Print the Fibonacci sequence. Check leap year. DSA Introduction What is an algorithm? Related Topics Insertion Sort Algorithm. Quicksort is a sorting algorithm based on the divide and conquer approach where An array is divided into subarrays by selecting a pivot element element selected from the array. While dividing the array, the pivot element should be positioned in such a way that elements less than pivot are kept on the left side and elements greater than pivot are on the right side of the pivot.
The left and right subarrays are also divided using the same approach. This process continues until each subarray contains a single element. At this point, elements are already sorted. Finally, elements are combined to form a sorted array. Working of Quicksort Algorithm 1.
Select the Pivot Element There are different variations of quicksort where the pivot element is selected from different positions.
Select a pivot element 2. Rearrange the Array Now the elements of the array are rearranged so that elements that are smaller than the pivot are put on the left and the elements greater than the pivot are put on the right. Put all the smaller elements on the left and greater on the right of pivot element Here's how we rearrange the array: A pointer is fixed at the pivot element. The pivot element is compared with the elements beginning from the first index.
Comparison of pivot element with element beginning from the first index If the element is greater than the pivot element, a second pointer is set for that element. If the element is greater than the pivot element, a second pointer is set for that element. 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. Based on our understanding of partitioning in quick sort, we will now try to write an algorithm for it, which is as follows.
This division of array takes place using a pivot point. The position of a pivot is selected such that the elements on the left of the pivot are less than the pivot element and also the element on the right is greater than the pivot element. This partitioning aims to obtain the sorted array in linear running time. Quick Sort uses a function partition to find the partitioning point for an array, and Quick Sort is further called for 2 sub-arrays.
This partition function uses an assumption to take the last element of the array as a pivot. Explanation: In the above algorithm, there is pseudocode for partition function used to find the partition element of the array followed by pseudocode for quicksort. Quick Sort algorithm calls the partition function to calculate the partitioning point. Quick Sort is a tail-recursive, in-place algorithm that makes it suitable for use in case of arrays of a large number of elements.
Code Explanation: The above program is for the recursive Quick Sort approach where myarr is defined to be sorted, and 0 th element, i. A partition function is called to find the partitioning element. Here we are considering the pivot element to be the last element and index of a smaller element less than the left of the array being passed as an argument. Then each element is compared with pivot and in case element smaller than pivot is found I get incremented and swapping of an element occurs.
And when no element is left to be swapped, all elements in the left are lesser than pivot and elements on the right are greater than the pivot. Further quicksort algorithm is called for this subarray, and this way algorithm keeps on dividing the array and sort the elements. Best Case : This case occurs when partition elements happen to be always the middle element of the array.
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