# What is an Algorithm?

#### What is an Algorithm?

In this lecture, we will learn what algorithms are with the help of examples.

In computer programming terms, an algorithm is a set of well-defined instructions to solve a particular problem. It takes a set of input(s) and produces the desired output. For example,

An algorithm to add two numbers:

1. Take two number inputs
2. Add numbers using the + operator
3. Display the result

#### Qualities of a Good Algorithm

* 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 add two numbers
* 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 of Fibonacci series

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

```python
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

```python
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 Roots of a Quadratic Equation ax2 + bx + c = 0

```python
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

```python
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

```python
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

```python
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
```


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