In the worst case, what is the time complexity of Merge Sort?

₹0.0

Question: In the worst case, what is the 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) because it always divides the array into halves.

In the worst case, what is the time complexity of Merge Sort?

In the worst case, what is the time complexity of Merge Sort?

Step 1: Understand that Merge Sort is a sorting algorithm that works by dividing an array into smaller parts.
Step 2: Realize that in each step, the array is split into two halves until each part has only one element.
Step 3: Note that splitting the array takes log(n) steps because you keep dividing by 2.
Step 4: After splitting, you need to merge the parts back together, which takes linear time, O(n), for each level of division.
Step 5: Combine the two parts: Since you have log(n) levels of division and each level takes O(n) time to merge, the total time is O(n log n).
Step 6: Conclude that in the worst case, Merge Sort will always take O(n log n) time to sort an array.

Time Complexity – The measure of the amount of time an algorithm takes to complete as a function of the length of the input.
Merge Sort – A divide-and-conquer algorithm that splits an array into halves, sorts them, and then merges them back together.
Worst Case Analysis – The scenario in which an algorithm takes the longest time to complete, often used to evaluate performance.