Sorting algorithm

History and Classification of Sorting Algorithms - Sorting problem has attracted research since the beginning of computing - Betty Holberton worked on early sorting algorithms in the 1950s - Bubble sort was analyzed in 1956 - Asymptotically optimal algorithms have been known since the mid-20th century - Timsort, widely used, was introduced in 2002 - Sorting algorithms can be classified by computational complexity - They can have best, worst, and average case behavior - Some algorithms are in-place, using minimal memory beyond the items being sorted - Algorithms can be recursive, non-recursive, or both - Stability refers to maintaining the relative order of records with equal keys Comparison-based Sorting Algorithms - Quicksort: O(n log n) average and best case, O(n^2) worst case, partitioning - Merge sort: O(n log n) worst case, merging - Heapsort: O(n log n) worst case, selection - Timsort: O(n log n) worst case, insertion and merging - Library sort: O(n log n) worst case, insertion Non-comparison Sorting Algorithms - Bucket sort (uniform keys): O(n + k) best and average case, O(n^2 * k) worst case, assumes uniform distribution - MSD Radix Sort: O(n * (k/d)) best and average case, O(n + 2^d) worst case, stable version uses external array - Spreadsort: O(n * (k/d) * 2^d) best case, O(n * ((k/s) + d) * 2^d) average case, asymptotic based on assumption - Burstsort: O(n * (k/d)) best and average case, O(n * (k/d)) worst case, better constant factor for sorting strings - Flashsort: O(n + r) best case, O(n^2) worst case, requires uniform distribution, in-place version not stable Analysis of Sorting Algorithms - Sorting networks have varying time complexity and stability. - Bitonic sorter has a logarithmic time complexity and can be parallelized. - Bogosort has an unbounded worst-case time complexity and uses random shuffling. - Stooge sort has a time complexity of log 3 / log 1.5 and can be made stable. - Slowsort has a time complexity of log n^(log n) and is a multiply and surrender algorithm. Popular Sorting Algorithms - Insertion sort is widely used for small data sets. - Heapsort, merge sort, and quicksort are commonly used for large data sets. - Hybrid algorithms combine an efficient algorithm with insertion sort for small lists. - Timsort and introsort are more sophisticated variants used in specific implementations. - Distribution sorts like counting sort and radix sort are used for restricted data.