What is the worst-case time complexity for bubble sort?
Practice Questions
Q1
What is the worst-case time complexity for bubble sort?
O(n)
O(n log n)
O(n^2)
O(log n)
Questions & Step-by-Step Solutions
What is the worst-case time complexity for bubble sort?
Step 1: Understand what bubble sort is. It is a sorting algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order.
Step 2: Identify the worst-case scenario for bubble sort. This happens when the array is sorted in reverse order, meaning every element needs to be compared and swapped.
Step 3: Analyze how many comparisons and swaps are needed in the worst-case scenario. For an array of size n, the first pass requires n-1 comparisons, the second pass requires n-2 comparisons, and so on.
Step 4: Calculate the total number of comparisons. This can be represented as (n-1) + (n-2) + ... + 1, which equals n(n-1)/2.
Step 5: Simplify the expression. The dominant term is n^2, so we express the time complexity as O(n^2).
Step 6: Conclude that the worst-case time complexity for bubble sort is O(n^2).
