নিচের কোনটি স্বায়ত্বশাসিত ব্যাংকের উদাহরণ?

Question:

Which of the following sorting algorithms guarantees an O(n log n) time complexity in the worst-case scenario?

Options:

    
• A) Quick Sort
    
• B) Bubble Sort
    
• C) Merge Sort
    
• D) Insertion Sort

Correct Answer: C) Merge Sort

Explanation:

Merge Sort is based on the divide-and-conquer paradigm. It consistently divides the array into two halves until single-element arrays remain, and then merges them in sorted order. Because it always splits the data evenly and the merging step takes linear time, its worst-case time complexity is strictly O(n log n).

Why other options are incorrect:

    
• A) Quick Sort: Although its average-case time complexity is O(n log n), its worst-case performance degrades to O(n²) if unbalanced partitions are selected repeatedly (e.g., when the array is already sorted and the last element is chosen as the pivot).
    
• B) Bubble Sort: It relies on adjacent comparisons and swaps. In the worst-case scenario (a reverse-sorted list), it requires O(n²) operations.
    
• D) Insertion Sort: Similar to Bubble Sort, inserting each element into an already reversed list requires shifting all preceding elements, yielding a worst-case time complexity of O(n²).

Key Takeaway: Unlike Quick Sort or Insertion Sort, Merge Sort provides guaranteed upper-bound performance at the expense of requiring additional O(n) auxiliary space.