For which of the following algorithms is O(n^2) the best-case time complexity?Quick sortMerge sortInsertion sortBubble sort
Question
For which of the following algorithms is O(n^2) the best-case time complexity?Quick sortMerge sortInsertion sortBubble sort
Solution
Bubble sort and Insertion sort can have a best-case time complexity of O(n^2).
For Bubble sort, the best-case scenario is when the input is already sorted. However, the algorithm still goes through the entire list comparing each pair of elements, which results in a time complexity of O(n^2).
For Insertion sort, the best-case scenario is also when the input is already sorted. The algorithm will only make one comparison per element, resulting in a time complexity of O(n). However, in the average and worst-case scenarios, the time complexity is O(n^2) as it has to compare and shift elements.
Quick sort and Merge sort, on the other hand, have a best-case time complexity of O(n log n). Quick sort achieves this when the pivot element is always the median, and Merge sort achieves this as it always divides the list in half and merges them in linear time.
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