How does quicksort work

Step 1 :. Thus the pivot 32 comes at its actual position and all elements to its left are lesser, and all elements to the right are greater than itself. Step 2 : The main array after the first step becomes. Step 3 : Now the list is divided into two parts:. Step 4 : Repeat the steps for the left and right sublists recursively. The final array thus becomes 9, 18, 23, 32, 50, The following diagram depicts the workflow of the Quick Sort algorithm which was described above.

Partition Method. Best case scenario: The best case scenario occurs when the partitions are as evenly balanced as possible, i. Worst case scenario: This happens when we encounter the most unbalanced partitions possible, then the original call takes n time, the recursive call on n-1 elements will take n-1 time, the recursive call on n-2 elements will take n-2 time, and so on.

The worst case time complexity of Quick Sort would be O n 2. The space complexity is calculated based on the space used in the recursion stack. The worst case space used will be O n. The average case space used will be of the order O log n. The worst case space complexity becomes O n , when the algorithm encounters its worst case where for getting a sorted list, we need to make n recursive calls. What is the average case run time complexity of Quick Sort? The average case run time of quick sort is O n logn.

This case happens when we dont exactly get evenly balanced partitions. We might get at worst a 3-to-1 split on either side of pivot element. The proof of this is quite mathematically rigorous and is out of scope of the discussion. Is Quick Sort a stable algorithm? A sorting algorithm is said to be stable if it maintains the relative order of records in the case of equality of keys. Is Quick Sort an inplace algorithm? A large array is partitioned into two arrays one of which holds values smaller than the specified value, say pivot, based on which the partition is made and another array holds values greater than the pivot value.

Quicksort partitions an array and then calls itself recursively twice to sort the two resulting subarrays. This algorithm is quite efficient for large-sized data sets as its average and worst-case complexity are O n 2 , respectively. The pivot value divides the list into two parts. And recursively, we find the pivot for each sub-lists until all lists contains only one element. Following is recurrence for best case. It can be solved using case 2 of Master Theorem.

Following is recurrence for this case. QuickSort can be implemented in different ways by changing the choice of pivot, so that the worst case rarely occurs for a given type of data. However, merge sort is generally considered better when data is huge and stored in external storage.

Is QuickSort stable? The default implementation is not stable. However any sorting algorithm can be made stable by considering indexes as comparison parameter. Is QuickSort In-place? As per the broad definition of in-place algorithm it qualifies as an in-place sorting algorithm as it uses extra space only for storing recursive function calls but not for manipulating the input.

What is 3-Way QuickSort? In simple QuickSort algorithm, we select an element as pivot, partition the array around pivot and recur for subarrays on left and right of pivot. Consider an array which has many redundant elements. If 4 is picked as pivot in Simple QuickSort, we fix only one 4 and recursively process remaining occurrences. In 3 Way QuickSort, an array arr[l.. See this for implementation.

How to implement QuickSort for Linked Lists? Can we implement QuickSort Iteratively? Yes, please refer Iterative Quick Sort. Allocating and de-allocating the extra space used for merge sort increases the running time of the algorithm.

Comparing average complexity we find that both type of sorts have O NlogN average complexity but the constants differ. For arrays, merge sort loses due to the use of extra O N storage space. Most practical implementations of Quick Sort use randomized version. The randomized version has expected time complexity of O nLogn.

Quick Sort is also a cache friendly sorting algorithm as it has good locality of reference when used for arrays. Quick Sort is also tail recursive, therefore tail call optimizations is done. In case of linked lists the case is different mainly due to difference in memory allocation of arrays and linked lists. Unlike arrays, linked list nodes may not be adjacent in memory. Unlike array, in linked list, we can insert items in the middle in O 1 extra space and O 1 time.