"Memory Consumption of Sorting Algorithms: An Introduction to Space Complexity"

The space complexity (memory consumption) of sorting algorithms is a critical consideration, especially in scenarios with limited memory. Space complexity describes the relationship between the additional storage space used by the algorithm during execution and the data size \( n \), denoted as \( O(1) \), \( O(n) \), or \( O(\log n) \). Key space characteristics of major sorting algorithms: - **In-place sorting** (Bubble Sort, Selection Sort, Insertion Sort, Heap Sort): Require no additional arrays, with space complexity \( O(1) \); - **Merge Sort**: Requires temporary arrays during the merge step of divide-and-conquer, with space complexity \( O(n) \); - **Quick Sort**: Uses recursive partitioning, with average space complexity \( O(\log n) \). Selection strategy: Prioritize \( O(1) \) algorithms when memory is limited; choose Merge Sort for stable sorting with sufficient memory; pursue average performance (e.g., standard library sorting) with Quick Sort. Understanding space characteristics enables balancing time and space to write efficient code.