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C++ > Mathematics Code Examples

C++ Program to Implement Naor-Reingold Pseudo Random Function

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/* C++ Program to Implement Naor-Reingold Pseudo Random Function This is a C++ Program to genrate random numbers using Naor-Reingold random function. Moni Naor and Omer Reingold described efficient constructions for various cryptographic primitives in private key as well as public-key cryptography. Their result is the construction of an efficient pseudorandom function. Let p and l be prime numbers with l |p-1. Select an element g ? {\mathbb F_p}^* of multiplicative order l. Then for each n-dimensional vector a = (a1, .... an)? (\mathbb F_{l})^{n} they define the function f_{a}(x) = g^{a_{1}^{x_{1}} a_{2}^{x_{2}}...a_{n}^{x_{n}}} \in \mathbb F_p where x = x1 ... xn is the bit representation of integer x, 0 = x = 2^n-1, with some extra leading zeros if necessary. */ #include <iostream> #include <math.h> #include <stdlib.h> using namespace std; int main(int argc, char **argv) { int p = 7, l = 3, g = 2, n = 4, x; int a[] = { 1, 2, 2, 1 }; int bin[4]; cout << "The Random numbers are: "; for (int i = 0; i < 10; i++) { x = rand() % 16; for (int j = 3; j >= 0; j--) { bin[j] = x % 2; x /= 2; } int mul = 1; for (int k = 0; k < 4; k++) mul *= pow(a[k], bin[k]); cout << pow(g, mul)<<" "; } }
main() Function in C++
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.
Syntax for main() Function in C++
void main() { ............ ............ }
void is a keyword in C++ language, void means nothing, whenever we use void as a function return type then that function nothing return. here main() function no return any value.
main is a name of function which is predefined function in C++ library. In place of void we can also use int return type of main() function, at that time main() return integer type value. 1) It cannot be used anywhere in the program a) in particular, it cannot be called recursively b) its address cannot be taken 2) It cannot be predefined and cannot be overloaded: effectively, the name main in the global namespace is reserved for functions (although it can be used to name classes, namespaces, enumerations, and any entity in a non-global namespace, except that a function called "main" cannot be declared with C language linkage in any namespace). 3) It cannot be defined as deleted or (since C++11) declared with C language linkage, constexpr (since C++11), consteval (since C++20), inline, or static. 4) The body of the main function does not need to contain the return statement: if control reaches the end of main without encountering a return statement, the effect is that of executing return 0;. 5) Execution of the return (or the implicit return upon reaching the end of main) is equivalent to first leaving the function normally (which destroys the objects with automatic storage duration) and then calling std::exit with the same argument as the argument of the return. (std::exit then destroys static objects and terminates the program). 6) (since C++14) The return type of the main function cannot be deduced (auto main() {... is not allowed). 7) (since C++20) The main function cannot be a coroutine.
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/* simple code example by main() function in C++ */ #include <iostream> using namespace std; int main() { int day = 4; switch (day) { case 1: cout << "Monday"; break; case 2: cout << "Tuesday"; break; case 3: cout << "Wednesday"; break; case 4: cout << "Thursday"; break; case 5: cout << "Friday"; break; case 6: cout << "Saturday"; break; case 7: cout << "Sunday"; break; } return 0; }
Assignment Operators in C++
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:
Simple assignment operator. Assigns values from right side operands to left side operand
Add AND assignment operator. It adds the right operand to the left operand and assign the result to the left operand.
Subtract AND assignment operator. It subtracts the right operand from the left operand and assigns the result to the left operand.
Multiply AND assignment operator. It multiplies the right operand with the left operand and assigns the result to the left operand.
Divide AND assignment operator. It divides the left operand with the right operand and assigns the result to the left operand.
Modulus AND assignment operator. It takes modulus using two operands and assigns the result to the left operand.
Left shift AND assignment operator.
Right shift AND assignment operator.
Bitwise AND assignment operator.
