What is the algorithm & How we can write algorithm

What is the algorithm?

In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are

used for calculation, data processing, and automated reasoning.

What is a mathematical algorithm?

An algorithm is a set of rules for solving a math problem which, if done properly, will give a correct answer each time. Algorithms generally

involve repeating a series of steps over and over, as in the borrowing and carrying algorithms and in the long multiplication and

division algorithms.

Who came up with algorithms?

The word algorithm comes from the name of the 9th century Persian mathematician Abu Abdullah Muhammad ibn Musa Al-Khwarizmi.

What is the difference between algorithm and pseudocode in computer science?

An algorithm is a systematic logical approach used to solve problems in a computer while Pseudocode is the statement in plain English which may

be translated later into a programming language (program). Analgorithm is the semantic while the pseudo-code is just a syntax of the

communication about solving a problem.

Qualities of a good algorithm

1.  Inputs and outputs should be defined precisely.
2.  Each steps in algorithm should be clear and unambiguous.
3. Algorithm should be most effective among many different ways to solve a problem.
4. An algorithm shouldn't have computer code. Instead, the algorithm should be written in such a way that, it can be used in similar programming languages.

Syntax Of Algorithms

Examples Of Algorithms In Programming

Write an algorithm to add two numbers entered by user.

Step 1: Start
Step 2: Declare variables num1, num2 and sum. 
Step 3: Read values num1 and num2. 
Step 4: Add num1 and num2 and assign the result to sum.
        sum←num1+num2 
Step 5: Display sum 
Step 6: Stop

Write an algorithm to find the largest among three different numbers entered by user.

Step 1: Start
Step 2: Declare variables a,b and c.
Step 3: Read variables a,b and c.
Step 4: If a>b
           If a>c
              Display a is the largest number.
           Else
              Display c is the largest number.
        Else
           If b>c
              Display b is the largest number.
           Else
              Display c is the greatest number.  
Step 5: Stop

Write an algorithm to find all roots of a quadratic equation ax²+bx+c=0.

Step 1: Start
Step 2: Declare variables a, b, c, D, x1, x2, rp and ip;
Step 3: Calculate discriminant
         D←b2-4ac
Step 4: If D≥0
              r1←(-b+√D)/2a
              r2←(-b-√D)/2a 
              Display r1 and r2 as roots.
        Else     
              Calculate real part and imaginary part
              rp←b/2a
              ip←√(-D)/2a
              Display rp+j(ip) and rp-j(ip) as roots
Step 5: Stop             

Write an algorithm to find the factorial of a number entered by user.

Step 1: Start
Step 2: Declare variables n,factorial and i.
Step 3: Initialize variables
          factorial←1
          i←1
Step 4: Read value of n
Step 5: Repeat the steps until i=n
     5.1: factorial←factorial*i
     5.2: i←i+1
Step 6: Display factorial
Step 7: Stop

Write an algorithm to check whether a number entered by user is prime or not.

Step 1: Start
Step 2: Declare variables n,i,flag.
Step 3: Initialize variables
        flag←1
        i←2  
Step 4: Read n from user.
Step 5: Repeat the steps until i<(n/2)
     5.1 If remainder of n÷i equals 0
            flag←0
            Go to step 6
     5.2 i←i+1
Step 6: If flag=0
           Display n is not prime
        else
           Display n is prime
Step 7: Stop 

Write an algorithm to find the Fibonacci series till term≤1000.

Step 1: Start 
Step 2: Declare variables first_term,second_term and temp. 
Step 3: Initialize variables first_term←0 second_term←1 
Step 4: Display first_term and second_term 
Step 5: Repeat the steps until second_term≤1000 
     5.1: temp←second_term 
     5.2: second_term←second_term+first term 
     5.3: first_term←temp 
     5.4: Display second_term 
Step 6: Stop