What are the 5 characteristics of an algorithm

Explain the characteristics of an algorithm.

1. Input – Zero or more quantities to be supplied.
2. Output – At least one quantity is produced.
3. Finiteness – Algorithms must terminate after a finite number of steps.
4. Definiteness – All operations should be well defined. For example, operations involving division by zero or taking square root for negative numbers are unacceptable.
5. Effectiveness – Every instruction must be carried out effectively.
6. Correctness – The algorithms should be error-free.
7. Simplicity – Easy to implement.
8. Unambiguous – The algorithm should be clear and unambiguous. Each of its steps and its inputs/outputs should be clear and must lead to only one meaning.
9. Feasibility – This should be feasible with the available resources.
10. Portable – An algorithm should be generic, independent of any programming language or an operating system able to handle all range of inputs.
11. Independent – An algorithm should have step-by-step directions, which should be independent of any programming code.

Concept: Introduction to Algorithmic Strategies

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An algorithm is made up of a finite number of stages, each of which may involve one or more actions. The probability of these operations being performed by a machine demands that certain restrictions be imposed on the type of operations that an algorithm might include. 

Basically algorithms are the finite steps to solve problems in computers. It can be the set of instructions that performs a certain task. The collection of unambiguous instructions occurring in some specific sequence and such a procedure should produce output for a given set of input in a finite amount of time is known as Algorithm.

Characteristics

In addition, all algorithms must satisfy the following criteria:

• Input : can be zero or more input
• Output : must produce output
• Finiteness : must have ending
• Definiteness : unambiguous and clear
• Effectiveness : should not be complex

How to Write an Algorithm?

Algorithm writing does not have any well-defined standards. Rather, it is a function of the situation and the available resources. Algorithms are never creates in order to support a specific programming language.

As we all know, basic code features such as loops (do, for, while), flow control (if-else), and so on are share across all programming languages. An algorithm can written using these standard constructs.

We usually create algorithms step by step, however this isn’t always the case. After the problem domain has been well-define, algorithm writing is a procedure that is carry out. To put it another way, we should be aware of the problem area for which we are developing a solution.

Complexity of Algorithm

It is highly useful to categorize algorithms according to the amount of time or space they require, and to indicate the development of time/space requirements as a function of input size. As a result, we have the concepts of:

1. Time Complexity: The program’s execution time as a function of the size of the input.

2. Space Complexity: The amount of computer memory required to run a programme as a function of the size of the input.

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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.

From the data structure point of view, following are some important categories of algorithms −

• Search − Algorithm to search an item in a data structure.

• Sort − Algorithm to sort items in a certain order.

• Insert − Algorithm to insert item in a data structure.

• Update − Algorithm to update an existing item in a data structure.

• Delete − Algorithm to delete an existing item from a data structure.

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.

How to Write an Algorithm?

There are no well-defined standards for writing algorithms. Rather, it is problem and resource dependent. Algorithms are never written to support a particular programming code.

As we know that all programming languages share basic code constructs like loops (do, for, while), flow-control (if-else), etc. These common constructs can be used to write an algorithm.

We write algorithms in a step-by-step manner, but it is not always the case. Algorithm writing is a process and is executed after the problem domain is well-defined. That is, we should know the problem domain, for which we are designing a solution.

Example

Let's try to learn algorithm-writing by using an example.

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

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

In design and analysis of algorithms, usually the second method is used to describe an algorithm. It makes it easy for the analyst to analyze the algorithm ignoring all unwanted definitions. He can observe what operations are being used and how the process is flowing.

Writing step numbers, is optional.

We design an algorithm to get a solution of a given problem. A problem can be solved in more than one ways.

Hence, many solution algorithms can be derived for a given problem. The next step is to analyze those proposed solution algorithms and implement the best suitable solution.

Algorithm Analysis

Efficiency of an algorithm can be analyzed at two different stages, before implementation and after implementation. They are the following −

• A Priori Analysis − This is a theoretical analysis of an algorithm. Efficiency of an algorithm is measured by assuming that all other factors, for example, processor speed, are constant and have no effect on the implementation.

• A Posterior Analysis − This is an empirical analysis of an algorithm. The selected algorithm is implemented using programming language. This is then executed on target computer machine. In this analysis, actual statistics like running time and space required, are collected.

We shall learn about a priori algorithm analysis. Algorithm analysis deals with the execution or running time of various operations involved. The running time of an operation can be defined as the number of computer instructions executed per operation.

Algorithm Complexity

Suppose 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 −

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.