The complexity of Bubble sort isans.O(n)O(n log n)O(log n)O(n3) Previous Marked for Review Next

Title: Understanding Bubble Sort Time Complexity

1. Break Down the Problem

   • The question asks for the time complexity classification of the Bubble Sort algorithm.
   • 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. Relevant Concepts

   • The time complexity of Bubble Sort in the average and worst case is $O(n^2)$, where $n$ is the number of items being sorted.
   • In the best case, when the array is already sorted, the time complexity is $O(n)$.

3. Analysis and Detail

   • Bubble Sort performs at least $n-1$ passes over the array of $n$ elements, where a pass involves $n-1$ comparisons.
   • In each pass, the largest unsorted element is moved to its correct position.
   • This leads to $\approx \frac{n(n-1)}{2}$ comparisons in the worst case, which simplifies to $O(n^2)$.
   • The best case, where no swaps are needed, results in only $n-1$ comparisons, leading to $O(n)$.

4. Verify and Summarize

   • The average and worst-case time complexities of Bubble Sort are $O(n^2)$, and the best case is $O(n)$.
   • Bubble sort is not considered efficient for large datasets.

Final Answer

The complexity of Bubble Sort is $O(n^2)$ for the average and worst cases, and $O(n)$ for the best case.