What is the time complexity of the bubble sort algorithm in the worst case?
Practice Questions
Q1
What is the time complexity of the bubble sort algorithm in the worst case?
O(n)
O(n log n)
O(n^2)
O(log n)
Questions & Step-by-Step Solutions
What is the time complexity of the bubble sort algorithm in the worst case?
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. The worst case occurs when the list is sorted in reverse order, meaning every element needs to be compared and swapped.
Step 3: Analyze the number of comparisons. In the worst case, for a list of n elements, the first element will be compared with n-1 elements, the second element with n-2 elements, and so on.
Step 4: Calculate the total number of comparisons. This results in (n-1) + (n-2) + ... + 1, which simplifies to n(n-1)/2. This is approximately n^2/2.
Step 5: Determine the time complexity notation. In Big O notation, we focus on the highest order term and ignore constants, so O(n^2/2) simplifies to O(n^2).
Step 6: Conclude that the worst-case time complexity of bubble sort is O(n^2).
