What is the worst-case time complexity of Merge Sort?

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Question: What is the worst-case time complexity of Merge Sort?

Options:

Correct Answer: O(n log n)

Solution:

The worst-case time complexity of Merge Sort is O(n log n), which is consistent regardless of the input data.

What is the worst-case time complexity of Merge Sort?

What is the worst-case time complexity of Merge Sort?

Step 1: Understand what time complexity means. It measures how the time to complete an algorithm grows as the size of the input data increases.
Step 2: Know that Merge Sort is a sorting algorithm that divides the input data into smaller parts, sorts them, and then merges them back together.
Step 3: Recognize that Merge Sort always divides the data in half, which creates a tree-like structure of divisions.
Step 4: Each level of this tree requires a linear amount of time (O(n)) to merge the sorted parts back together.
Step 5: The height of the tree (number of levels) is log(n) because we keep dividing the data in half.
Step 6: Combine the time for each level (O(n)) with the number of levels (log(n)) to get the total time complexity: O(n log n).
Step 7: Conclude that the worst-case time complexity of Merge Sort is O(n log n), and this remains the same for any input data.

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