Heaps Sort Algorithm Quiz
40 comprehensive questions exploring heap sort algorithm — with 16 code examples covering heap construction, repeated extraction, in-place sorting, and performance analysis in this cpp quiz.
40 Questions
~80 minutes
1
Question 1
What is heap sort?
A
A comparison-based sorting algorithm that uses a heap data structure to sort elements by building a max-heap and repeatedly extracting the maximum element, resulting in a sorted array with O(n log n) time complexity
B
A sorting algorithm that uses quicksort
C
A sorting algorithm that uses mergesort
D
Heap sort doesn't exist
2
Question 2
How does heap sort work?
cpp
Build max-heap from array
Repeatedly extract maximum
Place at end of arrayA
Heap sort works by first building a max-heap from the input array, then repeatedly extracting the maximum element and placing it at the end of the array, gradually building the sorted sequence from right to left while maintaining the heap property
B
Heap sort uses random ordering
C
Heap sort doesn't work
D
Heap sort requires additional space
3
Question 3
What is the first step in heap sort?
A
The first step in heap sort is heap construction, where the unsorted array is transformed into a max-heap by calling heapify on each non-leaf node starting from the bottom of the heap, ensuring the heap property is satisfied throughout the entire structure
B
The first step is sorting the array
C
The first step is finding the maximum element
D
Heap sort has no first step
4
Question 4
How is heap construction performed in heap sort?
cpp
Start from bottom of heap
Call heapify on each node
Work upwards to rootA
Heap construction in heap sort is performed by starting from the last non-leaf node and working upwards to the root, calling heapify on each node to ensure the max-heap property is maintained, with this bottom-up approach being more efficient than top-down construction
B
Heap construction starts from the root
C
Heap construction uses random order
D
Heap construction is not needed
5
Question 5
What happens during repeated extraction in heap sort?
A
During repeated extraction in heap sort, the maximum element (root) is swapped with the last element in the heap, the heap size is reduced by one, and heapify is called on the root to restore the max-heap property, repeating this process until all elements are extracted
B
Elements are extracted randomly
C
Extraction doesn't happen
D
Elements are extracted from the middle
6
Question 6
How does heap sort achieve in-place sorting?
cpp
Use same array for heap and result
Swap elements within array
No extra space neededA
Heap sort achieves in-place sorting by using the same array to store both the heap and the final sorted result, performing all operations through element swaps within the array without requiring additional memory allocation beyond a few variables
B
Heap sort uses extra space
C
Heap sort requires temporary arrays
D
In-place sorting is impossible
7
Question 7
What is the time complexity of heap sort?
A
Heap sort has O(n log n) time complexity in all cases, with heap construction taking O(n) time and each of the n extractions taking O(log n) time, providing guaranteed worst-case performance unlike quicksort's potential O(n²) worst case
B
Heap sort is O(n)
C
Heap sort is O(n²)
D
Heap sort has variable complexity
8
Question 8
How does heap sort compare to quicksort?
cpp
Heap sort: guaranteed O(n log n)
Quicksort: average O(n log n), worst O(n²)A
Heap sort provides guaranteed O(n log n) worst-case performance while quicksort has O(n log n) average case but O(n²) worst case, making heap sort more predictable for time-critical applications despite typically being slower in practice due to poorer cache performance
B
Heap sort is always faster than quicksort
C
Quicksort is always faster than heap sort
D
They have identical performance
9
Question 9
What is the space complexity of heap sort?
A
Heap sort has O(1) auxiliary space complexity since it performs all sorting operations in-place using only the input array and a few additional variables, making it memory-efficient compared to algorithms like mergesort that require O(n) additional space
B
Heap sort uses O(n) space
C
Heap sort uses O(log n) space
D
Heap sort requires significant extra space
10
Question 10
How does heap sort compare to mergesort?
cpp
Heap sort: in-place, O(1) space
Mergesort: stable, O(n) spaceA
Heap sort is in-place with O(1) auxiliary space while mergesort requires O(n) additional space, but mergesort is stable and typically faster in practice, with heap sort being preferred when memory constraints are critical and stability is not required
B
Heap sort is always better than mergesort
C
Mergesort is always better than heap sort
D
They are identical
11
Question 11
Is heap sort a stable sorting algorithm?