Bitwise exclusive OR and assignment operator.
Bitwise inclusive OR and assignment operator.
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/* Assignment operators are used to assigning value to a variable. The left side operand of the assignment operator is a variable and right side operand of the assignment operator is a value. The value on the right side must be of the same data-type of the variable on the left side otherwise the compiler will raise an error. */ // C++ program to demonstrate working of Assignment operators #include <iostream> using namespace std; int main() { // Assigning value 10 to a // using "=" operator int a = 10; cout << "Value of a is "<<a<<"\n"; // Assigning value by adding 10 to a // using "+=" operator a += 10; cout << "Value of a is "<<a<<"\n"; // Assigning value by subtracting 10 from a // using "-=" operator a -= 10; cout << "Value of a is "<<a<<"\n"; // Assigning value by multiplying 10 to a // using "*=" operator a *= 10; cout << "Value of a is "<<a<<"\n"; // Assigning value by dividing 10 from a // using "/=" operator a /= 10; cout << "Value of a is "<<a<<"\n"; return 0; }
rand() Function in C++
Generate random number. Returns a pseudo-random integral number in the range between 0 and RAND_MAX. This number is generated by an algorithm that returns a sequence of apparently non-related numbers each time it is called. This algorithm uses a seed to generate the series, which should be initialized to some distinctive value using function srand. RAND_MAX is a constant defined in <cstdlib>.
Syntax for rand() Function in C++
#include <cstdlib> int rand();
The rand() function in C++ is used to generate random numbers; it will generate the same number every time we run the program. In order to seed the rand() function, srand(unsigned int seed) is used. The srand() function sets the initial point for generating the pseudo-random numbers. The rand() function generates numbers randomly. When execute the rand() function in a program, the same random number gets represented. The srand() function along with the rand() function generates random numbers at compile time. The srand() function does not return any value while the rand() function returns the random number generated by it. C++ supports a wide range of powerful tools to generate random and pseudo-random numbers (see <random> for more info). The function accepts no parameter(s). The standard practice is to use the return value of time(0) function as the seed. Function returns an integer value between 0 and RAND_MAX. If random numbers are generated with rand() without first calling srand(), your program will create the same sequence of numbers each time it runs.
In C, the generation algorithm used by rand is guaranteed to only be advanced by calls to this function. In C++, this constraint is relaxed, and a library implementation is allowed to advance the generator on other circumstances (such as calls to elements of <random>).
Data races
The function accesses and modifies internal state objects, which may cause data races with concurrent calls to rand or srand. Some libraries provide an alternative function that explicitly avoids this kind of data race: rand_r (non-portable). C++ library implementations are allowed to guarantee no data races for calling this function.
No-throw guarantee: this function never throws exceptions.
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/* generate random number by rand() function code example */ #include <iostream> #include <cstdlib> #include <ctime> int main() { using namespace std; time_t qTime; time(&qTime); // Use a varying seed, like time, to generate new sequences. srand(qTime); cout << "A varying sequence of random numbers:" << endl; for (unsigned int uiIndex = 0; uiIndex < 10; ++uiIndex) { cout << " " << rand(); } cout << endl; // Use a constant with srand to generate the same sequence. srand(2); cout << "A fixed sequence of random numbers:" << endl; for (unsigned int uiIndex = 0; uiIndex < 10; ++uiIndex) { cout << " " << rand(); } cout << endl; cout << "The generated range is 0 to " << RAND_MAX << endl; return 0; }
Namespaces in 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. A namespace is designed to overcome this difficulty and is used as additional information to differentiate similar functions, classes, variables etc. with the same name available in different libraries. Using namespace, you can define the context in which names are defined. In essence, a namespace defines a scope.
Defining a Namespace
A namespace definition begins with the keyword namespace followed by the namespace name as follows:
namespace namespace_name { // code declarations }
To call the namespace-enabled version of either function or variable, prepend (::) the namespace name as follows:
name::code; // code could be variable or function.
