Introduction to Algorithms

What is an algorithm?

An algorithm is a step by step procedure to solve a problem. In normal language, the algorithm is defined as a sequence of statements which are used to perform a task. In computer science, an algorithm can be defined as follows...

An algorithm is a sequence of unambiguous instructions used for solving a problem, which can be implemented (as a program) on a computer.

Algorithms are used to convert our problem solution into step by step statements. These statements can be converted into computer programming instructions which form a program. This program is executed by a computer to produce a solution. Here, the program takes required data as input, processes data according to the program instructions and finally produces a result as shown in the following picture.

Specifications of Algorithms

Every algorithm must satisfy the following specifications...

1. Input - Every algorithm must take zero or more number of input values from external.
2. Output - Every algorithm must produce an output as result.
3. Definiteness - Every statement/instruction in an algorithm must be clear and unambiguous (only one interpretation).
4. Finiteness - For all different cases, the algorithm must produce result within a finite number of steps.
5. Effectiveness - Every instruction must be basic enough to be carried out and it also must be feasible.

Example for an Algorithm

Let us consider the following problem for finding the largest value in a given list of values.
Problem Statement : Find the largest number in the given list of numbers?
Input : A list of positive integer numbers. (List must contain at least one number).
Output : The largest number in the given list of positive integer numbers.

Consider the given list of numbers as 'L' (input), and the largest number as 'max' (Output).

Algorithm

1. Step 1: Define a variable 'max' and initialize with '0'.
2. Step 2: Compare first number (say 'x') in the list 'L' with 'max', if 'x' is larger than 'max', set 'max' to 'x'.
3. Step 3: Repeat step 2 for all numbers in the list 'L'. 
4. Step 4: Display the value of 'max' as a result.

 Code using C Programming Language

int findMax(L)
{
    int max = 0,i;
    for(i=0; i < listSize; i++)
    {
        if(L[i] > max)
             max = L[i];
    }
    return max;
}