"Two-Dimensional" View of Sorting Algorithms: An Introduction to Time and Space Complexity

The two-dimensional complexity (time and space) of sorting algorithms is a core criterion for algorithm selection. In terms of time complexity, for small datasets (n ≤ 1000), simple quadratic-time algorithms like bubble sort, selection sort, and insertion sort (O(n²)) are suitable, while for large datasets (n > 10000), efficient linearithmic algorithms such as quicksort, mergesort, and heapsort (O(n log n)) are preferred. Regarding space complexity, heapsort and bubble sort are in-place with O(1) space, quicksort requires O(log n) auxiliary space, and mergesort needs O(n) space. A balance between time and space is essential: mergesort trades O(n) space for stable O(n log n) time, while quicksort uses O(log n) space to optimize efficiency. Beginners should first master simple algorithms before advancing to high-performance ones, selecting based on data size and space constraints to achieve "on-demand sorting."