what is the time complexitry of std::sort

The time complexity of std::sort in C++ is typically O(n log n), where n is the size of the input array.

The std::sort algorithm uses a variation of the quicksort algorithm, called introsort, which combines quicksort, heapsort, and insertion sort. The algorithm starts by partitioning the input array into two subarrays, with elements in the left subarray less than or equal to the pivot element, and elements in the right subarray greater than the pivot element. This partitioning step is performed recursively until the subarrays are sorted.

In the worst case, where the input array is already sorted in ascending or descending order, the partitioning step may create subarrays of size 0 and n-1, resulting in a time complexity of O(n^2). However, the average and best-case time complexity of std::sort is O(n log n). This is because the algorithm is designed to choose a good pivot element and perform partitioning in a way that balances the size of the subarrays.

The O(n log n) time complexity can be explained as follows:

  1. Divide: The algorithm divides the input array into two subarrays around a pivot element. This step takes O(n) time, as it needs to iterate through all the elements of the array.

  2. Conquer: The algorithm recursively sorts the two subarrays. The size of the subarrays is halved with each recursive call. Since the algorithm performs O(log n) recursive calls, the total time complexity for this step is O(n log n).

  3. Combine: The algorithm combines the sorted subarrays into a single sorted array. This step takes O(n) time, as it needs to merge the subarrays.

The overall time complexity of std::sort is determined by the combination of these steps. Since the divide and combine steps both have a time complexity of O(n), and the conquer step has a time complexity of O(n log n), the dominant time complexity is O(n log n).

It's important to note that the time complexity analysis assumes that the comparison operator used by std::sort takes constant time. If the comparison operator has a time complexity greater than O(1), the overall time complexity of std::sort may be higher.