 # C++ Programming Code Examples

## C++ > Arrays and Matrices Code Examples

### Program to Compute Combinations using Matrix Multiplication

/* Program to Compute Combinations using Matrix Multiplication 1. This algorithm computes the combination using matrix multiplication method. 2. The time complexity to compute this is O(n*n*n). 3. This algorithm is very expensive to compute a combination. This is a C++ program to compute combinations using matrix multiplication. */ #include<iostream> using namespace std; // A function to find the factorial of a given number using matrix multiplication method. int MatFactorial(int n) { int x, j, k, matA[n+1][n+1], matB[n+1][n+1], matC[n+1][n+1], count; count = n; // Assigning numbers from 1 to n to the super diagonal indexes of the matrix. // Assigning result matric matC[][] to zero initially. for(x = 0; x < n+1; x++) { for(j = 0; j < n+1; j++) { if(j == x+1) matA[x][j] = x+1; else matA[x][j] = 0; // Assign matB[][] equal to initially to compute square. matB[x][j] = matA[x][j]; matC[x][j] = 0; } } flag: // Multiply matA[][] and matB[][] and store the data into matC[][]. for(x = 0; x < n+1; x++) { for(j = 0; j < n+1; j++) { for(k = 0; k < n+1; k++) { matC[x][j] += matA[x][k]*matB[k][j]; } } } // Assign matB as the result matrix matC[][] and then assign matC[x][j] element to zero again. for(x = 0; x < n+1; x++) { for(j = 0; j < n+1; j++) { matB[x][j] = matC[x][j]; matC[x][j] = 0; } } count--; // We need to compute the matA[][] raise to the power of n so if count is more than 1 then increase the power of matA[][]. if(count > 1) goto flag; // If matA[][] raise to n is calculated, then return the last element of the first row of matB[][], as the factorial of n. return matB[n]; } int main() { int n, r, result; cout<<"A program to find combination from nCr format using matrix multiplication method:-"; cout<<"\n\n\tEnter the value of n: "; cin>>n; cout<<"\tEnter the value of r: "; cin>>r; // Get result using formulae to calculate combinations. result = MatFactorial(n)/(MatFactorial(r)*MatFactorial(n-r)); cout<<"\nThe number of possible combinations is: "<<result; 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.

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.

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).

In C++, goto is a jump statement and sometimes also referred as unconditional jump statement. It can be used to jump from goto to a labeled statement within the same function. The target label must be within the same file and context. Please note that the use of goto statement is highly discouraged in any programming language because it makes difficult to trace the control flow of a program, making hard to understand and modify the program.

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.

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.

#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.

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:

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.

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.

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.