what is quick Sort Can some explain the complexity ?

Question

what is quick Sort Can some explain. the complexity ?

Shivam Payasi · Answer

Quick Sort is a popular divide-and-conquer sorting algorithm. It works by selecting a pivot element from the array and partitioning the other elements into two groups: those less than the pivot and those greater than the pivot. The process is then recursively applied to the sub-arrays. Eventually the array becomes sorted.

Shivam Payasi · Answer

Time Complexity: The time complexity of Quick Sort depends on how well the array is divided in each partition step. Best Case (O(n log n)): When the pivot divides the array into two roughly equal parts at each step the depth of recursion is log n  and at each level you do about O(n) work for partitioning. Therefore the total time complexity is O(n log n) . Average Case (O(n log n)): Even with a randomly chosen pivot the algorithm on average has log n levels of recursion with O(n) work at each level giving an average-case time complexity of O(n log n) . Worst Case (O(n²)): The worst case occurs when the pivot always ends up being the smallest or largest element (e.g. the array is already sorted in increasing or decreasing order). In this case there are n levels of recursion and at each level the partition takes O(n) time resulting in a worst-case time complexity of O(n²) . Space Complexity: In-place algorithm : Quick Sort typically sorts in place so the additional space used is for the recursion stack. Best case space complexity (O(log n)) : If the partitioning is balanced the depth of the recursion tree is O(log n) . Worst case space complexity (O(n)) : In the worst case (e.g. if the pivot is always the smallest or largest) the recursion depth can be O(n) .