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C++ > Mathematics Code Examples

Program to Calculate roots of 4th order algebraic equation

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/* Program to Calculate roots of 4th order algebraic equation of the form ax^4 + bx^3 + cx^2 + dx + e = 0. */ #include<iostream.h> #include<math.h> #include<conio.h> #include<stdlib.h> #include<graphics.h> const int IMAX = 800; class coeffs { public : float a, b, c, d, e, x, y, p, q, r, z; void getdata(void); void divide(void); void chkrealcmplx(void); void dispreal(float, float, float); void dispcomplx(float, float, float); }; void coeffs :: getdata() { cout<<"Enter coefficients 'a' through 'e' : "; cin>>a>>b>>c>>d>>e; } void coeffs :: divide(void) { int i; float y1,z1; b = b/a; c = c/a; d = d/a; e = e/a; a = 1; y = d/c; z = e/c; x = 1; for(i=1;i<=IMAX;i++) { y1 = (d-z*(b-y))/((c-z)-y*(b-y)); z1 = e/((c-z)-y*(b-y)); y = y1; z = z1; p = 1; q = b-y; r = (c-z)-y*(b-y); } } void coeffs :: chkrealcmplx(void) { float delta1,delta2; delta1 = q*q - 4*p*r; delta2 = y*y - 4*x*z; if(delta1<0) { cout<<" Roots R1 and R2 are complex "; cout<<"Roots are : "; dispcomplx(delta1,p,q); } if(delta2<0) { cout<<" Roots R3 and R4 are complex "; cout<<"Roots are : "; dispcomplx(delta2,x,y); } if(delta1>=0) { cout<<" Roots R1 and R2 are real "; cout<<"Roots are : "; dispreal(delta1,p,q); } if(delta2>=0) { cout<<" Roots R3 and R4 are real "; cout<<"Roots are : "; dispreal(delta2,x,y); } } void coeffs :: dispreal(float delta,float A,float B) { float r1,r2; r1 = (-B+sqrt(delta))/(2*A); r2 = (-B-sqrt(delta))/(2*A); cout<<r1<<endl; cout<<r2<<endl; } void coeffs :: dispcomplx(float delta,float A,float B) { float rp,ip; delta = -delta; rp = -B/(2*A); ip = (sqrt(delta))/(2*A); cout<<rp<<" +j "<<ip<<endl; cout<<rp<<" -j "<<ip<<endl; } void line() { char t = 0XC4; for(int i = 1;i<=80;i++) cout<<t; } void main() { clrscr(); int gdriver = EGA, gmode = VGAHI, errorcode; initgraph(&gdriver, &gmode, "c:\tc\bgi"); setbkcolor(BLUE); coeffs coefficients; line(); cout<<" PROGRAM TO SOLVE A FOURTH ORDER ALGEBRAIC EQUATION "; line(); coefficients.getdata(); line(); line(); coefficients.divide(); coefficients.chkrealcmplx(); line(); line(); getch(); closegraph(); }

The header file graphics.h contains line() function which is used to draw a line from a point(x1, y1) to point(x2, y2) i.e. (x1, y1) and (x2, y2) are end points of the line. The function line() draws a line on the graphics screen between two specified points. So this function requires four parameters namely x1, y1, x2, and y2 to represent two points. This function draws a line from (x1, y1) coordinates to (x2, y2) coordinates on the graphics screen.

In C++, constructor is a special method which is invoked automatically at the time of object creation. It is used to initialize the data members of new object generally. The constructor in C++ has the same name as class or structure. Constructors are special class functions which performs initialization of every object. The Compiler calls the Constructor whenever an object is created. Constructors initialize values to object members after storage is allocated to the object. Whereas, Destructor on the other hand is used to destroy the class object. • Default Constructor: A constructor which has no argument is known as default constructor. It is invoked at the time of creating object.

Arithmetic Operator is used to performing mathematical operations such as addition, subtraction, multiplication, division, modulus, etc., on the given operands. For example: 6 + 3 = 9, 5 - 3 = 2, 3 * 4 = 12, etc. are the examples of arithmetic operators. Let's discuss the different types of Arithmetic Operators in the C programming. Plus Operator is a simple Plus (+) Operator used to add two given operands. We can use Plus Operator with different data types such as integer, float, long, double, enumerated and string type data to add the given operand. The minus operator is denoted by the minus (-) symbol. It is used to return the subtraction of the first number from the second number. The data type of the given number can be different types, such as int, float, double, long double, etc., in the programing language.

The cout is a predefined object of ostream class. It is connected with the standard output device, which is usually a display screen. The cout is used in conjunction with stream insertion operator (<<) to display the output on a console. On most program environments, the standard output by default is the screen, and the C++ stream object defined to access it is cout. The "c" in cout refers to "character" and "out" means "output". Hence cout means "character output". The cout object is used along with the insertion operator << in order to display a stream of characters.

