Heaps Operations Quiz
40 comprehensive questions exploring heap operations — with 16 code examples covering insert, extract-min/max, peek, heapify-up/down, and time complexity in this cpp quiz.
40 Questions
~80 minutes
1
Question 1
What is a heap insert operation?
A
Adding a new element to the heap while maintaining the heap property through a series of comparisons and swaps with parent nodes, ensuring the element reaches its correct position in the heap structure
B
Removing the root element
C
Finding the maximum element
D
Sorting the heap
2
Question 2
How does heapify-up work in insertion?
cpp
Compare with parent
Swap if violates heap property
Continue until root or property satisfiedA
Starting from the newly inserted element, compare it with its parent and swap if the heap property is violated, continuing up the tree until the property is satisfied or the root is reached, effectively bubbling the element to its correct position
B
Comparing with children
C
Moving elements down
D
Heapify-up doesn't exist
3
Question 3
What is the worst-case time complexity of heap insert?
A
O(log n) due to the heapify-up operation potentially traversing from leaf to root, with the maximum path length being logarithmic in the number of elements in the heap
B
O(1)
C
O(n)
D
O(n log n)
4
Question 4
How does heap extract-min work?
cpp
Remove root, replace with last element
Heapify-down to maintain propertyA
Remove the root element (minimum), replace it with the last element in the heap array, then perform heapify-down starting from the root to restore the heap property throughout the entire heap structure
B
Remove a random element
C
Remove from the middle
D
Extract doesn't maintain heap property
5
Question 5
What is heapify-down operation?
A
A recursive process starting from a node that compares it with its children and swaps with the appropriate child if the heap property is violated, continuing down the tree until the property is restored or a leaf is reached
B
Moving elements up the heap
C
Removing elements
D
Heapify-down doesn't exist
6
Question 6
What is the time complexity of heap extract-min?
text
Extract: O(log n)
Heapify-down through heightA
O(log n) because the heapify-down operation may traverse from root to leaf in the worst case, with the maximum path length being logarithmic in the number of elements, making extraction efficient even for large heaps
B
O(1)
C
O(n)
D
O(n log n)
7
Question 7
What is the peek operation in heaps?
A
Accessing the root element (min/max) without removing it, providing O(1) time complexity since the extreme value is always at the root in a properly maintained heap structure
B
Removing the root element
C
Finding the middle element
D
Peek is not supported in heaps
8
Question 8
How does heapify-up compare to heapify-down?
text
Heapify-up: from leaf to root
Heapify-down: from root to leafA
Heapify-up starts from a leaf node and moves toward the root, used in insertions, while heapify-down starts from the root and moves toward leaves, used in extractions and heap construction, with both maintaining heap properties through local restructuring
B
They are identical
C
Heapify-up is slower
D
Heapify-down doesn't exist
9
Question 9
What happens during heap insert when the element is larger than its parent?
A
In a max-heap, if the inserted element is larger than its parent, heapify-up continues to swap it upward until it finds a parent that is larger or reaches the root, ensuring the heap property is maintained throughout the path
B
The element stays in place
C
The heap becomes invalid
D
The parent is removed
10
Question 10
How does heap extract handle the last element replacement?
cpp
Replace root with last element
Then heapify-down from rootA
After removing the root, the last element in the heap array is placed at the root position, then heapify-down is performed to trickle this element down to its correct position, ensuring the heap property is restored efficiently
B
The last element becomes the new root directly
C
The heap is rebuilt from scratch
D
The last element is discarded
11
Question 11
What is the best-case time complexity of heap insert?
A
O(1) when the inserted element doesn't need to move up the heap, meaning it satisfies the heap property with its parent immediately, requiring no swaps or comparisons beyond the initial parent check
B
O(log n)
C
O(n)
D
Heap insert is always O(log n)
12
Question 12
How does heapify-down choose which child to swap with?
cpp
Compare both children
Swap with smaller/larger childA
Heapify-down compares the current node with both children and swaps with the child that violates the heap property most severely, choosing the smaller child in min-heaps or larger child in max-heaps to ensure proper ordering
B
Always swaps with left child
C
Always swaps with right child
D
Random child selection
13
Question 13
What is the amortized cost of heap operations?
A
O(log n) amortized time for both insert and extract operations, as the total work across a sequence of operations is bounded by the sum of heap heights, providing an average-case performance guarantee over multiple operations
B
O(1) amortized
C
O(n) amortized
D
Amortized analysis doesn't apply
14
Question 14
How does heap insert handle array resizing?
cpp
Check array capacity
Resize if needed before insertionA
Before insertion, check if the array has sufficient capacity, and if not, resize the underlying array to accommodate the new element, then proceed with the standard heap insert algorithm to maintain the heap property
B
Arrays don't resize in heaps
C
Resize happens after insertion
D
Heap insert doesn't use arrays
15
Question 15
What is the relationship between heap height and operation time?
