Analysis of Algorithm

Introduction:-

Analysis of an Algorithm is done in order to estimate the complexity function for arbitrarily large input. The term "analysis of algorithms" was coined by Donald Knuth.

Algorithm analysis is an important part of computational complexity theory, which provides theoretical estimation for the required resources of an algorithm to solve a specific computational problem. Most algorithms are designed to work with inputs of arbitrary length. Analysis of algorithms is the determination of the amount of time and space resources required to execute it. 

the efficiency or running time of an algorithm is stated as a function relating the input length to the number of steps, known as time complexity, or volume of memory, known as space complexity. 

Algorithm Analysis

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

• A Priori(Pre) 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(Post) 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 −

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.


Making up an Algorithm beforehandedly clears many things out while making a particular program or doing anything out.



©SherilThomas

Arduino: About its Structure

Arduino

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1. Arduino is an open source platform.

2. It has a programmable circuit board that can be programmed with the help of its user-friendly Arduino IDE(Integrated development environment ).

3. This circuit board consists of programmable micro-controller which can sense and control object in the real world.

Here is the picture of the Arduino board :

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Types of Arduino:

There are different different types of Arduino micro-controller present in the market.

While selecting the Arduino board you have to consider the type of project you are doing.

Here is a picture demonstrating types of Arduino :

For example :

If you are making some wearable electronics you might be considering Lily pad. which is easy to be seen or integrated with wearable.

Arduino pro mini for small projects etc.

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Board Description:

1. Reset: Used to start code again from an initial state(i.e restart loaded code) in Arduino.

2. AREF: Analog Reference used to set external voltage as an upper limit for analog pins(0v to 5v).

3. Ground: It is used to give ground to your circuit. There are several ground pins in the circuit the in all works the same.

4. Digital pins: Used to take inputs and transmit output.

5. PWM :  (~) marked pin are able to simulate analog signals.

6. power: Arduino can be powered in no. of ways one of them is through the USB slot. you can connect Arduino to PC by using USB cable

7. TX & RX : TX(Transmitter) and RX(receiver). TX flashes according to the serial data transmission speed and RX flashes during the receiving process. Flashing depends upon the baud rate.

8. Micro-Controller: It is also known as the brain of the board. IC(Integrated Circuit a micro-controller) differs from board to board. As before uploading sketch you must know what IC you are using.

9. Power Indicator: This led lights every when the board is powered.

10. Regulator: Controls amount of voltage in Arduino board.

11.DC barrel: Used to power Arduino with DC(Direct Current) jack.

12. 3.3 volts: supplies 3.3v to external objects.

13. 5 volts: supplies 5v to external objects.

14.Ground: It is used to give ground to your circuit . There are several ground pins in circuit in all works same.

15. Analog pins: receives analog signals from sensors and convert it into digital signal.

  ©SherilThomas