Algorithm

Algorithm

“A process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.” Algorithm is a step-by-step procedure, which defines a set of instructions to be executed in a certain order to get the desired output. Algorithms are generally created independent of underlying languages, i.e. an algorithm can be implemented in more than one programming language.

Characteristics of an Algorithm

Not all procedures can be called an algorithm. An algorithm should have the following characteristics −

·        Unambiguous − Algorithm should be clear and unambiguous. Each of its steps (or phases), and their inputs/outputs should be clear and must lead to only one meaning.

·        Input − An algorithm should have 0 or more well-defined inputs.

·        Output − An algorithm should have 1 or more well-defined outputs, and should match the desired output.

·        Finiteness − Algorithms must terminate after a finite number of steps.

·        Feasibility − Should be feasible with the available resources.

·        Independent − An algorithm should have step-by-step directions, which should be independent of any programming code.

Control floating in algorithm:

Basically in algorithm there are 3 types of control floating in algorithm.

1.      Sequence

2.      Branching

3.      Looping.

Sequence control flow:

            Flow of instruction will be step after step.    

Example

Problem − Design an algorithm to add two numbers and display the result.

Step 1 − START

Step 2 − declare three integers a, b & c

Step 3 − define values of a & b

Step 4 − add values of a & b

Step 5 − store output of step 4 to c

Step 6 − print c

Step 7 − STOP

Algorithms tell the programmers how to code the program. Alternatively, the algorithm can be written as  

Step 1 − START ADD

Step 2 − get values of a & b

Step 3 − c ← a + b

Step 4 − display c

Step 5 − STOP

Branching control flow:

           Flow of instruction will have power of decision making.

Example

Problem − Design an algorithm to big number between two numbers.

Step 1 − START

Step 2 − declare two integers a, b.

Step 3 – is a>b

                Step 3.1— yes, print a is big.

                Step 3.2— no, print b is big

Step 4 − STOP

Looping control flow:

Flow of control make loop of instruction until condition false.

Example

Problem − Design an algorithm to print 1 to 10 numbers.

Step 1 − START

Step 2 − declare one integers a.

Step 3 – loop until a<=10

                Step 3.1— yes, print a, a=a+1 .

                Step 3.2— no, go to Step 4.

Step 4 − STOP

Algorithm Complexity

 X is an algorithm and n is the size of input data, the time and space used by the algorithm X are the two main factors, which decide the efficiency of X.

·        Time Factor − Time is measured by counting the number of key operations such as comparisons in the sorting algorithm.

·        Space Factor − Space is measured by counting the maximum memory space required by the algorithm.

The complexity of an algorithm f(n) gives the running time and/or the storage space required by the algorithm in terms of n as the size of input data.

Space Complexity

Space complexity of an algorithm represents the amount of memory space required by the algorithm in its life cycle. The space required by an algorithm is equal to the sum of the following two components −

·        A fixed part that is a space required to store certain data and variables, that are independent of the size of the problem. For example, simple variables and constants used, program size, etc.

·        A variable part is a space required by variables, whose size depends on the size of the problem. For example, dynamic memory allocation, recursion stack space, etc.

Space complexity S(P) of any algorithm P is S(P) = C + SP(I), where C is the fixed part and S(I) is the variable part of the algorithm, which depends on instance characteristic I. Following is a simple example that tries to explain the concept −

Algorithm: SUM(A, B)

Step 1 -  START

Step 2 -  C ← A + B + 10

Step 3 -  Stop

Here we have three variables A, B, and C and one constant. Hence S(P) = 1 + 3. Now, space depends on data types of given variables and constant types and it will be multiplied accordingly.

Time Complexity

Time complexity of an algorithm represents the amount of time required by the algorithm to run to completion. Time requirements can be defined as a numerical function T(n), where T(n) can be measured as the number of steps, provided each step consumes constant time.

For example, addition of two n-bit integers takes n steps. Consequently, the total computational time is T(n) = c ∗ n, where c is the time taken for the addition of two bits. Here, we observe that T(n) grows linearly as the input size increases.