time complexity of best sort algorithm

The time complexity of the best sorting algorithm is O(n log n). The explanation for each step is as follows:

1. Comparison: Each comparison operation takes constant time, denoted as O(1).
2. Splitting: In the case of merge sort or heap sort, the array is recursively divided into smaller subproblems until individual elements are reached. This recursive splitting takes O(log n) time.
3. Merging: In the case of merge sort, the sorted subarrays are merged back together, and in heap sort, the heap is reconstructed. Merging operations take O(n) time in the worst case.
4. Building the Heap (Heap Sort): Constructing a binary heap from the input array takes O(n) time.
5. Partitioning (Quick Sort): Partitioning the array into two halves around a pivot element in quicksort takes O(n) time.

Combining these steps, the overall time complexity of the best sorting algorithms is O(n log n).