### Finding square root of a number by Babylonian method

The Babylonian method for finding square roots involves dividing and averaging, over and over, to obtain a more accurate solution with each repeat of the process.
Inorder to find the square root of a number you need to follow the following steps.
1. Make an initial guess for the square root
2. Divide the original number by this guess
3. Find out the mean of the 2 numbers
4. check if the difference between guess and quotient is less than the error if not then repeat the process again.
5. use this mean value as your next guess
Let us take an example of finding out the square root of 7 to 3 decimal places

let n = 7 and error = 0.001
let us take an initial guess = 3

FIRST ITERATION
Step 1: Guess = 3
Step 2: Divide 7 by 3 = 2.3333333
Step 3: Find average of 3 and 2.333333 = 2.666666 (because (2+2.333333)/2 = 2.666666)
Step 4: difference (3 - 2.3333333) > error hence repeat the process again
Step 5: Next guess is 2.666666

SECOND ITERATION
Step 1: Guess 2.666666
Step 2: Divide 7 by 2.666666 = 2.624999
Step 3: Find average of 2.666666 and 2.624999 = 2.645832
Step 4: difference (2.666666 - 2.624999) > error hence repeat the process again
Step 5: Next guess is 2.645832

THIRD ITERATION
Step 1: Guess 2.645832
Step 2: Divide 7 by 2.645832 = 2.645670
Step 3: Find average of 2.645832 and 2.645670 = 2.645751
Step 4: difference (2.645832 - 2.645670) < error hence stop and print the answer
Step 4: FINAL guess is 2.645751

Now CHECK your final guess with a calculator: sqrt 7 = 2.645751

### 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 with Quadratic Probing

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…