What is the time complexity of Selection Sort in all cases?

Selection Sort consistently operates with a time complexity of O(n^2) in all cases—best, average, and worst. This is due to the algorithm's methodology, which involves two nested loops.

The outer loop runs n times, where n is the number of elements in the array. For each iteration of the outer loop, the inner loop scans through the remaining elements of the unsorted section to find the minimum (or maximum, depending on sorting order) value. This inner loop also runs up to n iterations for the first pass, n-1 for the second, and so on, resulting in a total of approximately n(n-1)/2 comparisons made throughout the entire sorting process.

Thus, as n grows larger, the fundamental operations of the algorithm scale quadratically, leading to the O(n^2) time complexity. This performance characteristic remains constant regardless of the initial arrangement of the elements in the array, making the selection sort's efficiency predictable but not optimal for large datasets compared to other algorithms like Merge Sort or Quick Sort which have better average time complexities.