In computer programming, we use the if statement to run a block code only when a certain condition is met. An if statement can be followed by an optional else statement, which executes when the boolean expression is false. There are three forms of if...else statements in C++: • if statement, • if...else statement, • if...else if...else statement, The if statement evaluates the condition inside the parentheses ( ). If the condition evaluates to true, the code inside the body of if is executed. If the condition evaluates to false, the code inside the body of if is skipped.

setbkcolor() function is used to set the background color in graphics mode. The default background color is black and default drawing color as we know is white. setbkcolor() function takes only one argument it would be either the name of color defined in graphics.h header file or number associated with those colors. If we write setbkcolor(yellow) it changes the background color in Green. The possible color values are from 0 - 15 black, blue, green, cyan, red, magenta, brown, lightgray, darkgray, lightblue, lightgreen, lightcyan, lightred, lightmagenta, yellow, white and blink (128).

The header file graphics.h contains closegraph() function which closes the graphics mode, deallocates all memory allocated by graphics system and restores the screen to the mode it was in before you called initgraph. closegraph() function is used to re-enter in the text mode and exit from the graphics mode. If you want to use both text mode and graphics mode in the program then you have to use both initgraph() and closegraph() function in the program. This function deallocates all memory allocated by graphics system and restores the screen to that mode in which it was presented before you called the initgraph() function.

A predefined object of the class called iostream class is used to insert the new line characters while flushing the stream is called endl in C++. This endl is similar to \n which performs the functionality of inserting new line characters but it does not flush the stream whereas endl does the job of inserting the new line characters while flushing the stream. Hence the statement cout<<endl; will be equal to the statement cout<< '\n' << flush; meaning the new line character used along with flush explicitly becomes equivalent to the endl statement in C++.

The main purpose of C++ programming is to add object orientation to the C programming language and classes are the central feature of C++ that supports object-oriented programming and are often called user-defined types. A class is used to specify the form of an object and it combines data representation and methods for manipulating that data into one neat package. The data and functions within a class are called members of the class.

To create a program in Graphics Mode, the first step would be to include the header file graphics.h. This file is required for Graphics programming. After this, the graphics have to be initialized. C Language supports 16 Bit's MS-DOS environment. Initializing the Graphics mode is to call various functions, one such is called initgraph. initgraph initializes the graphics system by loading a graphics driver from disk (or validating a registered driver), and putting the system into graphics mode. To start the graphics system, first call the initgraph function. initgraph loads the graphics driver and puts the system into graphics mode. You can tell initgraph to use a particular graphics driver and mode, or to autodetect the attached video adapter at run time and pick the corresponding driver. If you tell initgraph to autodetect, it calls detectgraph to select a graphics driver and mode. initgraph also resets all graphics settings to their defaults (current position, palette, color, viewport, and so on)

#include is a way of including a standard or user-defined file in the program and is mostly written at the beginning of any C/C++ program. This directive is read by the preprocessor and orders it to insert the content of a user-defined or system header file into the following program. These files are mainly imported from an outside source into the current program. The process of importing such files that might be system-defined or user-defined is known as File Inclusion. This type of preprocessor directive tells the compiler to include a file in the source code program.

The getch() is a predefined non-standard function that is defined in conio.h header file. It is mostly used by the Dev C/C++, MS- DOS's compilers like Turbo C to hold the screen until the user passes a single value to exit from the console screen. It can also be used to read a single byte character or string from the keyboard and then print. It does not hold any parameters. It has no buffer area to store the input character in a program. The getch() function does not accept any parameter from the user. It returns the ASCII value of the key pressed by the user as an input.

Compute square root. Returns the square root of x. The sqrt() function in C++ returns the square root of a number. This function is defined in the cmath header file. There are various functions available in the C++ Library to calculate the square root of a number. Most prominently, sqrt is used. It takes double as an argument. The <cmath> header defines two more inbuilt functions for calculating the square root of a number (apart from sqrt) which has an argument of type float and long double. Therefore, all the functions used for calculating square root in C++ are. Mathematically, sqrt(x) = √x.

In computer programming, loops are used to repeat a block of code. For example, when you are displaying number from 1 to 100 you may want set the value of a variable to 1 and display it 100 times, increasing its value by 1 on each loop iteration. When you know exactly how many times you want to loop through a block of code, use the for loop instead of a while loop. A for loop is a repetition control structure that allows you to efficiently write a loop that needs to execute a specific number of times.

A program shall contain a global function named main, which is the designated start of the program in hosted environment. main() function is the entry point of any C++ program. It is the point at which execution of program is started. When a C++ program is executed, the execution control goes directly to the main() function. Every C++ program have a main() function.

The cin object is used to accept input from the standard input device i.e. keyboard. It is defined in the iostream header file. C++ cin statement is the instance of the class istream and is used to read input from the standard input device which is usually a keyboard. The extraction operator(>>) is used along with the object cin for reading inputs. The extraction operator extracts the data from the object cin which is entered using the keyboard. The "c" in cin refers to "character" and "in" means "input". Hence cin means "character input". The cin object is used along with the extraction operator >> in order to receive a stream of characters.

It is a predefined function in "conio.h" (console input output header file) used to clear the console screen. It is a predefined function, by using this function we can clear the data from console (Monitor). Using of clrscr() is always optional but it should be place after variable or function declaration only. It is often used at the beginning of the program (mostly after variable declaration but not necessarily) so that the console is clear for our output.

C++ program displays the maximum number of edge disjoint paths present between two vertices. 'Maximum number' of edge disjoint paths refers to the maximum flow or shortest