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C++ > Mathematics Code Examples

C++ Program to Find Fibonacci Numbers using Matrix Exponentiation

/* C++ Program to Find Fibonacci Numbers using Matrix Exponentiation This C++ Program demonstrates the the computation of Fibonacci Numbers using Matrix Exponentiation. */ #include <cstring> #include <iostream> #include <cstdlib> #define ll long long using namespace std; /* function to multiply two matrices */ void multiply(ll F[2][2], ll M[2][2]) { ll x = F[0][0] * M[0][0] + F[0][1] * M[1][0]; ll y = F[0][0] * M[0][1] + F[0][1] * M[1][1]; ll z = F[1][0] * M[0][0] + F[1][1] * M[1][0]; ll w = F[1][0] * M[0][1] + F[1][1] * M[1][1]; F[0][0] = x; F[0][1] = y; F[1][0] = z; F[1][1] = w; } /* function to calculate power of a matrix */ void power(ll F[2][2], int n) { if (n == 0 || n == 1) return; ll M[2][2] = {{1,1},{1,0}}; power(F, n / 2); multiply(F, F); if (n % 2 != 0) multiply(F, M); } /* function that returns nth Fibonacci number */ ll fibo_matrix(ll n) { ll F[2][2] = {{1,1},{1,0}}; if (n == 0) return 0; power(F, n - 1); return F[0][0]; } /* Main */ int main() { int n; while (1) { cout<<"Enter the integer n to find nth fibonnaci no.(0 to exit): "; cin>>n; if (n == 0) break; cout<<fibo_matrix(n)<<endl; } return 0; }

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 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.

Logical Operators are used to compare and connect two or more expressions or variables, such that the value of the expression is completely dependent on the original expression or value or variable. We use logical operators to check whether an expression is true or false. If the expression is true, it returns 1 whereas if the expression is false, it returns 0. Assume variable A holds 1 and variable B holds 0:

In while loop, condition is evaluated first and if it returns true then the statements inside while loop execute, this happens repeatedly until the condition returns false. When condition returns false, the control comes out of loop and jumps to the next statement in the program after while loop. The important point to note when using while loop is that we need to use increment or decrement statement inside while loop so that the loop variable gets changed on each iteration, and at some point condition returns false. This way we can end the execution of while loop otherwise the loop would execute indefinitely. A while loop that never stops is said to be the infinite while loop, when we give the condition in such a way so that it never returns false, then the loops becomes infinite and repeats itself indefinitely.

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.

Break statement in C++ is a loop control statement defined using the break keyword. It is used to stop the current execution and proceed with the next one. When a compiler calls the break statement, it immediately stops the execution of the loop and transfers the control outside the loop and executes the other statements. In the case of a nested loop, break the statement stops the execution of the inner loop and proceeds with the outer loop. The statement itself says it breaks the loop. When the break statement is called in the program, it immediately terminates the loop and transfers the flow control to the statement mentioned outside the loop.

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.

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++.

In the C++ Programming Language, the #define directive allows the definition of macros within your source code. These macro definitions allow constant values to be declared for use throughout your code. Macro definitions are not variables and cannot be changed by your program code like variables. You generally use this syntax when creating constants that represent numbers, strings or expressions. The syntax for creating a constant using #define in the C++ is: #define token value

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.

#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.

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 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.






To add digits of any number in C++, we enter the number to add their digits & displays the "Addition Result" of the digits of the entered number on the output screen as shown here




Learn to "multiply two matrices" and display it using user defined function. This program asks user to enter the size of the matrix (rows and columns). Then, it asks the user to enter