Introduction to Algorithms

What is an Algorithm?

•       An Algorithm is the finite set of sequential instructions to accomplished a task where instructions are written in a simple English language.

•       It is called as a step by step solution of the problems.

•       It is a well-developed, organized approach to solving complex problems

•       It refers to logic of a program.

What are the Characteristics of an Algorithm?

An Algorithm should have the following characteristics:

1. Finiteness: – An algorithm terminates (end) after a finite number of steps.

2. Input: – An algorithm accepts zero or more input.

3. Output: – An algorithm produces at least one output and should match the      desired output.

4.   Definiteness: – Each step in an algorithm is unambiguous i.e. each
step should have a unique meaning.

 5.   Effectiveness: – An algorithm consists of basic instruction that are
realizable.

 6.   Independent: – An algorithm should have step by step directions
which should be independent of any programming code.

 7.   Feasibility: – An Algorithm should be feasible with the available resources.

 Why Algorithms?

•       Computer is quite fast, accurate and powerful machine to execute number of tasks.

•         But computer has no intelligence (mindless or no thinking capability or no decision power) of its own.

•         It can perform a task only in a manner in which it is instructed to do.

•         During the process of solving any problem, one tries to find the necessary steps to be taken in a sequence.

•         Steps can be written in some natural language.

•         Natural language means the language which we use in our day to day life such as Hindi or English.

•         Later, these instructions are written in some computer language such as C, C++, JAVA, PHP etc.

 Example 1: Write an algorithm to calculate area and circumference of circle.

Solution: Let r is denote to radius of circle and circum is denote to circumference of circle.

1.    Start

2.    Read r

3.    area = 22/7 x r x r

4.    circum = 2 x 22/7 x r

5.    Write area, circum

6.    Stop

Example 2: Write an algorithm to find largest number among three numbers

Solution: Let a is first number, b is second number, c is third number and l is largest number which stored the result.

      1.    Start

2.    Read a, b, c

3.    If a > b then

               goto step 4

      otherwise

              goto step 5

4.    if a > c then

               l = a

     otherwise

               l = c

5.    if b > c then

                l = b

          otherwise

               l = c

6.    Write “Largest No “, l

7.    stop

 Example 3: Write an algorithm to display and find sum of first N terms Natural Number.

Solution: Let i is denote to generate natural number and sum is denote to addition of all-natural number and n is denote the last value.

Required algorithm is:

Step 1: Start

Step 2: Read n

Step 3: sum = 0

Step 4: i = 1

Step 5: Repeat steps 6 to 8 until (i<=n)

Step 6: display i

Step 7: sum = sum + i

Step 8: i = i + 1

Step 9: write sum

Step 10: End