 # C++ Programming Code Examples

## C++ > Mathematics Code Examples

### Program to Perform LU Decomposition of any Matrix

/* Program to Perform LU Decomposition of any Matrix This is a C++ Program to perform LU Decomposition of any matrix. In numerical analysis, LU decomposition (where 'LU' stands for 'Lower Upper', and also called LU factorization) factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. The LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using the LU decomposition, and it is also a key step when inverting a matrix, or computing the determinant of a matrix */ #include<iostream> #include<cstdio> using namespace std; int main(int argc, char **argv) { void lu(float[], float[], float[], int n); void output(float[], int); float a, l, u; int n = 0, i = 0, j = 0; cout << "Enter size of 2d array(Square matrix) : "; cin >> n; for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { cout << "Enter values no:" << i << ", " << j << ": "; cin >> a[i][j]; } } lu(a, l, u, n); cout << "\nL Decomposition\n\n"; output(l, n); cout << "\nU Decomposition\n\n"; output(u, n); return 0; } void lu(float a[], float l[], float u[], int n) { int i = 0, j = 0, k = 0; for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { if (j < i) l[j][i] = 0; else { l[j][i] = a[j][i]; for (k = 0; k < i; k++) { l[j][i] = l[j][i] - l[j][k] * u[k][i]; } } } for (j = 0; j < n; j++) { if (j < i) u[i][j] = 0; else if (j == i) u[i][j] = 1; else { u[i][j] = a[i][j] / l[i][i]; for (k = 0; k < i; k++) { u[i][j] = u[i][j] - ((l[i][k] * u[k][j]) / l[i][i]); } } } } } void output(float x[], int n) { int i = 0, j = 0; for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { printf("%f ", x[i][j]); } cout << "\n"; } }

#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.

Put character. Inserts character c into the stream. Internally, the function accesses the output sequence by first constructing a sentry object. Then (if good), it inserts c into its associated stream buffer object as if calling its member function sputc, and finally destroys the sentry object before returning. Function returns the ostream object (*this).

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.

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.

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).

The if...else statement executes two different codes depending upon whether the test expression is true or false. Sometimes, a choice has to be made from more than 2 possibilities. The if...else ladder allows you to check between multiple test expressions and execute different statements. In C/C++ if-else-if ladder helps user decide from among multiple options. The C/C++ if statements are executed from the top down. As soon as one of the conditions controlling the if is true, the statement associated with that if is executed, and the rest of the C else-if ladder is bypassed. If none of the conditions is true, then the final else statement will be executed.

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.

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.

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 defined as the collection of similar type of data items stored at contiguous memory locations. Arrays are the derived data type in C++ programming language which can store the primitive type of data such as int, char, double, float, etc. It also has the capability to store the collection of derived data types, such as pointers, structure, etc. The array is the simplest data structure where each data element can be randomly accessed by using its index number. C++ array is beneficial if you have to store similar elements. For example, if we want to store the marks of a student in 6 subjects, then we don't need to define different variables for the marks in the different subject. Instead of that, we can define an array which can store the marks in each subject at the contiguous memory locations.

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.

This C++ example uses a class that contains a constructor used to 'initialize the object'. The class is called ShoeBox. When supplied with a Length, a Height, a Width, the object should

Construct Binary Search tree for the unsorted data array. 'Search the element' starting from the Root of the Tree. Proceed with the search by comparing an element to the data of node