A
Heap sort is not a stable sorting algorithm because the heapify operations can change the relative order of equal elements during the sorting process, making it unsuitable for applications where maintaining the original order of equal elements is important
B
Heap sort is stable
C
Stability doesn't apply to heap sort
D
Heap sort is conditionally stable
12
Question 12
What is the heapify operation in heap sort?
cpp
Ensure max-heap property
Compare with children
Swap if necessaryA
Heapify operation in heap sort ensures the max-heap property by comparing a node with its children and swapping with the largest child if necessary, then recursively heapifying the affected subtree to maintain the heap property throughout the structure
B
Heapify sorts the entire array
C
Heapify is not used in heap sort
D
Heapify works randomly
13
Question 13
How does heap sort handle duplicate elements?
A
Heap sort can handle duplicate elements but may not preserve their relative order due to the unstable nature of the algorithm, with equal elements potentially being reordered during heapify operations depending on their positions in the heap structure
B
Duplicates are removed
C
Duplicates cause errors
D
Duplicates are sorted first
14
Question 14
What is the best case time complexity of heap sort?
cpp
Always O(n log n)
No best case optimizationA
Heap sort has O(n log n) time complexity in all cases including the best case, as the algorithm performs the same heap construction and extraction operations regardless of the input order, unlike algorithms like insertion sort that can have O(n) best case
B
Heap sort is O(n) in best case
C
Heap sort is O(n²) in best case
D
Best case varies
15
Question 15
How does heap sort perform on nearly sorted arrays?
A
Heap sort performs the same O(n log n) operations on nearly sorted arrays as on random arrays, as it always performs full heap construction and repeated extractions regardless of the input's initial order, unlike adaptive algorithms like insertion sort
B
Heap sort is faster on nearly sorted arrays
C
Heap sort fails on nearly sorted arrays
D
Nearly sorted arrays don't affect heap sort
16
Question 16
What is the cache performance of heap sort?
cpp
Poor cache locality
Frequent heapify operationsA
Heap sort typically has poor cache performance due to frequent heapify operations that access elements scattered throughout the array, causing many cache misses compared to algorithms like quicksort that have better locality of reference during partitioning
B
Heap sort has excellent cache performance
C
Cache performance is irrelevant
D
Heap sort causes no cache misses
17
Question 17
How does heap sort compare to selection sort?
A
Heap sort is generally faster than selection sort with O(n log n) vs O(n²) time complexity, as heap sort uses a more efficient data structure for finding and removing maximum elements compared to selection sort's linear search in each iteration
B
Selection sort is faster than heap sort
C
They have identical performance
D
Performance depends on input size
18
Question 18
What is the practical performance of heap sort?
cpp
Slower than quicksort in practice
Better worst-case guaranteeA
Heap sort is typically slower than quicksort in practice due to poor cache performance and higher constant factors, but provides valuable worst-case O(n log n) guarantees that make it suitable for real-time systems and applications requiring predictable performance
B
Heap sort is always the fastest
C
Heap sort is always the slowest
D
Practical performance is unpredictable
19
Question 19
How does heap sort handle large datasets?
A
Heap sort scales well to large datasets due to its O(n log n) time complexity and O(1) auxiliary space usage, making it suitable for sorting large arrays where memory constraints are important and worst-case performance guarantees are valued
B
Heap sort fails on large datasets
C
Heap sort requires exponential space
D
Large datasets cause heap sort to be slow
20
Question 20
What is the relationship between heap sort and priority queues?
cpp
Heap sort uses heap as priority queue
Extract-max operationsA
Heap sort is essentially an implementation of sorting using a priority queue, where the heap serves as the priority queue data structure and repeated extract-max operations produce the sorted sequence, demonstrating the close relationship between these fundamental algorithms
B
Heap sort and priority queues are unrelated
C
Priority queues use heap sort
D
Heap sort doesn't use priority queues
21
Question 21
How does heap sort compare to bubble sort?
