What are the 4 characteristics of an algorithm?

The word Algorithm means ” A set of finite rules or instructions to be followed in calculations or other problem-solving operations ” Or ” A procedure for solving a mathematical problem in a finite number of steps that frequently involves recursive operations”.

Therefore Algorithm refers to a sequence of finite steps to solve a particular problem.

Algorithms can be simple and complex depending on what you want to achieve.

It can be understood by taking the example of cooking a new recipe. To cook a new recipe, one reads the instructions and steps and executes them one by one, in the given sequence. The result thus obtained is the new dish is cooked perfectly. Every time you use your phone, computer, laptop, or calculator you are using Algorithms. Similarly, algorithms help to do a task in programming to get the expected output.

The Algorithm designed are language-independent, i.e. they are just plain instructions that can be implemented in any language, and yet the output will be the same, as expected.

What are the Characteristics of an Algorithm?

As one would not follow any written instructions to cook the recipe, but only the standard one. Similarly, not all written instructions for programming is an algorithms. In order for some instructions to be an algorithm, it must have the following characteristics:

• Clear and Unambiguous: The algorithm should be clear and unambiguous. Each of its steps should be clear in all aspects and must lead to only one meaning.
• Well-Defined Inputs: If an algorithm says to take inputs, it should be well-defined inputs. It may or may not take input.
• Well-Defined Outputs: The algorithm must clearly define what output will be yielded and it should be well-defined as well. It should produce at least 1 output.
• Finite-ness: The algorithm must be finite, i.e. it should terminate after a finite time.
• Feasible: The algorithm must be simple, generic, and practical, such that it can be executed with the available resources. It must not contain some future technology or anything.
• Language Independent: The Algorithm designed must be language-independent, i.e. it must be just plain instructions that can be implemented in any language, and yet the output will be the same, as expected.

Properties of Algorithm:

• It should terminate after a finite time.
• It should produce at least one output.
• It should take zero or more input.
• It should be deterministic means giving the same output for the same input case.
• Every step in the algorithm must be effective i.e. every step should do some work.

Types of Algorithms:

There are several types of algorithms available. Some important algorithms are:

1. Brute Force Algorithm: It is the simplest approach for a problem. A brute force algorithm is the first approach that comes to finding when we see a problem.

2. Recursive Algorithm: A recursive algorithm is based on recursion. In this case, a problem is broken into several sub-parts and called the same function again and again.

3. Backtracking Algorithm: The backtracking algorithm basically builds the solution by searching among all possible solutions. Using this algorithm, we keep on building the solution following criteria. Whenever a solution fails we trace back to the failure point and build on the next solution and continue this process till we find the solution or all possible solutions are looked after.

4. Searching Algorithm: Searching algorithms are the ones that are used for searching elements or groups of elements from a particular data structure. They can be of different types based on their approach or the data structure in which the element should be found.

5. Sorting Algorithm: Sorting is arranging a group of data in a particular manner according to the requirement. The algorithms which help in performing this function are called sorting algorithms. Generally sorting algorithms are used to sort groups of data in an increasing or decreasing manner.

6. Hashing Algorithm: Hashing algorithms work similarly to the searching algorithm. But they contain an index with a key ID. In hashing, a key is assigned to specific data.

7. Divide and Conquer Algorithm: This algorithm breaks a problem into sub-problems, solves a single sub-problem and merges the solutions together to get the final solution. It consists of the following three steps:

• Divide
• Solve
• Combine

8. Greedy Algorithm: In this type of algorithm the solution is built part by part. The solution of the next part is built based on the immediate benefit of the next part. The one solution giving the most benefit will be chosen as the solution for the next part.

9. Dynamic Programming Algorithm: This algorithm uses the concept of using the already found solution to avoid repetitive calculation of the same part of the problem. It divides the problem into smaller overlapping subproblems and solves them.

10. Randomized Algorithm: In the randomized algorithm we use a random number so it gives immediate benefit. The random number helps in deciding the expected outcome.

To learn more about the types of algorithms refer to the article about “Types of Algorithms“.

Advantages of Algorithms:

• It is easy to understand.
• An algorithm is a step-wise representation of a solution to a given problem.
• In Algorithm the problem is broken down into smaller pieces or steps hence, it is easier for the programmer to convert it into an actual program.