A
Heap operation time is directly proportional to heap height, with both insert and extract operations taking O(h) time in the worst case where h is the height, making height a critical factor in heap performance analysis
B
Height has no effect on time
C
Operations are always O(1)
D
Height affects memory only
16
Question 16
How does heap extract-min handle empty heaps?
cpp
Check if heap is empty
Return error or special valueA
Before extraction, check if the heap is empty, and if so, return an error condition or special sentinel value instead of attempting to remove the root, preventing undefined behavior in empty heap scenarios
B
Empty heaps return null
C
Empty heaps crash
D
Extract works on empty heaps
17
Question 17
What is the space complexity of heap operations?
A
O(1) auxiliary space for individual operations since heapify procedures only require a constant amount of additional space for temporary variables, making heap operations memory-efficient beyond the heap storage itself
B
O(n) space
C
O(log n) space
D
Heap operations require O(n) auxiliary space
18
Question 18
How does heap insert maintain stability?
text
Stability: equal elements maintain order
Heapify may break stabilityA
Heap insert operations are not inherently stable because heapify-up may reorder elements with equal priorities, breaking the relative ordering of equal elements that existed before insertion, unlike stable sorting algorithms
B
Heap insert is always stable
C
Stability doesn't apply to heaps
D
Heap insert preserves all ordering
19
Question 19
What is the difference between peek and extract operations?
A
Peek provides O(1) access to the extreme element without modifying the heap, while extract removes the element and performs O(log n) restructuring to maintain the heap property, making peek suitable for inspection and extract for consumption
B
They are identical
C
Peek is slower than extract
D
Extract is O(1)
20
Question 20
How does heapify-down handle nodes with one child?
cpp
Check if only one child exists
Compare with existing child onlyA
When a node has only one child (typically the left child in array representation), heapify-down compares the current node with that single child and performs the swap if necessary, following the same heap property rules as with two children
B
Nodes can't have one child
C
One child case is ignored
D
Heapify-down fails with one child
21
Question 21
What is the impact of heap operations on cache performance?
A
Heap operations generally have good cache performance due to the array-based representation providing spatial locality, with heapify operations accessing nearby elements that are likely cached, though the random access patterns can cause some cache misses
B
Heap operations have poor cache performance
C
Cache performance is irrelevant
D
Heap operations always cause cache misses
22
Question 22
How does heap extract-min handle the heap size reduction?
cpp
Decrement heap size after extraction
Last element becomes garbageA
After successful extraction and heapify-down, the heap size is decremented, effectively removing the last element from consideration while keeping it in the array as unused space that will be overwritten by future insertions
B
Heap size stays the same
C
The array is resized
D
Extract-min increases heap size
23
Question 23
What is the worst-case path for heapify-up?
A
From a leaf node all the way to the root, requiring log n comparisons and swaps in the worst case when the inserted element is more extreme than all its ancestors, making it traverse the entire height of the heap
B
Only one level up
C
Halfway to root
D
Heapify-up never reaches root
24
Question 24
How does heap insert handle duplicate values?
text
Duplicates allowed
Heap property still maintainedA
Heap insert operations handle duplicate values naturally by maintaining the heap property regardless of equal values, allowing multiple identical elements while preserving the required ordering relationships with other elements in the heap
B
Duplicates are not allowed
C
Duplicates break the heap
D
Duplicates are removed during insert
25
Question 25
What is the average-case performance of heap operations?
A
O(log n) average time for both insert and extract operations, as the expected path length in random heaps is logarithmic, providing efficient performance across typical usage patterns and input distributions
B
O(1) average
C
O(n) average
D
Average case is same as worst case
26
Question 26
How does heapify-down terminate?
cpp
Continue until: at leaf level
Or heap property satisfied with both childrenA
Heapify-down terminates when the current node has no children (leaf level) or when the heap property is satisfied with both children, meaning no further swaps are needed to maintain the correct ordering in the subtree
B
It never terminates
C
It terminates after one swap
D
It terminates at root
27
Question 27
What is the constant factors in heap operation complexity?