A
Heap sort is significantly faster than bubble sort with O(n log n) vs O(n²) time complexity, as heap sort uses an efficient heap data structure while bubble sort performs excessive comparisons and swaps in each pass through the array
B
Bubble sort is faster than heap sort
C
They have similar performance
D
Performance depends on element size
22
Question 22
What is the memory access pattern in heap sort?
cpp
Scattered access during heapify
Poor spatial localityA
Heap sort exhibits scattered memory access patterns during heapify operations that jump between different parts of the array, resulting in poor spatial locality and frequent cache misses compared to algorithms with more sequential access patterns
B
Heap sort has sequential memory access
C
Memory access is random
D
Heap sort has perfect memory access
23
Question 23
How does heap sort handle different data types?
A
Heap sort works with any data type that supports comparison operations, requiring only a less-than operator to establish the ordering, making it suitable for sorting arrays of integers, strings, custom objects, or any comparable elements
B
Heap sort only works with integers
C
Heap sort requires specific data types
D
Heap sort cannot handle different data types
24
Question 24
What is the advantage of heap sort over insertion sort?
cpp
Better worst-case performance
O(n log n) vs O(n²)A
Heap sort provides better worst-case O(n log n) performance compared to insertion sort's O(n²) worst case, making heap sort more suitable for applications where worst-case time bounds are important, although insertion sort may be faster on small or nearly sorted arrays
B
Insertion sort is always better
C
They have identical performance
D
Heap sort is worse in all cases
25
Question 25
How does heap sort perform in embedded systems?
A
Heap sort is well-suited for embedded systems due to its in-place operation requiring minimal memory, predictable O(n log n) worst-case performance, and lack of recursion that could cause stack overflow in memory-constrained environments
B
Heap sort is unsuitable for embedded systems
C
Embedded systems require different algorithms
D
Heap sort causes memory issues
26
Question 26
What is the recursive nature of heapify?
cpp
Heapify calls itself recursively
Maintains heap property down the treeA
Heapify operation is recursive, calling itself on the affected subtree after swapping elements to ensure the max-heap property is maintained throughout the entire path from the current node down to the leaves of the heap structure
B
Heapify is iterative
C
Heapify doesn't recurse
D
Recursion is not used
27
Question 27
How does heap sort handle array indexing?
A
Heap sort uses 0-based array indexing with parent-child relationships defined by index calculations (parent at (i-1)/2, children at 2*i+1 and 2*i+2), allowing efficient navigation through the implicit binary tree structure stored in the array
B
Heap sort uses 1-based indexing
C
Array indexing is not used
D
Heap sort requires linked structures
28
Question 28
What is the heap construction time complexity?
cpp
O(n) for heap construction
O(log n) per heapify callA
Heap construction takes O(n) time because each of the O(n) heapify calls takes O(log n) time in the worst case, but the average heapify cost decreases with tree depth, resulting in the linear time bound for building the initial heap
B
Heap construction is O(n log n)
C
Heap construction is O(n²)
D
Heap construction time varies
29
Question 29
How does heap sort compare to counting sort?
A
Heap sort is a comparison-based algorithm with O(n log n) time complexity while counting sort is non-comparison-based with O(n + k) time complexity where k is the range of values, making counting sort faster when the range is limited but heap sort more general
B
Counting sort is always better
C
Heap sort is always better
D
They have identical performance
30
Question 30
What is the stability consideration in heap sort implementation?
cpp
Heap sort is unstable
Equal elements may reorderA
Heap sort implementations must consider that the algorithm is inherently unstable, meaning equal elements may not maintain their relative input order, which is important when sorting objects where original order of equal elements needs to be preserved
B
Heap sort is always stable
C
Stability is not a consideration
D
Heap sort can be made stable
31
Question 31
How does heap sort handle very small arrays?