Disadvantages of Algorithms:

• Writing an algorithm takes a long time so it is time-consuming.
• Understanding complex logic through algorithms can be very difficult.
• Branching and Looping statements are difficult to show in Algorithms(imp).

How to Design an Algorithm?

In order to write an algorithm, the following things are needed as a pre-requisite: 
 

1. The problem that is to be solved by this algorithm i.e. clear problem definition.
2. The constraints of the problem must be considered while solving the problem.
3. The input to be taken to solve the problem.
4. The output to be expected when the problem is solved.
5. The solution to this problem, is within the given constraints.

Then the algorithm is written with the help of the above parameters such that it solves the problem.
Example: Consider the example to add three numbers and print the sum.
 

• Step 1: Fulfilling the pre-requisites 
  As discussed above, in order to write an algorithm, its pre-requisites must be fulfilled. 
  1. The problem that is to be solved by this algorithm: Add 3 numbers and print their sum.
  2. The constraints of the problem that must be considered while solving the problem: The numbers must contain only digits and no other characters.
  3. The input to be taken to solve the problem: The three numbers to be added.
  4. The output to be expected when the problem is solved: The sum of the three numbers taken as the input i.e. a single integer value.
  5. The solution to this problem, in the given constraints: The solution consists of adding the 3 numbers. It can be done with the help of ‘+’ operator, or bit-wise, or any other method.
• Step 2: Designing the algorithm
  Now let’s design the algorithm with the help of the above pre-requisites:
  Algorithm to add 3 numbers and print their sum: 
  1. START
  2. Declare 3 integer variables num1, num2 and num3.
  3. Take the three numbers, to be added, as inputs in variables num1, num2, and num3 respectively.
  4. Declare an integer variable sum to store the resultant sum of the 3 numbers.
  5. Add the 3 numbers and store the result in the variable sum.
  6. Print the value of the variable sum
  7. END
• Step 3: Testing the algorithm by implementing it.
  In order to test the algorithm, let’s implement it in C language.

Program:

C++

// C++ program to add three numbers

// with the help of above designed

// algorithm

#include

using namespace std;

int // C++ program to add three numbers0

// C++ program to add three numbers1

// C++ program to add three numbers2 

// C++ program to add three numbers2// C++ program to add three numbers4

// C++ program to add three numbers2// C++ program to add three numbers6

// C++ program to add three numbers2int // C++ program to add three numbers9

// C++ program to add three numbers2// with the help of above designed2

// C++ program to add three numbers2int // with the help of above designed5

// C++ program to add three numbers2// with the help of above designed8

// C++ program to add three numbers2// algorithm0// algorithm1// algorithm2

// C++ program to add three numbers2// algorithm4

// C++ program to add three numbers2// algorithm0// algorithm7 // algorithm8

// C++ program to add three numbers2// algorithm0#include 2// algorithm2

// C++ program to add three numbers2#include 5

// C++ program to add three numbers2// algorithm0// algorithm7 #include 9

// C++ program to add three numbers2// algorithm0using3// algorithm2

// C++ program to add three numbers2using6

// C++ program to add three numbers2// algorithm0// algorithm7 namespace0

// C++ program to add three numbers2namespace3

// C++ program to add three numbers2namespace5

// C++ program to add three numbers2namespace7

// C++ program to add three numbers2std;0

// C++ program to add three numbers2// algorithm0std;3

std;4std;5

// C++ program to add three numbers2std;8 std;9

 0

 1

C

 2

 3

 4

int // C++ program to add three numbers0

// C++ program to add three numbers1

// C++ program to add three numbers2 9

// C++ program to add three numbers2int // C++ program to add three numbers9

// C++ program to add three numbers2// with the help of above designed2

// C++ program to add three numbers2int // with the help of above designed5

// C++ program to add three numbers2// with the help of above designed8

// C++ program to add three numbers2// C++ program to add three numbers01// C++ program to add three numbers02// algorithm1// C++ program to add three numbers04

// C++ program to add three numbers2// C++ program to add three numbers06// C++ program to add three numbers02// C++ program to add three numbers08// C++ program to add three numbers09

// C++ program to add three numbers2// C++ program to add three numbers01// C++ program to add three numbers02// C++ program to add three numbers13// C++ program to add three numbers14

// C++ program to add three numbers2// C++ program to add three numbers01// C++ program to add three numbers02#include 2// C++ program to add three numbers04

