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What is the time complexity of the Bubble Sort algorithm in the worst-case scenario?

Question

What is the time complexity of the Bubble Sort algorithm in the worst-case scenario?

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Solution

The time complexity of the Bubble Sort algorithm in the worst-case scenario is O(n^2). Here's why:

  1. Bubble Sort is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order.

  2. The worst-case scenario for Bubble Sort is when the input list is in reverse order. In this case, Bubble Sort would need to compare each element with every other element, hence it would take n*(n-1)/2 comparisons, where n is the number of elements in the list.

  3. In terms of time complexity, we usually drop the constants and lower order terms, so the time complexity in the worst-case scenario becomes O(n^2).

  4. This means that if the size of the input list doubles, the time it takes to sort the list would increase by a factor of four, making Bubble Sort inefficient for large lists.

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