Which data structure sorting algorithm operates according to the time complexity of n log n?

Which data structure sorting algorithm operates according to the time complexity of n log n?

• A. Quicksort
• B. Mergesort
• C. Heapsort
• D. Bubblesort

Answer: (C)

The time complexity of n log n is characteristic of several efficient sorting algorithms, including Mergesort and Heapsort, both of which are designed to handle larger datasets more effectively compared to simpler algorithms. Mergesort utilizes a divide-and-conquer approach to recursively split the array into smaller subarrays, sort those subarrays, and then merge them back together in sorted order. This consistent splitting and merging leads to a time complexity of n log n. Heapsort also achieves a time complexity of n log n through a two-step process: first constructing a binary heap from the input data, and then repeatedly extracting the maximum element from the heap and reconstructing it until all elements are sorted. While Quicksort is on average n log n, its worst-case time complexity can degrade to O(n²), depending on the choice of the pivot element. Bubblesort, on the other hand, has a worst-case and average complexity of O(n²), making it inefficient for large datasets. In this case, while Heapsort does operate with a time complexity of n log n, Mergesort also shares this characteristic. Therefore, when considering which algorithms generally guarantee n log n across all cases, both Mergesort and Heapsort

The time complexity of n log n is characteristic of several efficient sorting algorithms, including Mergesort and Heapsort, both of which are designed to handle larger datasets more effectively compared to simpler algorithms.

Mergesort utilizes a divide-and-conquer approach to recursively split the array into smaller subarrays, sort those subarrays, and then merge them back together in sorted order. This consistent splitting and merging leads to a time complexity of n log n.

Heapsort also achieves a time complexity of n log n through a two-step process: first constructing a binary heap from the input data, and then repeatedly extracting the maximum element from the heap and reconstructing it until all elements are sorted.

While Quicksort is on average n log n, its worst-case time complexity can degrade to O(n²), depending on the choice of the pivot element. Bubblesort, on the other hand, has a worst-case and average complexity of O(n²), making it inefficient for large datasets.

In this case, while Heapsort does operate with a time complexity of n log n, Mergesort also shares this characteristic. Therefore, when considering which algorithms generally guarantee n log n across all cases, both Mergesort and Heapsort