// C++ program to add three numbers2// C++ program to add three numbers06// C++ program to add three numbers02// C++ program to add three numbers08// C++ program to add three numbers24

// C++ program to add three numbers2// C++ program to add three numbers01// C++ program to add three numbers02// C++ program to add three numbers13// C++ program to add three numbers29

// C++ program to add three numbers2// C++ program to add three numbers01// C++ program to add three numbers02using3// C++ program to add three numbers04

// C++ program to add three numbers2// C++ program to add three numbers06// C++ program to add three numbers02// C++ program to add three numbers08// C++ program to add three numbers39

// C++ program to add three numbers2// C++ program to add three numbers01// C++ program to add three numbers02// C++ program to add three numbers13// C++ program to add three numbers44

// C++ program to add three numbers2namespace3

// C++ program to add three numbers2namespace5

// C++ program to add three numbers2namespace7

// C++ program to add three numbers2std;0

// C++ program to add three numbers2// C++ program to add three numbers01// C++ program to add three numbers02// C++ program to add three numbers56// C++ program to add three numbers57

// C++ program to add three numbers2std;8 std;9

 0

Java

// C++ program to add three numbers62

// with the help of above designed

// algorithm

// C++ program to add three numbers65 // C++ program to add three numbers66

// C++ program to add three numbers67 // C++ program to add three numbers68

// C++ program to add three numbers2// C++ program to add three numbers70 // C++ program to add three numbers71 // C++ program to add three numbers72 // C++ program to add three numbers73

// C++ program to add three numbers2// C++ program to add three numbers1

// C++ program to add three numbers76 

// C++ program to add three numbers77// with the help of above designed2

// C++ program to add three numbers77int // C++ program to add three numbers81// C++ program to add three numbers82// algorithm2

// C++ program to add three numbers76 

// C++ program to add three numbers77// C++ program to add three numbers86

// C++ program to add three numbers77// C++ program to add three numbers88

// C++ program to add three numbers77// C++ program to add three numbers90

// C++ program to add three numbers91// C++ program to add three numbers92// C++ program to add three numbers93 // C++ program to add three numbers94// C++ program to add three numbers95

// C++ program to add three numbers77 

// C++ program to add three numbers76// C++ program to add three numbers4

// C++ program to add three numbers77// C++ program to add three numbers6

// C++ program to add three numbers77// with the help of above designed02// algorithm1// C++ program to add three numbers04

// C++ program to add three numbers77int // with the help of above designed07

// C++ program to add three numbers76 

// C++ program to add three numbers76// with the help of above designed10

// C++ program to add three numbers77// with the help of above designed12

// C++ program to add three numbers77// with the help of above designed02// algorithm7 // with the help of above designed16

// C++ program to add three numbers77// with the help of above designed02#include 2// C++ program to add three numbers04

// C++ program to add three numbers77int // with the help of above designed23

// C++ program to add three numbers77// with the help of above designed02// algorithm7 // with the help of above designed27

// C++ program to add three numbers77// with the help of above designed02using3// C++ program to add three numbers04

// C++ program to add three numbers77int // with the help of above designed34

// C++ program to add three numbers77// with the help of above designed02// algorithm7 // with the help of above designed38

// C++ program to add three numbers76 

// C++ program to add three numbers77namespace3

// C++ program to add three numbers77namespace5

// C++ program to add three numbers77namespace7

// C++ program to add three numbers77// with the help of above designed02// with the help of above designed48

// with the help of above designed49// with the help of above designed50

// C++ program to add three numbers2 0

 0

// with the help of above designed54

Python3

// with the help of above designed55

// with the help of above designed56

// with the help of above designed57

// with the help of above designed58 // with the help of above designed59// C++ program to add three numbers92// C++ program to add three numbers92 // with the help of above designed62// with the help of above designed63

// C++ program to add three numbers2// with the help of above designed65

// C++ program to add three numbers2// with the help of above designed67

// C++ program to add three numbers2// with the help of above designed69// C++ program to add three numbers92 // with the help of above designed71// C++ program to add three numbers92 // with the help of above designed73// C++ program to add three numbers92 // C++ program to add three numbers82

// C++ program to add three numbers2// with the help of above designed77

// C++ program to add three numbers2// with the help of above designed79 // C++ program to add three numbers92 // C++ program to add three numbers82