Using Directive
You can also avoid prepending of namespaces with the using namespace directive. This directive tells the compiler that the subsequent code is making use of names in the specified namespace.
Discontiguous Namespaces
A namespace can be defined in several parts and so a namespace is made up of the sum of its separately defined parts. The separate parts of a namespace can be spread over multiple files. So, if one part of the namespace requires a name defined in another file, that name must still be declared. Writing a following namespace definition either defines a new namespace or adds new elements to an existing one:
namespace namespace_name { // code declarations }
Nested Namespaces
Namespaces can be nested where you can define one namespace inside another name space as follows:
namespace namespace_name1 { // code declarations namespace namespace_name2 { // code declarations } }
• Namespace is a feature added in C++ and not present in C. • A namespace is a declarative region that provides a scope to the identifiers (names of the types, function, variables etc) inside it. • Multiple namespace blocks with the same name are allowed. All declarations within those blocks are declared in the named scope. • Namespace declarations appear only at global scope. • Namespace declarations can be nested within another namespace. • Namespace declarations don't have access specifiers. (Public or private) • No need to give semicolon after the closing brace of definition of namespace. • We can split the definition of namespace over several units.
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/* namespaces in C++ language */ // A C++ code to demonstrate that we can define // methods outside namespace. #include <iostream> using namespace std; // Creating a namespace namespace ns { void display(); class happy { public: void display(); }; } // Defining methods of namespace void ns::happy::display() { cout << "ns::happy::display()\n"; } void ns::display() { cout << "ns::display()\n"; } // Driver code int main() { ns::happy obj; ns::display(); obj.display(); return 0; }
For Loop Statement in C++
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.
Syntax of For Loop Statement in C++
for (initialization; condition; update) { // body of-loop }
initializes variables and is executed only once.
if true, the body of for loop is executed, if false, the for loop is terminated.
updates the value of initialized variables and again checks the condition. A new range-based for loop was introduced to work with collections such as arrays and vectors.
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/* For Loop Statement in C++ Language */ // C++ program to find the sum of first n natural numbers // positive integers such as 1,2,3,...n are known as natural numbers #include <iostream> using namespace std; int main() { int num, sum; sum = 0; cout << "Enter a positive integer: "; cin >> num; for (int i = 1; i <= num; ++i) { sum += i; } cout << "Sum = " << sum << endl; return 0; }
#include Directive in C++
#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.
Syntax for #include Directive in C++
#include "user-defined_file"
Including using " ": When using the double quotes(" "), the preprocessor access the current directory in which the source "header_file" is located. This type is mainly used to access any header files of the user's program or user-defined files.
#include <header_file>
Including using <>: While importing file using angular brackets(<>), the the preprocessor uses a predetermined directory path to access the file. It is mainly used to access system header files located in the standard system directories. Header File or Standard files: This is a file which contains C/C++ function declarations and macro definitions to be shared between several source files. Functions like the printf(), scanf(), cout, cin and various other input-output or other standard functions are contained within different header files. So to utilise those functions, the users need to import a few header files which define the required functions. User-defined files: These files resembles the header files, except for the fact that they are written and defined by the user itself. This saves the user from writing a particular function multiple times. Once a user-defined file is written, it can be imported anywhere in the program using the #include preprocessor. • In #include directive, comments are not recognized. So in case of #include <a//b>, a//b is treated as filename. • In #include directive, backslash is considered as normal text not escape sequence. So in case of #include <a\nb>, a\nb is treated as filename. • You can use only comment after filename otherwise it will give error.
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/* using #include directive in C language */ #include <stdio.h> int main() { /* * C standard library printf function * defined in the stdio.h header file */ printf("I love you Clementine"); printf("I love you so much"); printf("HappyCodings"); return 0; }
Arithmetic Operators in C++
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 multiplication operator is represented as an asterisk (*) symbol, and it is used to return the product of n1 and n2 numbers. The data type of the given number can be different types such as int, float, and double in the C programing language.
