Build Heap from Array Heapify in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to get the index of the last non-leaf node in the heap array.

DSA C++

int lastNonLeaf = (n [1] 2) - 1;

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.

Forgetting to subtract 1 after division.

The last non-leaf node in a heap array of size n is at index (n / 2) - 1.

2fill in blank

medium

Complete the code to call heapify on each non-leaf node starting from the last non-leaf node.

DSA C++

for (int i = lastNonLeaf; i >= 0; i--) {
    heapify(arr, n, [1]);
}

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

Ai

Bn

C0

DlastNonLeaf

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the size n instead of the node index.

Passing 0 or lastNonLeaf instead of the current index.

We call heapify on each node index i from lastNonLeaf down to 0.

3fill in blank

hard

Fix the error in the heapify function call inside the buildHeap function.

DSA C++

void buildHeap(int arr[], int n) {
    int startIdx = (n / 2) - 1;
    for (int i = startIdx; i >= 0; i--) {
        heapify(arr, [1], i);
    }
}

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

Ai

Bn

CstartIdx

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the current index i as the size parameter.

Confusing the order of parameters in heapify.

heapify needs the size of the array n and the current index i to work correctly.

4fill in blank

hard

Fill both blanks to complete the heapify function's left and right child index calculations.

DSA C++

int left = 2 * [1] + [2];
int right = 2 * [1] + 2;

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

Ai

B1

C0

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 instead of 1 for left child offset.

Using n or other variables instead of i.

Left child index is 2*i + 1 and right child index is 2*i + 2 in a zero-indexed heap array.

5fill in blank

hard

Fill all three blanks to complete the heapify function's swap and recursive call.

DSA C++

if (largest != [1]) {
    std::swap(arr[[2]], arr[[3]]);
    heapify(arr, n, largest);
}

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

Ai

Blargest

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping wrong indices.

Not calling heapify recursively after swap.

We swap arr[i] with arr[largest] and then call heapify on largest to fix the subtree.

Practice

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

easy

A. To find the maximum element in the array

B. To sort the array in ascending order

C. To rearrange elements to satisfy the heap property

D. To reverse the array elements

Solution

1. Step 1: Understand heap property

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

2. Step 2: Role of heapify

   Heapify rearranges elements so this property holds for every subtree starting from a node.

3. Final Answer:

   To rearrange elements to satisfy the heap property -> Option C

4. Quick Check:

   Heapify = rearrange for heap property [OK]

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

Common Mistakes:

• Thinking heapify sorts the array
• Confusing heapify with finding max element
• Assuming heapify reverses the array

2. Which of the following is the correct way to call heapify on an array arr of size n starting from index i in C++?

easy

A. heapify(i, arr, n);

B. heapify(arr, i, n);

C. heapify(n, i, arr);

D. heapify(arr, n, i);

Solution

1. Step 1: Understand heapify parameters

   Heapify usually takes the array, its size, and the index to heapify from in that order.

2. Step 2: Match correct syntax

   heapify(arr, n, i); matches the standard signature: heapify(arr, n, i); others have wrong order.

3. Final Answer:

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

4. Quick Check:

   heapify(arr, size, index) = B [OK]

Hint: Remember: array, size, then index for heapify call [OK]

Common Mistakes:

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

3. Given the array arr = [4, 10, 3, 5, 1], what will be the array after calling heapify(arr, 5, 0) assuming a max-heap?

medium

A. [10, 5, 3, 4, 1]

B. [5, 10, 3, 4, 1]

C. [10, 4, 3, 5, 1]

D. [4, 10, 3, 5, 1]

Solution

1. Step 1: Identify root and children

   Index 0 has value 4; children at indices 1 and 2 are 10 and 3.

2. Step 2: Swap with largest child and heapify

   Swap 4 with 10 (largest child). Now at index 1, value 4 has children 5 and 1. Swap 4 with 5. Final array: [10, 5, 3, 4, 1]

3. Final Answer:

   [10, 5, 3, 4, 1] -> Option A

4. Quick Check:

   Max-heap root fixed = [10, 5, 3, 4, 1] [OK]

Hint: Swap root with largest child, then heapify child subtree [OK]

Common Mistakes:

• Not swapping with largest child
• Stopping after first swap
• Confusing min-heap with max-heap

4. Consider this code snippet to build a max heap from array arr of size n. Identify the error:

for (int i = 0; i <= n/2; i++) {
    heapify(arr, n, i);
}

medium

A. Heapify should be called with index i+1

B. Loop should start from n/2 - 1 and go down to 0

C. Loop should run from 0 to n-1

D. No error, code is correct

Solution

1. Step 1: Understand heap building order

   Heap building requires heapify from last non-leaf node down to root, i.e., from n/2 - 1 down to 0.

2. Step 2: Identify loop direction and range error

   The loop incorrectly goes from 0 up to n/2, which is wrong direction and range.

3. Final Answer:

   Loop should start from n/2 - 1 and go down to 0 -> Option B

4. Quick Check:

   Build heap loops down from n/2-1 [OK]

Hint: Build heap loops backward from last parent to root [OK]

Common Mistakes:

• Looping forward instead of backward
• Starting loop at 0 without decrement
• Calling heapify with wrong index

5. You have an array arr = [3, 9, 2, 1, 4, 5]. After building a max heap using the standard heapify method, what is the final array?

hard

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

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

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

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

Solution

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

   Last non-leaf index = n/2 -1 = 2. Heapify at index 2: children 5 and none, 2 < 5, swap to get [3,9,5,1,4,2].

2. Step 2: Heapify at index 1

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

3. Step 3: Heapify at index 0

   Index 0 value 3, children 9 and 5. Swap 3 with 9: [9,3,5,1,4,2]. Heapify at index 1: value 3, children 1 and 4. Swap 3 with 4: [9,4,5,1,3,2].

4. Final Answer:

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

5. Quick Check:

   Max heap built = [9,4,5,1,3,2] [OK]

Hint: Heapify bottom-up, swap with largest child repeatedly [OK]

Common Mistakes:

• Not heapifying all parents
• Swapping with wrong child
• Stopping heapify early