What is the time complexity of a bubble sort algorithm in the worst case?

What is the time complexity of a bubble sort algorithm in the worst case?

Step 1: Understand what bubble sort does. It repeatedly goes through a list of numbers.
Step 2: In each pass, it compares adjacent numbers and swaps them if they are in the wrong order.
Step 3: The process is repeated until no swaps are needed, meaning the list is sorted.
Step 4: In the worst case, the list is sorted in reverse order, so every element needs to be compared and swapped.
Step 5: For a list of n elements, the first pass requires n-1 comparisons, the second pass requires n-2 comparisons, and so on.
Step 6: The total number of comparisons in the worst case is (n-1) + (n-2) + ... + 1, which equals n(n-1)/2.
Step 7: This simplifies to O(n^2) because we focus on the highest order term when describing time complexity.

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