Build Heap from Array Heapify in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to find the parent index of a node in a heap.

DSA Go

parent := (index - 1) [1] 2

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

A*

B/

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of division

Adding instead of subtracting 1

The parent index in a heap is calculated by subtracting 1 from the current index and dividing by 2.

2fill in blank

medium

Complete the code to swap two elements in the heap array.

DSA Go

heap[i], heap[j] = heap[[1]], heap[i]

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Aj

Bi

Clen(heap)-1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with the wrong index

Assigning the same element twice

To swap elements at positions i and j, assign heap[i] to heap[j] and heap[j] to heap[i].

3fill in blank

hard

Fix the error in the condition to check if left child exists in heapify.

DSA Go

if left < [1] {

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Alen(heap) + 1

Blen(heap) - 1

Clen(heap)

Dcap(heap)

Attempts:

3 left

💡 Hint

Common Mistakes

Using length-1 instead of length

Using capacity instead of length

The left child index must be less than the length of the heap array to exist.

4fill in blank

hard

Fill both blanks to complete the heapify function's recursive call and comparison.

DSA Go

if right < len(heap) && heap[right] [1] heap[largest] {
    largest = [2]
}

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

A>

B<

Cright

Dleft

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' instead of '>'

Assigning left instead of right

We check if the right child is greater than the current largest, then update largest to right.

5fill in blank

hard

Complete the code to complete the buildHeap function that heapifies from bottom up.

DSA Go

for i := len(heap)/2 - 1; i >= 0; i[1] {
    heapify(heap, i, len(heap))
}

func heapify(heap []int, i, n int) {
    largest := i
    left := 2*i + 1
    right := 2*i + 2
    if left < n && heap[left] > heap[largest] {
        largest = left
    }
    if right < n && heap[right] > heap[largest] {
        largest = right
    }
    if largest != i {
        heap[i], heap[largest] = heap[largest], heap[i]
        heapify(heap, largest, n)
    }
}

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

A--

B+

C)

D]

Attempts:

3 left

💡 Hint

Common Mistakes

Using + instead of -- in loop

Missing closing parenthesis

Incorrect argument for heapify

The loop decreases i by 1 each time (--). The heapify function needs the size n, so len(heap) + 0 is just len(heap). The closing parenthesis is needed to close the function call.

Practice

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

easy

A. To rearrange the array elements to satisfy the heap property

B. To sort the array in ascending order

C. To find the maximum element in the array

D. To reverse the array elements

Solution

1. Step 1: Understand heap property

   A heap is a special tree-based structure where each parent node is greater (max-heap) or smaller (min-heap) than its children.

2. Step 2: Role of heapify

   The heapify process rearranges elements to ensure this property holds for every subtree starting from a given node.

3. Final Answer:

   To rearrange the array elements to satisfy the heap property -> Option A

4. Quick Check:

   Heapify = Rearrange for heap property [OK]

Hint: Heapify fixes subtree to maintain heap order [OK]

Common Mistakes:

• Confusing heapify with sorting
• Thinking heapify finds max element only
• Assuming heapify reverses array

2. Which of the following is the correct way to call heapify on a node index i in Go when building a max heap from an array arr of size n?

easy

A. heapify(n, arr, i)

B. heapify(i, arr, n)

C. heapify(arr, i, n)

D. heapify(arr, n, i)

Solution

1. Step 1: Understand heapify function parameters

   Heapify usually takes the array, size of heap, and the index to heapify as parameters in that order.

2. Step 2: Match parameter order

   heapify(arr, n, i) matches the correct order: array, size, index.

3. Final Answer:

   heapify(arr, n, i) -> Option D

4. Quick Check:

   heapify(arr, n, i) is correct call [OK]

Hint: Remember: heapify(array, size, index) [OK]

Common Mistakes:

• Mixing parameter order
• Passing index before array
• Confusing size and index positions

3. Given the array [3, 9, 2, 1, 4, 5], what is the array after building a max heap using heapify from the bottom up?

medium

A. [5, 4, 9, 1, 3, 2]

B. [9, 4, 5, 3, 1, 2]

C. [9, 4, 5, 1, 3, 2]

D. [9, 3, 5, 1, 4, 2]

Solution

1. Step 1: Start heapify from last non-leaf node

   Last non-leaf node index = n/2 -1 = 6/2 -1 = 2. Heapify nodes 2, 1, 0 in order.

2. Step 2: Heapify index 2

   Node 2 value=2, children 5 (index 5). Swap 2 and 5. Array becomes [3, 9, 5, 1, 4, 2].

3. Step 3: Heapify index 1

   Node 1 value=9, children 1 and 4. 9 is largest, no change.

4. Step 4: Heapify index 0

   Node 0 value=3, children 9 and 5. Swap 3 and 9. Array becomes [9, 3, 5, 1, 4, 2]. Heapify index 1 again: 3 with children 1 and 4, swap 3 and 4. Final array: [9, 4, 5, 1, 3, 2].

5. Final Answer:

   [9, 4, 5, 1, 3, 2] -> Option C

6. Quick Check:

   Bottom-up heapify gives [9,4,5,1,3,2] [OK]

Hint: Heapify bottom-up swaps to fix largest child first [OK]

Common Mistakes:

• Not heapifying children after swap
• Starting heapify from wrong index
• Confusing max-heap with min-heap

4. Consider this Go code snippet to build a max heap from array arr. What is the error?

func buildHeap(arr []int) {
    n := len(arr)
    for i := n / 2; i >= 0; i-- {
        heapify(arr, n, i)
    }
}

medium

A. heapify function is missing the array size parameter

B. The loop should start from n/2 - 1, not n/2

C. The loop should increment i, not decrement

D. The loop condition should be i > 0, not i >= 0

Solution

1. Step 1: Identify correct start index for heapify

   Heapify starts from last non-leaf node at index n/2 - 1, not n/2.

2. Step 2: Analyze loop range

   Starting at n/2 includes one extra index which is a leaf node, unnecessary and may cause incorrect behavior.

3. Final Answer:

   The loop should start from n/2 - 1, not n/2 -> Option B

4. Quick Check:

   Start heapify at n/2 - 1 [OK]

Hint: Start heapify at last non-leaf node: n/2 - 1 [OK]

Common Mistakes:

• Starting loop at n/2 instead of n/2 - 1
• Loop increment instead of decrement
• Wrong loop condition excluding index 0

5. You have an array [4, 10, 3, 5, 1]. After building a max heap using heapify, you want to insert a new element 15 and maintain the max heap property. Which sequence of operations correctly maintains the heap?

hard

A. Append 15, then bubble up the new element until heap property is restored

B. Append 15, then heapify only the root node

C. Append 15, then heapify from last non-leaf node down to root

D. Replace root with 15, then heapify entire array

Solution

1. Step 1: Understand insertion in heap

   To insert, add element at end, then restore heap by bubbling up (swapping with parent if larger).

2. Step 2: Why bubble up?

   Heapify from bottom up is for building heap initially; for insertion, bubbling up fixes heap efficiently.

3. Final Answer:

   Append 15, then bubble up the new element until heap property is restored -> Option A

4. Quick Check:

   Insert + bubble up maintains heap [OK]

Hint: Insert at end, bubble up to fix heap [OK]

Common Mistakes:

• Using heapify from root after insertion
• Heapifying only root node
• Replacing root without adjusting heap