Which recurrence relation represents the typical running time of Merge Sort?
Options
- A. T(N) = T(N - 1) + O(1)
- B. T(N) = 2T(N/2) + O(N)
- C. T(N) = T(N/2) + O(1)
- D. More than one of the above
- E. None of the above
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Quiz Practice:
Correct Answer (Detailed Explanation is Below)
B. T(N) = 2T(N/2) + O(N)
Detailed Explanation
The typical recurrence for Merge Sort is T(N) = 2T(N/2) + O(N). The term 2T(N/2) represents recursively sorting two halves, while O(N) represents merging the two sorted halves. Applying the Master Theorem gives O(N log N). Understanding recurrence relations is useful for analyzing recursive algorithms such as Merge Sort, Binary Search, and many tree-based algorithms.