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C++ > Mathematics Code Examples

C++ Program to Implement Gauss Jordan Elimination

/* C++ Program to Implement Gauss Jordan Elimination This is a C++ Program to implement Gauss Jordan Elimination algorithm. In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations. It is usually understood as a sequence of operations performed on the associated matrix of coefficients. This method can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix. Gauss Jordan method for inverse matrix */ #include<iostream> #include<conio.h> using namespace std; int main() { int i, j, k, n; float a[10][10] = { 0 }, d; cout << "No of equations ? "; cin >> n; cout << "Read all coefficients of matrix with b matrix too " << endl; for (i = 1; i <= n; i++) for (j = 1; j <= n; j++) cin >> a[i][j]; for (i = 1; i <= n; i++) for (j = 1; j <= 2 * n; j++) if (j == (i + n)) a[i][j] = 1; /* partial pivoting */ for (i = n; i > 1; i--) { if (a[i - 1][1] < a[i][1]) for (j = 1; j <= n * 2; j++) { d = a[i][j]; a[i][j] = a[i - 1][j]; a[i - 1][j] = d; } } cout << "pivoted output: " << endl; for (i = 1; i <= n; i++) { for (j = 1; j <= n * 2; j++) cout << a[i][j] << " "; cout << endl; } /* reducing to diagonal matrix */ for (i = 1; i <= n; i++) { for (j = 1; j <= n * 2; j++) if (j != i) { d = a[j][i] / a[i][i]; for (k = 1; k <= n * 2; k++) a[j][k] -= a[i][k] * d; } } /* reducing to unit matrix */ for (i = 1; i <= n; i++) { d = a[i][i]; for (j = 1; j <= n * 2; j++) a[i][j] = a[i][j] / d; } cout << "your solutions: " << endl; for (i = 1; i <= n; i++) { for (j = n + 1; j <= n * 2; j++) cout << a[i][j] << " "; cout << endl; } getch(); return 0; }

C supports nesting of loops in C. Nesting of loops is the feature in C that allows the looping of statements inside another loop. Any number of loops can be defined inside another loop, i.e., there is no restriction for defining any number of loops. The nesting level can be defined at n times. You can define any type of loop inside another loop; for example, you can define 'while' loop inside a 'for' loop. A loop inside another loop is called a nested loop. The depth of nested loop depends on the complexity of a problem. We can have any number of nested loops as required. Consider a nested loop where the outer loop runs n times and consists of another loop inside it. The inner loop runs m times. Then, the total number of times the inner loop runs during the program execution is n*m.

An array is a collection of data items, all of the same type, accessed using a common name. A one-dimensional array is like a list; A two dimensional array is like a table; The C++ language places no limits on the number of dimensions in an array, though specific implementations may. Some texts refer to one-dimensional arrays as vectors, two-dimensional arrays as matrices, and use the general term arrays when the number of dimensions is unspecified or unimportant. (2D) array in C++ programming is also known as matrix. A matrix can be represented as a table of rows and columns. In C/C++, we can define multi dimensional arrays in simple words as array of arrays. Data in multi dimensional arrays are stored in tabular form (in row major order).

#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 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.

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.

As the name already suggests, these operators help in assigning values to variables. These operators help us in allocating a particular value to the operands. The main simple assignment operator is '='. We have to be sure that both the left and right sides of the operator must have the same data type. We have different levels of operators. Assignment operators are used to assign the value, variable and function to another variable. Assignment operators in C are some of the C Programming Operator, which are useful to assign the values to the declared variables. Let's discuss the various types of the assignment operators such as =, +=, -=, /=, *= and %=. The following table lists the assignment operators supported by the C language:

Consider a situation, when we have two persons with the same name, jhon, in the same class. Whenever we need to differentiate them definitely we would have to use some additional information along with their name, like either the area, if they live in different area or their mother's or father's name, etc. Same situation can arise in your C++ applications. For example, you might be writing some code that has a function called xyz() and there is another library available which is also having same function xyz(). Now the compiler has no way of knowing which version of xyz() function you are referring to within your code.

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.

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.

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.

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.

Algorithm finds the median of 2 sorted arrays using binary search approach. Takes the input of 'n' Data Elements of both the arrays. Using decrease, conquer method find the combined

Return the least recently inserted item in the queue or throw "Underflow" if empty. Return and remove the least "recently inserted" item from the queue. "Throw Underflow" if empty.

Whenever the 'character' does not match, we slide the pattern in such a way that aligns the bad character with the last occurrence of it in pattern. We preprocess the pattern and store