Heap Concept Structure and Properties in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to insert an element into a max heap list.

DSA Python

def insert_max_heap(heap, element):
    heap.append(element)
    i = len(heap) - 1
    while i > 0 and heap[(i - 1) // 2] < heap[i]:
        heap[i], heap[(i - 1) // 2] = heap[(i - 1) // 2], heap[i]
        i = [1]

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

A(i - 1) // 2

Bi // 2

Ci - 1

Di + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using i // 2 as parent index which is incorrect for zero-based indexing.

Using i - 1 or i + 1 which are not parent indices.

In a heap represented as a list, the parent index of a node at index i is (i - 1) // 2.

2fill in blank

medium

Complete the code to get the left child index of a node in a heap list.

DSA Python

def left_child(i):
    return [1]

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

Ai + 1

B2 * i

C2 * i + 1

D2 * i - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 2*i which is the formula for left child in one-based indexing.

Using i + 1 which is just the next element.

In a heap list, the left child of node at index i is at 2*i + 1.

3fill in blank

hard

Fix the error in the code that heapifies a subtree rooted at index i in a max heap.

DSA Python

def max_heapify(heap, n, i):
    largest = i
    left = 2 * i + 1
    right = 2 * i + 2

    if left < n and heap[left] > heap[[1]]:
        largest = left

    if right < n and heap[right] > heap[largest]:
        largest = right

    if largest != i:
        heap[i], heap[largest] = heap[largest], heap[i]
        max_heapify(heap, n, largest)

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

Alargest

Bi

Cleft

Dright

Attempts:

3 left

💡 Hint

Common Mistakes

Comparing left child with largest which is initially set to i but not updated yet.

Using left or right as index which is incorrect here.

We compare heap[left] with heap[i], the root of the subtree, to find the largest.

4fill in blank

hard

Fill both blanks to complete the code that builds a max heap from an unordered list.

DSA Python

def build_max_heap(arr):
    n = len(arr)
    for i in range([1], -1, -1):
        [2](arr, n, i)

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

An // 2 - 1

Bmax_heapify

Cn - 1

Dheapify

Attempts:

3 left

💡 Hint

Common Mistakes

Starting from n - 1 which is a leaf node and does not need heapify.

Using a wrong function name like heapify instead of max_heapify.

We start heapifying from the last parent node at n//2 - 1 down to 0 using max_heapify function.

5fill in blank

hard

Fill all three blanks to complete the code that extracts the maximum element from a max heap.

DSA Python

def extract_max(heap):
    if len(heap) == 0:
        return None
    max_element = heap[[1]]
    heap[[2]] = heap.pop()
    max_heapify(heap, len(heap), [3])
    return max_element

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

A0

B-1

Dlen(heap) - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using -1 or len(heap)-1 as index for max element which is incorrect.

Not heapifying from root after replacement.

The max element is at index 0. We replace root with last element at index 0 and heapify from root.

Practice

1. What is the main property of a min-heap data structure?

easy

A. The value of each node is less than or equal to its parent.

B. The tree is always a balanced binary search tree.

C. The tree is always a complete binary tree.

D. The value of each node is less than or equal to its children.

Solution

1. Step 1: Understand min-heap property

   In a min-heap, every parent node has a value less than or equal to its children.

2. Step 2: Compare options with definition

   The value of each node is less than or equal to its children. matches the min-heap property exactly. The value of each node is less than or equal to its parent. is the opposite, The tree is always a complete binary tree. is true but not the main property, The tree is always a balanced binary search tree. is incorrect.

3. Final Answer:

   The value of each node is less than or equal to its children. -> Option D

4. Quick Check:

   Min-heap property = parent ≤ children [OK]

Hint: Min-heap means parent ≤ children values [OK]

Common Mistakes:

• Confusing min-heap with max-heap property
• Thinking heap is a binary search tree
• Ignoring the complete tree structure

2. Which of the following is the correct Python syntax to create an empty min-heap using the heapq module?

easy

A. heap = []

B. heap = heapq()

C. heap = heapq.heapify([])

D. heap = new heapq.minheap()

Solution

1. Step 1: Recall heapq usage in Python

   heapq works on a list; an empty list represents an empty heap.

