Final answer:
The correct option is Option A. The selection sort algorithm displays the same performance across best-case, average-case, and worst-case scenarios with O(n^2) complexity, as it checks every element against each other to sort the list.
Step-by-step explanation:
The algorithm whose best-case, average-case, and worst-case behaviors are the same is the selection sort. Regardless of the initial arrangement of the data, selection sort will always have the same performance because every element is checked against every other element. It consistently performs at O(n^2) complexity as it goes through the list to find the smallest or largest element depending on the sort order and places it at the beginning or end of the list, respectively. This process is repeated until the entire list is sorted. Unlike algorithms like insertion sort or sequential search, the performance of selection sort does not improve even if the list is already sorted or nearly sorted.
An example of an algorithm whose best-case, average-case, and worst-case behaviors are the same is selection sort. Selection sort is a simple sorting algorithm that works by repeatedly finding the minimum element from the unsorted part of the array and putting it at the beginning. Regardless of the initial order of the elements, selection sort always performs the same number of comparisons and swaps, resulting in the same time complexity for all cases.