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What is the average time complexity of Merge Sort?

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Question: What is the average time complexity of Merge Sort?

Options:

  1. O(n)
  2. O(n log n)
  3. O(n^2)
  4. O(log n)

Correct Answer: O(n log n)

Solution: 

Merge Sort has an average time complexity of O(n log n) due to its recursive division of the array.

What is the average time complexity of Merge Sort?

Practice Questions

Q1
What is the average time complexity of Merge Sort?
  1. O(n)
  2. O(n log n)
  3. O(n^2)
  4. O(log n)

Questions & Step-by-Step Solutions

What is the average 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 increases.
  • Step 2: Know that Merge Sort is a sorting algorithm that divides an array into smaller parts.
  • Step 3: Realize that Merge Sort works by repeatedly splitting the array in half until each part has one element.
  • Step 4: After splitting, Merge Sort combines (or merges) these parts back together in sorted order.
  • Step 5: The process of splitting the array takes log(n) time because you keep dividing it in half.
  • Step 6: Merging the parts back together takes linear time, which is O(n), because you have to look at each element.
  • Step 7: Combine the two parts: The total time complexity is O(n) for merging and O(log n) for splitting, resulting in O(n log n).
  • Step 8: Conclude that the average time complexity of Merge Sort is O(n log n).
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