Quicksort

Quicksort is an efficient, general-purpose sorting algorithm. Quicksort was developed by British computer scientist Tony Hoare in 1959 and published in 1961. It is still a commonly used algorithm for sorting. Overall, it is slightly faster than merge sort and heapsort for randomized data, particularly on larger distributions. Quicksort is a divide-and-conquer algorithm. It works by selecting a "pivot" element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. For this reason, it is sometimes called partition-exchange sort. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory to perform the sorting. Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. It is a comparison-based sort since elements a and b are only swapped in case their relative order has been obtained in the transitive closure of prior comparison-outcomes. Most implementations of quicksort are not stable, meaning that the relative order of equal sort items is not preserved. Mathematical analysis of quicksort shows that, on average, the algorithm takes O ( n log ⁡ n ) {\displaystyle O(n\log {n})} comparisons to sort n items. In the worst case, it makes O ( n 2 ) {\displaystyle O(n^{2})} comparisons.