A
Heap sort is generally less efficient than simpler algorithms like insertion sort for very small arrays due to its higher constant factors and O(n log n) complexity, making it more suitable for larger datasets where the asymptotic advantage becomes significant
B
Heap sort is optimal for small arrays
C
Heap sort fails on small arrays
D
Array size doesn't affect heap sort
32
Question 32
What is the binary heap variant used in heap sort?
cpp
Max-heap for ascending sort
Min-heap for descending sortA
Heap sort typically uses a max-heap where the largest element is at the root, allowing repeated extraction of maximum elements to build the sorted array in ascending order, with min-heaps being used for descending order sorting when needed
B
Heap sort uses min-heap
C
Heap sort uses both types
D
Heap variant doesn't matter
33
Question 33
How does heap sort compare to Timsort?
A
Timsort is generally faster than heap sort in practice due to its adaptive nature and good cache performance, while heap sort provides better worst-case guarantees, making the choice dependent on whether worst-case performance or average-case speed is more important
B
Heap sort is always faster
C
Timsort is always faster
D
They have identical performance
34
Question 34
What is the impact of heap sort on parallel processing?
cpp
Heap sort is hard to parallelize
Sequential heapify operationsA
Heap sort is difficult to parallelize effectively due to the sequential nature of heapify operations and dependencies between heap construction and extraction steps, making it less suitable for parallel processing compared to algorithms like mergesort
B
Heap sort parallelizes perfectly
C
Parallel processing doesn't affect heap sort
D
Heap sort requires parallel hardware
35
Question 35
How does heap sort handle floating point comparisons?
A
Heap sort handles floating point comparisons using the same comparison operators as other data types, but must account for floating point precision issues like NaN values and comparison consistency, requiring careful implementation to ensure correct sorting behavior
B
Heap sort cannot handle floating point
C
Floating point requires special handling
D
Heap sort treats floats as integers
36
Question 36
What is the heap sort implementation consideration for very large arrays?
cpp
In-place sorting saves memory
No additional space allocationA
For very large arrays, heap sort's in-place nature becomes particularly valuable as it requires no additional space allocation beyond the input array, making it suitable for memory-constrained environments where algorithms like mergesort would require O(n) extra space
B
Heap sort requires extra space for large arrays
C
Large arrays cause heap sort to fail
D
Array size doesn't matter
37
Question 37
How does heap sort compare to introsort?
A
Introsort combines quicksort, heapsort, and insertion sort to achieve good practical performance with heap sort's worst-case guarantees, making introsort generally faster in practice while maintaining the O(n log n) worst-case bounds that heap sort provides
B
Heap sort is always better
C
Introsort is always better
D
They have identical performance
38
Question 38
What is the constant factor in heap sort performance?
cpp
Higher constant factors
More operations per elementA
Heap sort has higher constant factors than simpler algorithms due to the overhead of heapify operations and index calculations, requiring more operations per element compared to algorithms like selection sort, affecting its practical performance on small to medium datasets
B
Heap sort has low constant factors
C
Constant factors are irrelevant
D
Heap sort has no constant factors
39
Question 39
How does heap sort handle custom comparison functions?
A
Heap sort can use custom comparison functions by passing comparator objects or function pointers to the heapify operations, allowing sorting of complex objects based on multiple criteria or custom ordering requirements beyond simple less-than comparisons
B
Heap sort cannot use custom comparisons
C
Custom comparisons break heap sort
D
Heap sort requires built-in comparisons
40
Question 40
Considering heap sort algorithm and its fundamental operations, which property makes heap sort particularly valuable for applications requiring guaranteed performance despite its practical speed disadvantages compared to adaptive sorting algorithms?
A
Heap sort provides guaranteed O(n log n) worst-case time complexity with in-place sorting using O(1) auxiliary space, making it invaluable for real-time systems, embedded applications, and scenarios where maximum execution time must be predictable and bounded, even if average-case algorithms like quicksort are faster in practice due to better cache performance and lower constant factors
B
Heap sort is always the fastest
C
Heap sort requires no comparisons
D
Heap sort is only useful for small arrays