Quicksort is a sorting algorithm that has a time complexity of O(n log n) in the average case and O(n^2) in the worst case. The time complexity of quicksort depends on how the pivot is chosen. If the pivot is chosen randomly, then the algorithm will have an average-case time complexity of O(n log n). However, if the pivot is always chosen to be the smallest or largest element in the array, then the algorithm will have a worst-case time complexity of O(n^2).

Quicksort is a divide-and-conquer algorithm. It works by recursively splitting the array into two smaller subarrays, sorting the subarrays, and then merging the sorted subarrays. The pivot is used to select the element that is used to split the array.

The average-case time complexity of quicksort is O(n log n) because the pivot is usually chosen randomly. This means that the two subarrays will be roughly equal in size. The algorithm will then recursively sort the subarrays, and the time complexity will be O(n log n) for each subarray. The total time complexity will then be O(n log n) + O(n log n) = O(2n log n) = O(n log n).

The worst-case time complexity of quicksort is O(n^2) because the pivot can be chosen to be the smallest or largest element in the array. This means that one of the subarrays will be empty, and the algorithm will have to sort the other subarray recursively. The time complexity of sorting the subarray will be O(n), and the total time complexity will be O(n) + O(n) = O(2n) = O(n^2).

Quicksort is a very efficient sorting algorithm in the average case. However, it has a worst-case time complexity of O(n^2), which can be a problem for large arrays. If you are sorting a large array, you may want to use a different sorting algorithm, such as merge sort, which has a worst-case time complexity of O(n log n).