In counting sort, what does the count array store?
The frequency of each distinct element in the input array.
The sorted elements of the input array.
The cumulative sum of frequencies of elements less than or equal to each element in the input array.
The indices of elements in the input array.
Why is Merge Sort often preferred over simpler algorithms like Bubble Sort for large datasets?
Merge Sort's recursive approach is easier to implement.
Merge Sort is an in-place sorting algorithm, while Bubble Sort is not.
Merge Sort has a lower space complexity than Bubble Sort.
Merge Sort's time complexity scales better with increasing data size.
Is counting sort inherently stable?
Yes, counting sort is always stable.
No, counting sort is inherently unstable.
Counting sort can be made stable with modifications to the algorithm.
The stability of counting sort depends on the input data.
What is the worst-case time complexity of Merge Sort?
O(log n)
O(n)
O(n^2)
O(n log n)
What is a key characteristic of in-place partitioning within the context of Quick Sort?
In-place partitioning is only applicable when the input array is already sorted in reverse order.
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.
The partitioning process is performed entirely within the original array, without requiring the allocation of substantial additional memory proportional to the input size.
In computational geometry, how is sorting used in finding the closest pair of points from a set of points in a 2D plane?
The points are sorted based on their x-coordinates, and then a divide-and-conquer approach is used to efficiently compare distances between points in the sorted order.
Sorting is not directly relevant to finding the closest pair of points; it can be solved more efficiently using hashing techniques.
The points are sorted randomly, and the distances between consecutive points are compared to find the closest pair.
Sorting is only used if the points are uniformly distributed in the plane; otherwise, a different approach is required.
How does sorting contribute to efficient data organization in databases and file systems?
Sorting reduces the overall storage space required for the data.
Sorting makes data retrieval faster by enabling the use of efficient search algorithms like binary search.
Sorting has no direct impact on data organization; it's solely used for arranging data in a specific order.
Sorting enhances data security by making it more difficult for unauthorized users to access sensitive information.
What is the space complexity of Merge Sort?
O(1)
How does the time complexity of Radix Sort compare to comparison-based sorting algorithms like Merge Sort and Quick Sort for integers with a wide range?
Radix Sort is always slower
Radix Sort has the same time complexity
Radix Sort can be faster under certain conditions
Radix Sort is consistently faster
Why is binary search a preferred algorithm for searching in sorted arrays compared to linear search?
Binary search uses less memory than linear search.
Binary search is easier to implement and understand than linear search.
Binary search works correctly even on unsorted arrays, while linear search does not.
Binary search has a time complexity of O(log n), which is significantly faster than linear search's O(n) complexity for large datasets.