// C++ program to add three numbers2// with the help of above designed83

// C++ program to add three numbers2// with the help of above designed69// C++ program to add three numbers92 int// C++ program to add three numbers02// with the help of above designed89// C++ program to add three numbers02// algorithm1// with the help of above designed92

// C++ program to add three numbers2// with the help of above designed71// C++ program to add three numbers92 int// C++ program to add three numbers02// with the help of above designed89// C++ program to add three numbers02#include 2// with the help of above designed92

// C++ program to add three numbers2// with the help of above designed73// C++ program to add three numbers92 int// C++ program to add three numbers02// with the help of above designed89// C++ program to add three numbers02using3// with the help of above designed92

// C++ program to add three numbers2// algorithm12

// C++ program to add three numbers2// algorithm14

// C++ program to add three numbers2// with the help of above designed79 // C++ program to add three numbers92 // with the help of above designed69// algorithm19 // with the help of above designed71// algorithm19 // with the help of above designed73

// C++ program to add three numbers2// algorithm24

// C++ program to add three numbers2// algorithm26// C++ program to add three numbers02// algorithm28// algorithm29// with the help of above designed79// algorithm31

Output

Enter the 1st number: 0
Enter the 2nd number: 0
Enter the 3rd number: -1577141152

Sum of the 3 numbers is: -1577141152

One problem, many solutions: The solution to an algorithm can be or cannot be more than one. It means that while implementing the algorithm, there can be more than one method to implement it. For example, in the above problem to add 3 numbers, the sum can be calculated in many ways like:

• + operator
• Bit-wise operators
• . . etc

How to analyze an Algorithm? 

For a standard algorithm to be good, it must be efficient. Hence the efficiency of an algorithm must be checked and maintained. It can be in two stages:

1. Priori Analysis: “Priori” means “before”. Hence Priori analysis means checking the algorithm before its implementation. In this, the algorithm is checked when it is written in the form of theoretical steps. This 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. This is done usually by the algorithm designer. This analysis is independent of the type of hardware and language of the compiler. It gives the approximate answers for the complexity of the program.
2. Posterior Analysis: “Posterior” means “after”. Hence Posterior analysis means checking the algorithm after its implementation. In this, the algorithm is checked by implementing it in any programming language and executing it. This analysis helps to get the actual and real analysis report about correctness(for every possible input/s if it shows/returns correct output or not), space required, time consumed etc. That is, it is dependent on the language of the compiler and the type of hardware used.

What is Algorithm complexity and how to find it?

An algorithm is defined as complex based on the amount of Space and Time it consumes. Hence the Complexity of an algorithm refers to the measure of the Time that it will need to execute and get the expected output, and the Space it will need to store all the data (input, temporary data and output). Hence these two factors define the efficiency of an algorithm. 
The two factors of Algorithm Complexity are:

• 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 to run/execute.

Therefore the complexity of an algorithm can be divided into two types:

1. Space Complexity: The space complexity of an algorithm refers to the amount of memory required by the algorithm to store the variables and get the result. This can be for inputs, temporary operations, or outputs. 

How to calculate Space Complexity?
The space complexity of an algorithm is calculated by determining the following 2 components: 
 

• Fixed Part: This refers to the space that is definitely required by the algorithm. For example, input variables, output variables, program size, etc.
• Variable Part: This refers to the space that can be different based on the implementation of the algorithm. For example, temporary variables, dynamic memory allocation, recursion stack space, etc.
  Therefore 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.

Example: Consider the below algorithm for Linear Search

Step 1: START
Step 2: Get n elements of the array in arr and the number to be searched in x
Step 3: Start from the leftmost element of arr[] and one by one compare x with each element of arr[]
Step 4: If x matches with an element, Print True.
Step 5: If x doesn’t match with any of the elements, Print False.
Step 6: END
Here, There are 2 variables arr[], and x, where the arr[] is the variable part of n elements and x is the fixed part. Hence S(P) = 1+n. So, the space complexity depends on n(number of elements). Now, space depends on data types of given variables and constant types and it will be multiplied accordingly.

2. Time Complexity: The time complexity of an algorithm refers to the amount of time that is required by the algorithm to execute and get the result. This can be for normal operations, conditional if-else statements, loop statements, etc.

What are the 4 types of algorithm?

What are five main characteristics of algorithms?

What are the six characteristics of an algorithm?

How many characteristics of algorithm are there?