What is the average case complexity of quick sort

There is a main hash table of size 4. The 2 least significant bits of a key is used to index into the main hash table. Initially, the main hash table entries are empty. Thereafter, when more keys are hashed into it, to resolve collisions, the set of all keys corresponding to a main hash table entry is organized as a binary tree that grows on demand.

First, the 3rd least significant bit is used to divide the keys into left and right subtrees. A split is done only if it is needed, i.

Consider the following state of the hash table. Which of the following sequence of key insertions can cause the above state of the hash table assume the keys are in decimal notation? Suggested Test Series. Suggested Exams. More Algorithms Questions Q1. What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges? What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?

A subsequence of a sequence is obtained by deleting some elements from the sequence, keeping the order of the remaining elements the same. Let X denote the maximum possible weight of a subsequence of a0, a1, Two alternative packages A and B are available for processing a database having 10k records.

Package A requires 0. What is the smallest value of k for which package B will be preferred over A? 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. The algorithm was developed by a British computer scientist Tony Hoare in The name "Quick Sort" comes from the fact that, quick sort is capable of sorting a list of data elements significantly faster twice or thrice faster than any of the common sorting algorithms.

It is one of the most efficient sorting algorithms and is based on the splitting of an array partition into smaller ones and swapping exchange based on the comparison with 'pivot' element selected. Due to this, quick sort is also called as "Partition Exchange" sort.

Like Merge sort, Quick sort also falls into the category of divide and conquer approach of problem-solving methodology. Before diving into any algorithm, its very much necessary for us to understand what are the real world applications of it. Quick sort provides a fast and methodical approach to sort any lists of things. Following are some of the applications where quick sort is used. Basically, quick sort is used everywhere for faster results and in the cases where there are space constraints.

Taking the analogical view in perspective, consider a situation where one had to sort the papers bearing the names of the students, by name from A-Z. One might use the approach as follows:. Consider the following array: 50, 23, 9, 18, 61, We need to sort this array in the most efficient manner without using extra place inplace sorting. 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.