Question: What is the best-case time complexity of Merge Sort?
Options:
O(n)
O(n log n)
O(log n)
O(n^2)
Correct Answer: O(n log n)
Solution:
The best-case time complexity of Merge Sort is O(n log n), as it always divides the array regardless of the order.
What is the best-case time complexity of Merge Sort?
Practice Questions
Q1
What is the best-case time complexity of Merge Sort?
O(n)
O(n log n)
O(log n)
O(n^2)
Questions & Step-by-Step Solutions
What is the best-case time complexity of Merge Sort?
Step 1: Understand what Merge Sort is. It is a sorting algorithm that divides an array into smaller parts, sorts them, and then merges them back together.
Step 2: Recognize that Merge Sort always divides the array into two halves, regardless of how the elements are arranged.
Step 3: Note that each time the array is divided, it takes O(log n) time because the array is halved repeatedly until we reach individual elements.
Step 4: Understand that after dividing, we need to merge the sorted halves back together, which takes O(n) time for each level of division.
Step 5: Combine the two parts: Since there are log n levels of division and merging takes O(n) time at each level, the total time complexity is O(n log n).
Step 6: Conclude that the best-case time complexity of Merge Sort is O(n log n) because it always performs the same number of operations regardless of the initial order of elements.
Time Complexity – Understanding how the performance of an algorithm is measured in terms of the time it takes to complete as a function of the input size.
Merge Sort – A divide-and-conquer algorithm that splits an array into halves, sorts them, and then merges them back together.
Best-Case Analysis – Evaluating the performance of an algorithm under the most favorable conditions.
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