The division operator is an arithmetic operator that divides the first (n1) by the second (n2) number. Using division operator (/), we can divide the int, float, double and long data types variables.
The modulus operator is represented by the percentage sign (%), and it is used to return the remainder by dividing the first number by the second number.
Increment Operator is the type of Arithmetic operator, which is denoted by double plus (++) operator. It is used to increase the integer value by 1.
Decrement Operator is denoted by the double minus (--) symbol, which decreases the operand value by 1.
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/* Perhaps you have warm memories of doing arithmetic drills in grade school. You can give that same pleasure to your computer. C++ uses operators to do arithmetic. It provides operators for five basic arithmetic calculations: addition, subtraction, multiplication, division, and taking the modulus. Each of these operators uses two values (called operands) to calculate a final answer. Together, the operator and its operands constitute an expression. */ #include <iostream> using namespace std; int main() { int a, b; a = 7; b = 2; // printing the sum of a and b cout << "a + b = " << (a + b) << endl; // printing the difference of a and b cout << "a - b = " << (a - b) << endl; // printing the product of a and b cout << "a * b = " << (a * b) << endl; // printing the division of a by b cout << "a / b = " << (a / b) << endl; // printing the modulo of a by b cout << "a % b = " << (a % b) << endl; return 0; }
Nested Loop Statement in C++
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.
Syntax for Nested Loop Statement in C++
Outer_loop { Inner_loop { // inner loop statements. } // outer loop statements. }
Outer_loop and Inner_loop are the valid loops that can be a 'for' loop, 'while' loop or 'do-while' loop.
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/* nested loop statement in C++ language */ // C++ program that uses nested for loop to print a 2D matrix #include <bits/stdc++.h> using namespace std; #define ROW 3 #define COL 3 // Driver program int main() { int i, j; // Declare the matrix int matrix[ROW][COL] = { { 4, 8, 12 }, { 16, 20, 24 }, { 28, 32, 36 } }; cout << "Given matrix is \n"; // Print the matrix using nested loops for (i = 0; i < ROW; i++) { for (j = 0; j < COL; j++) cout << matrix[i][j]; cout << "\n"; } return 0; }
Math Library pow() Function in C++
Raise to power. The pow() function returns the result of the first argument raised to the power of the second argument. This function is defined in the cmath header file. pow() function is a library function of cmath header, it is used to find the raise to the power, it accepts two arguments and returns the first argument to the power of the second argument. power = baseexponent
Syntax for Math pow() Function in C++
#include<cmath> double pow (double base , double exponent); float pow (float base , float exponent); long double pow (long double base, long double exponent); double pow (Type1 base , Type2 exponent); // additional overloads
Base value
Exponent value Additional overloads are provided in this header (<cmath>) for other combinations of arithmetic types (Type1 and Type2): These overloads effectively cast its arguments to double before calculations, except if at least one of the arguments is of type long double (in which case both are casted to long double instead). This function is also overloaded in <complex> and <valarray>. Function returns the result of raising base to the power exponent. If the base is finite negative and the exponent is finite but not an integer value, it causes a domain error. If both base and exponent are zero, it may also cause a domain error on certain implementations. If base is zero and exponent is negative, it may cause a domain error or a pole error (or none, depending on the library implementation). The function may also cause a range error if the result is too great or too small to be represented by a value of the return type.
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/* get base raised to the power exponent by pow() function */ // CPP program code example to illustrate power function #include <bits/stdc++.h> using namespace std; int main() { double x = 6.1, y = 4.8; // Storing the answer in result. double result = pow(x, y); // printing the result upto 2 // decimal place cout << fixed << setprecision(2) << result << endl; return 0; }

In program, user enter 2 integers (divisor and dividend), computes quotient and remainder. To compute 'quotient and remainder', divisor and dividend should be integers. The division
Program takes a "positive integer" from user, then displays the value of '1+2+3+....+n'. This C++ program code assumes that user always enters positive number. So if enters negative