What is the time complexity of bubble sort in the worst case?
Practice Questions
Q1
What is the time complexity of bubble sort 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 bubble sort 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. This occurs when the list is sorted in reverse order, meaning every element needs to be compared and swapped.
Step 3: Note that bubble sort uses two nested loops. The outer loop goes through each element in the list, and the inner loop compares adjacent elements.
Step 4: For each element in the outer loop, the inner loop runs through the remaining elements. This means that for n elements, the inner loop runs n-1 times, then n-2 times, and so on.
Step 5: Calculate the total number of comparisons. The total number of comparisons can be represented as n + (n-1) + (n-2) + ... + 1, which equals n(n-1)/2.
Step 6: Simplify the expression. The dominant term is n^2, so we say the time complexity is O(n^2).
Step 7: Conclude that the worst-case time complexity of bubble sort is O(n^2) because of the nested loops and the number of comparisons made.
