An algorithm is a set of well-defined instructions in sequence to solve a problem.

## Qualities of Good Algorithms

- Input and output should be defined precisely.
- Each step in the algorithm should be clear and unambiguous.
- Algorithms should be most effective among many different ways to solve a problem.
- An algorithm shouldn't include computer code. Instead, the algorithm should be written in such a way that it can be used in different programming languages.

## Algorithm Examples

Algorithm to find the largest among three numbers

Algorithm to find all the roots of the quadratic equation

Algorithm to find the factorial

Algorithm to check prime number

### Algorithm 1: Add two numbers entered by the 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

### Algorithm 2: Find the largest number among three numbers

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

### Algorithm 3: Find Root of the quadratic equatin ax^{2} + 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

### Algorithm 4: Find the factorial of a number

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

### Algorithm 5: Check whether a number 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 the 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

### Algorithm 6: Find the Fibonacci series till the term less than 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