### Quick Sort Algorithm using Recursion

Quick sort is one of the most important and widely used sorting algorithm. Quick sort is a very efficient algorithm which if implemented well can run two to three times faster than its competitors merge sort and and heap sort.
The algorithm is a divide and conquer algorithm. The algorithm works by selecting a pivot element, this pivot element is usually the first element and choice of the pivot element affects the running time of the algorithm. The algorithm is basically to select a pivot element and then moving all the element less than the pivot element to its left and all the elements greater than pivot element to its right. Then we divide the array into 2 parts, one on the left of the pivot and other on the right of the pivot and then pass these 2 arrays to the algorithm for further sorting.

Algorithm :
1. Choose a Pivot element.
2. Take 2 variables left_marker and right_marker excluding the pivot element.
3. Set left_marker as the first element of the array
4. Set right_marker as the last element of the array
5. while the value at the left_marker is less than pivot keep increasing it.
6. While the value at the right_marker is greater than pivot element keep decreasing it.
7. if the left_marker is less than the right_marker then swap the elements and go to step 5.
8. if the left marker is greater than right marker then stop and swap pivot and the right_marker.

Selection of pivot Element : Pivot element selection affects the running time of the algorithm. the following are the most common choices for selecting the pivot element,

1. Selecting first element as the pivot element.
2. Selecting last element as the pivot element.
3. Selecting median as the pivot element.
4. Randomly taking an element as pivot element.

Parallelization : As we divide the array of elements into 2 and separately pass them into the recursive call, we can do this using separate threads and decrease the running time of the algorithm.

Running time :
Worst case performance : O(n^2)
Best case performance : O(n* log(n))

Let us now see the code

### Sample input and output to check the program

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Infix to Prefix Conversion

### Infix to Prefix conversion using Stack

This post is about conversion of Infix expression to Prefix conversion. For this conversion we take help of stack data structure, we need to push and pop the operators in and out of the stack.

Infix expressions are the expressions that we normally use,eg. 5+6-7; a+b*c etc. Prefix expressions are the expressions in which the 2 operands are preceded by the operator eg. -+567 , +a*bc etc.

This method is very similar to the method that we used to convert Infix to Postfix but the only difference is that here we need to reverse the input string before conversion and then reverse the final output string before displaying it.

NOTE: This changes one thing that is instead of encountering the opening bracket we now first encounter the closing bracket and we make changes accordingly in our code.

So, to convert an infix expression to a prefix expression we follow the below steps
(we have 2 string, 1st is the input infix expression string 2nd is the output string which is empty initially)

We first revers…

Hashing is a technique used for storing , searching and removing elements in almost constant time. Hashing is done with help of a hash function that generates index for a given input, then this index can be used to search the elements, store an element, or remove that element from that index.

A hash function is a function that is used to map the data elements to their position in the data structure used. For example if we use an array to store the integer elements then the hash function will generate position for each element so that searching, storing and removing operation on the array can be done in constant time that is independent of the number of elements in the array. For better look at the example below.

now we face a problem if for 2 numbers same position is generated example consider elements 1 and 14

1 % 13 = 1

14 % 13 = 1

so when we get 1 we store it at the first position, but when we get 14 we see that the position 1 is already taken, this is a case of collision.

Inorder…