Problem Solving Tools

Algorithm

Definition ⇒ It is a finite set of instructions which perform a specific task using computational manner.
Father of algorithm → Mohammad Ibn Musa al-Khwarizmi

Any algorithm must follow 5 criteria

Input ⇒ An algorithm should take finite number of inputs.
- It is essential for any algorithm before starting.
- Input should be given to it initially before the Algorithm begins.
Output ⇒ An algorithm must give at least one required result from the given set of input values. These output values are known as the solution to a problem.
Definiteness ⇒ Each step should be unique
- No step should be repeated
- Each step must be clear and precisely defined.
Finiteness ⇒ It means algorithm should be terminated after a finite number of steps.
- Also, each step should be finished in a finite amout of time.
Correctness ⇒ Output should be correct.

3 Types of Algorithm

Sequential
Conditional
Looping

Algorithm Questions

1. Write an algorithm to calculate sum of two numbers.

step 1 : start
step 2 : input n1, n2
step 3 : sum = n1 + n2
step 4 : print sum
step 5 : stop

2. Write an algorithm to calculate area of rectangle.

step 1 : start
step 2 : input l, b
step 3 : area = l * b
step 4 : print area
step 5 : stop

3. Write an algorithm to calculate area of circle.

step 1 : start
step 2 : input r
step 3 : area = 3.14 * r * r
step 4 : print area
step 5 : stop

4. Shopkeeper sells mangos @ 10 Rs/mango a customer buys 5 mangoes from shop keeper, write an algorithm to calculate bill

step 1 : start
step 2 : amount = 10 * 5
step 3 : print amount
step 4 : stop

4. Shopkeeper sells mangos @ 10 Rs/mango, write an algorithm to calculate bill

step 1 : start
step 2 : input n(no. of mangoes)
step 3 : amount = 10 * n
step 4 : print amount
step 5 : stop

Flowchart

Diagramatic representation of a process.
It help us to maintain proper sequence of algorithm.

Sum of two numbers

Area of rectangle

Swapping of two number

Swapping using 3 variables

Algorithm

Step 1 : start
step 2 : input a & b
step 3 : c = a
a = b
b = c
step 4 : print a and b
step 5 : stop

Flowchart

Swapping without using third variable (+, - operator)

Algorithm

Step 1 : start
step 2 : input a & b
step 3 : a = a + b
b = a - b
a = a - b
step 4 : print a and b
step 5 : stop

Flowchart

Swapping without using third variable (*, / operator)

Algorithm

Step 1 : start
step 2 : input a & b
step 3 : a = a * b
b = a / b
a = a / b
step 4 : print a and b
step 5 : stop

Flowchart

Algorithm + Flowchart

Check whether any positive number is single digit or multi digit.

Algorithm

Step 1 : start
Step 2 : input n
Step 3 : if n ≤ 9
- print number is single digit
- else
- print number is multi digit
Step 4 : stop

Flowchart

Check whether a number is even or odd.

Algorithm

Step 1 : start
Step 2 : input n
Step 3 : if n % 2 == 0
- print n is even
- else
- print n is odd
Step 4 : stop

Flowchart

Check whether any number is positive, negative or zero

Algorithm

Step 1 : start
Step 2 : input n
Step 3 : if (n < 0)
- print n is negative number
- else if (n > 0)
- print n is positive number
- else
- print n is zero
Step 4 : stop

Flowchart

(Assignment) Input 4 marks of subject and calculate percentage
and make result according to following
percentage >= 70 → 1^st division with honours
60 <= percentage <= 70 → 1^st division
50 <= percentage <= 60 → second division
40 <= percentage <= 50 → third division
percentage < 40 → failed

Algorithm

Step 1 : start
Step 2 : input m1, m2, m3 & m4
Step 3 : percentage = (m1 + m2 + m3 + m4)/4
Step 4 : if (percentage >= 70)
- print 1st division with honours
- else if (percentage >= 60)
- print 1st division
- else if (percentage >= 50)
- print 2nd division
- else if (percentage >= 40)
- print 3rd division
- else
- print failed
Step 5 : stop

Flowchart

Looping

If we want to repeat code of blocks many times we use looping
It helps in reducing complexity.
There are three types of loops
- for
- while
- do while
Mandatory statements in loop are -
- Initialization → entry point → Provide initial value
- Condition → terminating condition
- Updation → updates value to reach terminating condition.
An algorithm is used to reduce space & time complexity.