heap' in the condition incorrectly.

The bubbling up process continues while the current index i is greater than 0, meaning the node is not the root.

4fill in blank

hard

Fill both blanks to swap the current element with its parent if the heap property is violated.

Data Structures Theory

if heap[[1]] > heap[[2]]:
    heap[[1]], heap[[2]] = heap[[2]], heap[[1]]

Drag options to blanks, or click blank then click option'

Ai

Bparent

Cvalue

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'value' or 'root' instead of indices to access heap elements.

Swapping without checking the heap property.

To maintain the max-heap property, if the current element at index i is greater than its parent at index parent, they are swapped.

5fill in blank

hard

Fill all three blanks to update the current index to the parent's index after swapping during bubble up.

Data Structures Theory

heap[[1]], heap[[2]] = heap[[2]], heap[[1]]
i = [3]

Drag options to blanks, or click blank then click option'

Ai

Bparent

Dvalue

Attempts:

3 left

💡 Hint

Common Mistakes

Not updating the current index after swapping.

Using 'value' instead of indices for swapping.

After swapping the current element at index i with its parent at index parent, update i to parent to continue bubbling up.

Practice

1. What is the first step when inserting a new element into a binary heap using the bubble up method?

easy

A. Add the new element at the end of the heap

B. Compare the new element with the root

C. Remove the smallest element

D. Sort all elements in the heap

Solution

1. Step 1: Add new element at the end

   The new element is always added at the end of the heap to maintain the complete tree property.

2. Step 2: Prepare for bubble up

   After adding, the element will be compared with its parent to restore heap order.

3. Final Answer:

   Add the new element at the end of the heap -> Option A

4. Quick Check:

   Insertion starts by adding at the end [OK]

Hint: New elements always start at the end before bubbling up [OK]

Common Mistakes:

• Starting at the root instead of the end
• Removing elements before insertion
• Sorting the entire heap immediately

2. Which of the following correctly describes the condition to continue bubbling up in a min-heap after insertion?

easy

A. Never bubble up after insertion

B. Continue bubbling up if the new element is greater than its parent

C. Continue bubbling up if the new element is equal to its parent

D. Continue bubbling up if the new element is less than its parent

Solution

1. Step 1: Understand min-heap property

   In a min-heap, parents must be less than or equal to their children.

2. Step 2: Bubble up condition

   If the new element is less than its parent, it violates the heap property and must bubble up.

3. Final Answer:

   Continue bubbling up if the new element is less than its parent -> Option D

4. Quick Check:

   Bubble up when child < parent in min-heap [OK]

Hint: Bubble up when new element is smaller than parent in min-heap [OK]

Common Mistakes:

• Bubbling up when new element is greater
• Ignoring equality cases
• Not bubbling up at all

3. Given a min-heap represented as an array: [2, 5, 8, 10, 15], what will be the array after inserting 1 and performing bubble up?

medium

A. [1, 2, 8, 10, 15, 5]

B. [1, 2, 5, 10, 15, 8]

C. [1, 5, 2, 10, 15, 8]

D. [2, 5, 8, 10, 15, 1]

Solution

1. Step 1: Insert 1 at the end

   Array becomes [2, 5, 8, 10, 15, 1].

2. Step 2: Bubble up 1

   Compare 1 with parent 8 (index 2). Since 1 < 8, swap: [2, 5, 1, 10, 15, 8]. Then compare 1 with parent 5 (index 1). Since 1 < 5, swap: [2, 1, 8, 10, 15, 5]. Then compare 1 with parent 2 (index 0). Since 1 < 2, swap: [1, 2, 8, 10, 15, 5].

3. Final Answer:

   [1, 2, 5, 10, 15, 8] -> Option B

4. Quick Check:

   Bubble up swaps until heap property restored [OK]

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

Common Mistakes:

• Not swapping enough times
• Swapping with wrong parent
• Leaving new element at the end

4. Consider the following code snippet for inserting into a min-heap. What is the error?

def bubble_up(heap, index):
    while index > 0:
        parent = (index - 1) // 2
        if heap[index] > heap[parent]:
            heap[index], heap[parent] = heap[parent], heap[index]
            index = parent
        else:
            break

medium

A. The comparison should be heap[index] < heap[parent] for min-heap

B. The parent index calculation is incorrect

C. The loop condition should be index >= 0

D. Swapping should happen only if heap[index] == heap[parent]

Solution

1. Step 1: Analyze comparison logic

   For a min-heap, bubble up should swap when child is less than parent, not greater.

2. Step 2: Identify correct condition

   The code uses '>' which is wrong; it should be '<' to maintain min-heap property.

3. Final Answer:

   The comparison should be heap[index] < heap[parent] for min-heap -> Option A

4. Quick Check:

   Bubble up swaps when child < parent in min-heap [OK]

Hint: Use < comparison for min-heap bubble up [OK]

Common Mistakes:

• Using > instead of <
• Wrong parent index formula
• Incorrect loop condition

5. You have a max-heap represented as [20, 15, 18, 8, 10, 17]. You insert 19. After bubble up, what is the correct heap array?

hard

A. [20, 15, 18, 8, 10, 17, 19]

B. [20, 19, 18, 8, 10, 17, 15]

C. [20, 15, 19, 8, 10, 17, 18]

D. [20, 19, 18, 15, 10, 17, 8]

Solution

1. Step 1: Insert 19 at the end

   Array becomes [20, 15, 18, 8, 10, 17, 19].

2. Step 2: Bubble up 19 in max-heap

   Parent of index 6 is index 2 (value 18). Since 19 > 18, swap: [20, 15, 19, 8, 10, 17, 18]. Next parent is index 0 (value 20). Since 19 < 20, stop bubbling up.

3. Step 3: Final heap array

   The final array is [20, 15, 19, 8, 10, 17, 18].

4. Final Answer:

   [20, 15, 19, 8, 10, 17, 18] -> Option C

5. Quick Check:

   Bubble up swaps child > parent in max-heap [OK]

Hint: In max-heap, bubble up while child is greater than parent [OK]

Common Mistakes:

• Not swapping enough times
• Swapping with wrong parent
• Leaving new element at the end