What is an Algorithm?

Algorithms are the sequence of instructions that takes input, process the data, and produces the desired output.

In other words, algorithms are sets of well-defined instructions to solve a problem.

For example:

Algorithm to add two numbers:

• Take two numbers
• Add them using + operator
• Display output of two numbers

Characteristics of Good Algorithms:

• Input and Output should be well-defined.
• The algorithm should be clear and unambiguous.
• Algorithms should be most effective and optimized.
• The algorithm should be written in such a way that it can be used in different programming languages.

Examples of Algorithms

1. Sum of two Numbers

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 the sum.
        sum←num1+num2 
Step 5: Display the sum 
Step 6: Stop

2. Find the largest number among three numbers

Step 1: Start
Step 2: Declare variables num1, num2, and num3.
Step 3: Read variables num1, num2, and num3.
Step 4: If num1 > num2
           If num1 > num3
              Display num1 is the largest number.
           Else
              Display num3 is the largest number.
        Else
           If num2 > num3
              Display num2 is the largest number.
           Else
              Display num3 is the greatest number.  
Step 5: Stop

3. Find Root of the quadratic equation $$ ax^2 + bx + c = 0 $$

Step 1: Start
Step 2: Declare variables a, b, c, Discriminant, root and imaginary,root1, root2;
Step 3 : Read values of a,b,c;
Step 4: Calculate discriminant
          Discriminant ← b*b-4*a*c 
Step 5: If D ≥ 0
              root1 ← (-b+√Discriminant)/2*a
              root2 ← (-b-√Discriminant)/2*a 
              Display root1 and root2 as roots.
        Else     
              Calculate real part and imaginary part
              root ← -b/2*a
              imaginary ← √(-Discriminant)/2*a
              Display root+j(imaginary) and root-j(imaginary) as roots
Step 6: Stop

4. Find the factorial of a number

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

5. Check whether a number is prime or not

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

6. Find the Fibonacci series till 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 
      temp ← second_term 
      second_term ← second_term + first_term 
      first_term ← temp 
      Display second_term 
Step 6: Stop