sorting algorithms with o(n log n) complexity

Sorting algorithms with O(n log n) complexity are algorithms that can sort a list of elements in an efficient manner. The O(n log n) complexity signifies that the time required by these algorithms grows in proportion to the number of elements (n) being sorted multiplied by the logarithm of that number (log n). These algorithms, such as merge sort, quicksort, and heapsort, employ divide and conquer techniques to efficiently sort large lists of elements. They divide the original list into smaller sublists, sort them separately, and then merge or combine the sorted sublists to obtain the final sorted list. The "O" in O(n log n) represents the upper-bound or worst-case time complexity, indicating that the sorting time will not exceed a multiple of n log n for larger inputs. It is an important measure for analyzing the scalability and efficiency of sorting algorithms.

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