Which sorting algorithm has the best average-case time complexity?a)Bu...
Merge sort has a time complexity of O(n log n) in the average case, making it more efficient than other sorting algorithms.
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Which sorting algorithm has the best average-case time complexity?a)Bu...
Bubble Sort:
- Bubble sort is a simple comparison-based sorting algorithm.
- It repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order.
- The time complexity of bubble sort is O(n^2), where n is the number of elements in the list.
- In the average case, bubble sort compares and swaps elements multiple times, making it less efficient compared to other sorting algorithms.
Insertion Sort:
- Insertion sort is another comparison-based sorting algorithm.
- It builds the final sorted list one item at a time by inserting each item into its correct position.
- The time complexity of insertion sort is O(n^2), where n is the number of elements in the list.
- In the average case, insertion sort performs fewer comparisons and swaps compared to bubble sort, but it still has a quadratic time complexity.
Merge Sort:
- Merge sort is a divide-and-conquer sorting algorithm.
- It divides the input list into smaller sublists, sorts them recursively, and then merges the sorted sublists to obtain the final sorted list.
- The time complexity of merge sort is O(n log n), where n is the number of elements in the list.
- In the average case, merge sort has a better time complexity compared to bubble sort and insertion sort.
- Merge sort divides the list into two halves at each step, reducing the number of comparisons and swaps required.
Selection Sort:
- Selection sort is a simple comparison-based sorting algorithm.
- It repeatedly finds the minimum element from the unsorted part of the list and swaps it with the first element of the unsorted part.
- The time complexity of selection sort is O(n^2), where n is the number of elements in the list.
- In the average case, selection sort performs a large number of comparisons and swaps, making it less efficient compared to merge sort.
Conclusion:
- Among the given options, merge sort has the best average-case time complexity of O(n log n).
- Merge sort reduces the number of comparisons and swaps by dividing the list into smaller sublists and merging them in the correct order.
- Bubble sort and insertion sort have a quadratic time complexity of O(n^2), while selection sort also has a quadratic time complexity but performs more comparisons and swaps.
- Therefore, merge sort is the most efficient sorting algorithm among the given options in terms of average-case time complexity.