2. Step 2: Check options for correct syntax

   heap = [] creates an empty list. heapq.heapify([]) transforms a list but returns None, so C is wrong. A and D are invalid syntax.

3. Final Answer:

   heap = [] -> Option A

4. Quick Check:

   Empty heap = empty list [OK]

Hint: Empty heap is just an empty list [] [OK]

Common Mistakes:

• Using heapq() as a constructor (heapq is a module)
• Expecting heapify to return a new heap
• Trying to instantiate heapq class (does not exist)

3. What will be the output of the following Python code using heapq?

import heapq
heap = []
heapq.heappush(heap, 5)
heapq.heappush(heap, 3)
heapq.heappush(heap, 8)
min_val = heapq.heappop(heap)
print(min_val, heap)

medium

A. 8 [3, 5]

B. 5 [3, 8]

C. 3 [5, 8]

D. 3 [8, 5]

Solution

1. Step 1: Push values into the heap

   Values 5, 3, 8 are pushed. The heap maintains min-heap order internally.

2. Step 2: Pop the smallest value

   heapq.heappop removes and returns the smallest value, which is 3. Remaining heap is [5, 8].

3. Final Answer:

   3 [5, 8] -> Option C

4. Quick Check:

   Pop min = 3, heap after pop = [5, 8] [OK]

Hint: heappop returns smallest, heap keeps order [OK]

Common Mistakes:

• Assuming heappop returns last pushed value
• Confusing heap order with insertion order
• Expecting heap to be sorted list

4. Identify the error in the following code snippet that tries to create a max-heap using heapq:

import heapq
heap = []
heapq.heappush(heap, 10)
heapq.heappush(heap, 5)
heapq.heappush(heap, 20)
max_val = heapq.heappop(heap)
print(max_val)

medium

A. heapq does not support max-heap directly; it creates a min-heap.

B. heappush is used incorrectly; it should be heap.push().

C. heappop returns the maximum value, so no error.

D. heap must be initialized with heapq.heapify() before pushing.

Solution

1. Step 1: Understand heapq behavior

   heapq module implements a min-heap, so heappop returns the smallest value.

2. Step 2: Check code for max-heap usage

   The code expects max_val to be maximum, but it will get minimum (5). So the error is assuming max-heap behavior.

3. Final Answer:

   heapq does not support max-heap directly; it creates a min-heap. -> Option A

4. Quick Check:

   heapq = min-heap only [OK]

Hint: heapq is min-heap; max-heap needs value negation [OK]

Common Mistakes:

• Expecting heappop to return max value
• Using wrong method names for heapq
• Not initializing heap before push

5. Given a list of numbers, how can you efficiently find the k largest elements using a heap in Python?

hard

A. Sort the list and slice the last k elements.

B. Use heapq.nlargest(k, list) which uses a heap internally.

C. Push all elements into a min-heap and pop k times.

D. Push all elements into a max-heap and pop k times.

Solution

1. Step 1: Understand efficient k largest retrieval

   heapq.nlargest(k, list) uses a heap internally optimized for this task.

2. Step 2: Compare options for efficiency and correctness

   Use heapq.nlargest(k, list) which uses a heap internally. is the built-in efficient method. Sort the list and slice the last k elements. sorts entire list (less efficient). Push all elements into a min-heap and pop k times. gives k smallest, not largest. Push all elements into a max-heap and pop k times. is not directly supported by heapq.

3. Final Answer:

   Use heapq.nlargest(k, list) which uses a heap internally. -> Option B

4. Quick Check:

   heapq.nlargest = efficient k largest [OK]

Hint: Use heapq.nlargest for quick k largest [OK]

Common Mistakes:

• Sorting whole list instead of using heap
• Trying to build max-heap manually
• Not knowing heapq.nlargest exists