A
The constant factors depend on the number of children per node and comparison costs, with binary heaps having smaller constants than higher-arity heaps due to fewer comparisons per level, affecting practical performance despite same asymptotic complexity
B
Constant factors are always 1
C
Constant factors don't matter
D
Heap operations have no constant factors
28
Question 28
How does heap insert work with custom comparators?
cpp
Use comparator for parent-child comparisons
Maintain heap property with custom orderingA
Heap insert uses the custom comparator function for all parent-child comparisons during heapify-up, ensuring the heap property is maintained according to the user-defined ordering rather than natural ordering of elements
B
Custom comparators don't work with heaps
C
Comparators are only used for extract
D
Insert ignores comparators
29
Question 29
What is the heap property violation detection?
A
Heap property violations are detected by comparing a node with its parent (for heapify-up) or children (for heapify-down) and identifying when the ordering relationship doesn't hold according to the heap type (min or max)
B
Violations are never detected
C
Only root violations matter
D
Violations are detected randomly
30
Question 30
How does heap extract-min handle the boundary case of size 1?
cpp
Size 1: root is min, remove it
Heap becomes emptyA
When the heap contains only one element, extract-min simply removes the root element and decrements the size to zero, requiring no heapify-down since there are no other elements to reorder
B
Size 1 heaps cannot be extracted
C
Size 1 requires full heapify-down
D
Size 1 causes errors
31
Question 31
What is the recursive nature of heapify operations?
A
Heapify operations are naturally recursive, with each call potentially making recursive calls to heapify the affected subtree, though iterative implementations are often preferred for better performance and to avoid stack overflow in large heaps
B
Heapify operations are never recursive
C
Only heapify-up is recursive
D
Recursion causes heap corruption
32
Question 32
How does heap insert affect heap height?
text
Insert may increase height
When array needs expansionA
Heap insert operations can increase the heap height when the array capacity is exhausted and needs expansion, potentially creating a new level in the complete binary tree representation of the heap
B
Insert never affects height
C
Insert always decreases height
D
Height changes randomly
33
Question 33
What is the relationship between heap operations and complete binary trees?
A
Heap operations rely on the complete binary tree property to ensure that the array representation remains contiguous and allows efficient index calculations for parent-child relationships during heapify operations
B
Heaps don't use complete binary trees
C
Complete trees make operations slower
D
Operations work with any tree
34
Question 34
How does heapify-up handle the root case?
cpp
When current node is root
Heapify-up terminatesA
When heapify-up reaches the root node (index 0), the operation terminates because there is no parent to compare with, ensuring the algorithm doesn't attempt to access invalid array indices beyond the heap bounds
B
Root case causes errors
C
Root is always swapped
D
Heapify-up never reaches root
35
Question 35
What is the impact of heap operations on stability?
A
Heap operations generally destroy stability because heapify procedures may reorder elements with equal keys, making heaps unsuitable for applications requiring stable sorting or priority queue operations where insertion order matters
B
Heap operations preserve stability
C
Stability is irrelevant for heaps
D
Heaps are always stable
36
Question 36
How does heap extract-min maintain the complete tree property?
text
Size reduction maintains completeness
No gaps in array representationA
By reducing the logical heap size without physically removing elements from the array, extract-min maintains the complete binary tree property by ensuring all levels remain completely filled except possibly the last level
B
Extract-min breaks completeness
C
Complete property is irrelevant
D
Extract creates gaps in the tree
37
Question 37
What is the difference between heap operations in min-heap vs max-heap?
A
The only difference is the comparison direction: min-heaps swap when parent is larger than child, while max-heaps swap when parent is smaller than child, making the algorithms structurally identical but with reversed comparison logic
B
They use completely different algorithms
C
Min-heaps are faster
D
Max-heaps don't exist
38
Question 38
How does heap insert handle overflow conditions?
cpp
Check size vs capacity
Resize array if neededA
Before insertion, check if the current heap size equals the array capacity, and if so, resize the underlying array to a larger capacity before proceeding with the insertion, preventing array bounds errors
B
Overflow causes crashes
C
Insert ignores overflow
D
Overflow is impossible in heaps
39
Question 39
What is the practical performance difference between heapify-up and heapify-down?
A
In practice, heapify-down often performs better than heapify-up due to better cache locality when traversing from root toward leaves, though both have the same asymptotic complexity, with the difference becoming more pronounced in larger heaps
B
They have identical practical performance
C
Heapify-up is always faster
D
Practical performance doesn't matter
40
Question 40
Considering heap operations and their implementation challenges, which fundamental property makes heapify procedures essential for maintaining the heap invariant despite the complexity of parent-child comparisons and potential element reordering?
A
Heapify procedures provide the local restructuring mechanism that restores the heap property after insertions and extractions, ensuring logarithmic-time operations while maintaining the complete binary tree structure that enables efficient array-based implementation and optimal priority access
B
Guaranteed O(1) performance
C
Minimal memory overhead
D
Simplicity of implementation