Which of the following describes the space complexity of counting sort?
O(1)
O(n)
O(n + k), where k is the range of input values
O(log n)
What is a key characteristic of in-place partitioning within the context of Quick Sort?
The partitioning process is performed entirely within the original array, without requiring the allocation of substantial additional memory proportional to the input size.
The algorithm sorts the array by recursively dividing it into smaller subarrays and then merging them back together.
The partitioning step always selects the first element of the subarray as the pivot.
In-place partitioning is only applicable when the input array is already sorted in reverse order.
Which of the following best describes the role of the base case in a recursive implementation of Quick Sort?
To select the pivot element for each recursive call
To define the condition when the array is fully sorted and the recursion should stop
To partition the array around a chosen pivot element
To handle the comparison and swapping of elements during the sorting process
Bucket Sort can be considered a stable sorting algorithm under which condition?
Bucket Sort is inherently stable regardless of the input or implementation.
The input data is already sorted.
The underlying sorting algorithm used within each bucket is stable.
The number of buckets is equal to the number of elements.
Bucket Sort achieves its efficiency by:
Exploiting the relative order of elements within the input
Recursively dividing the input into smaller subproblems
Using a priority queue to maintain sorted order during insertion
Distributing elements into buckets based on their range
What is the purpose of the partitioning step in the Quick Sort algorithm?
To find the median element of the array
To merge two sorted subarrays into a single sorted array
To divide the array into two subarrays such that all elements in the left subarray are less than or equal to the pivot and all elements in the right subarray are greater than the pivot
To sort the entire array in ascending order
How does using the median-of-three partitioning strategy in Quick Sort help optimize its performance?
It has no impact on the performance of Quick Sort; it's simply an alternative partitioning approach.
It eliminates the need for recursive calls in the sorting process, making it significantly faster.
It guarantees the selection of the median element as the pivot, always leading to perfectly balanced partitions.
It reduces the likelihood of selecting a very small or very large element as the pivot, thereby decreasing the chances of worst-case scenarios.
How does the space complexity of Heap Sort compare to other comparison-based sorting algorithms?
Heap Sort has a lower space complexity
Heap Sort's space complexity depends on the input data
Heap Sort has a higher space complexity
Heap Sort typically has the same space complexity
Why is Merge Sort often preferred over simpler algorithms like Bubble Sort for large datasets?
Merge Sort has a lower space complexity than Bubble Sort.
Merge Sort is an in-place sorting algorithm, while Bubble Sort is not.
Merge Sort's recursive approach is easier to implement.
Merge Sort's time complexity scales better with increasing data size.
What is a potential limitation of Heap Sort compared to some other efficient sorting algorithms?
It is less efficient when the input data is already nearly sorted.
It is not well-suited for sorting linked lists.
Its average-case time complexity is worse than some other algorithms.
It requires the entire dataset to be in memory.