Which sorting algorithm typically achieves a performance of n log n?

Which sorting algorithm typically achieves a performance of n log n?

• A. Bubble Sort
• B. Insertion Sort
• C. Quick Sort
• D. Selection Sort

Answer: (C)

Quick Sort is a highly efficient sorting algorithm that typically achieves an average performance of \( n \log n \), making it suitable for large datasets. The efficiency of Quick Sort comes from its divide-and-conquer strategy. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays: those less than the pivot and those greater than the pivot. This partitioning step is essential and efficiently reduces the problem size, allowing the algorithm to apply the same process recursively to the sub-arrays. In the average case, Quick Sort’s partitioning operation is done in linear time, while the depth of the recursion tree is logarithmic, resulting in the \( n \log n \) average complexity. Even in the worst-case scenario, where the pivot is always the smallest or largest element, optimizations like choosing a random pivot or using the median can help maintain performance. The other sorting algorithms mentioned (Bubble Sort, Insertion Sort, and Selection Sort) primarily operate with a performance of \( O(n^2) \) in their average cases, which makes them less efficient than Quick Sort when handling larger collections of data.

Quick Sort is a highly efficient sorting algorithm that typically achieves an average performance of ( n \log n ), making it suitable for large datasets. The efficiency of Quick Sort comes from its divide-and-conquer strategy. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays: those less than the pivot and those greater than the pivot. This partitioning step is essential and efficiently reduces the problem size, allowing the algorithm to apply the same process recursively to the sub-arrays.

In the average case, Quick Sort’s partitioning operation is done in linear time, while the depth of the recursion tree is logarithmic, resulting in the ( n \log n ) average complexity. Even in the worst-case scenario, where the pivot is always the smallest or largest element, optimizations like choosing a random pivot or using the median can help maintain performance.

The other sorting algorithms mentioned (Bubble Sort, Insertion Sort, and Selection Sort) primarily operate with a performance of ( O(n^2) ) in their average cases, which makes them less efficient than Quick Sort when handling larger collections of data.