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C++ Programming Code Examples

C++ > Mathematics Code Examples

Program to Find Basis and Dimension of a Matrix

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/* Program to Find Basis and Dimension of a Matrix This is a C++ Program to find the basis and dimension of the given matrix. */ #include<conio.h> #include<iostream> #include<math.h> using namespace std; double d = 0; double det(int n, double mat[10][10]); double det(int n, double mat[10][10]) { double submat[10][10]; if (n == 2) return ((mat[0][0] * mat[1][1]) - (mat[1][0] * mat[0][1])); else { for (int c = 0; c < n; c++) { int subi = 0; //submatrix's i value for (int i = 1; i < n; i++) { int subj = 0; for (int j = 0; j < n; j++) { if (j == c) continue; submat[subi][subj] = mat[i][j]; subj++; } subi++; } d = d + (pow(-1, c) * mat[0][c] * det(n - 1, submat)); } } return d; } int main(int argc, char **argv) { cout << "Enter the number of vectors:\n"; int n; cin >> n; double mat[10][10]; cout << "Enter the vectors one by one:\n"; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { cin >> mat[j][i]; } } d = det(n, mat); if (d != 0) cout << "The vectors forms the basis of R" << n << " as the determinant is non-zero"; else cout << "The vectors doesn't form the basis of R" << n << " as the determinant is zero"; }
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 }
initialization
initializes variables and is executed only once.
condition
if true, the body of for loop is executed, if false, the for loop is terminated.
update
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; }
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
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
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; }
Continue Statement in C++
Continue statement is used inside loops. Whenever a continue statement is encountered inside a loop, control directly jumps to the beginning of the loop for next iteration, skipping the execution of statements inside loop's body for the current iteration. The continue statement works somewhat like the break statement. Instead of forcing termination, however, continue forces the next iteration of the loop to take place, skipping any code in between. For the for loop, continue causes the conditional test and increment portions of the loop to execute. For the while and do...while loops, program control passes to the conditional tests.
Syntax for Continue Statement in C++
loop-statement{ continue; }
As the name suggest the continue statement forces the loop to continue or execute the next iteration. When the continue statement is executed in the loop, the code inside the loop following the continue statement will be skipped and next iteration of the loop will begin.
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/* continue statement skips the execution of further statements in the block and continues with the next iteration. */ // program to calculate positive numbers till 50 only // if the user enters a negative number, // that number is skipped from the calculation // negative number -> loop terminate // numbers above 50 -> skip iteration #include <iostream> using namespace std; int main() { int sum = 0; int number = 0; while (number >= 0) { // add all positive numbers sum += number; // take input from the user cout << "Enter a number: "; cin >> number; // continue condition if (number > 50) { cout << "The number is greater than 50 and won't be calculated." << endl; number = 0; // the value of number is made 0 again continue; } } // display the sum cout << "The sum is " << sum << endl; return 0; }
If Else Statement in C++
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,
Syntax for If Statement in C++
if (condition) { // body of if 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.
Syntax for If...Else Statement
if (condition) { // block of code if condition is true } else { // block of code if condition is false }
The if..else statement evaluates the condition inside the parenthesis. If the condition evaluates true, the code inside the body of if is executed, the code inside the body of else is skipped from execution. If the condition evaluates false, the code inside the body of else is executed, the code inside the body of if is skipped from execution. The if...else statement is used to execute a block of code among two alternatives. However, if we need to make a choice between more than two alternatives, we use the if...else if...else statement.
Syntax for If...Else...Else If Statement in C++
if (condition1) { // code block 1 } else if (condition2){ // code block 2 } else { // code block 3 }
• If condition1 evaluates to true, the code block 1 is executed. • If condition1 evaluates to false, then condition2 is evaluated. • If condition2 is true, the code block 2 is executed. • If condition2 is false, the code block 3 is executed. There can be more than one else if statement but only one if and else 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.
Syntax for If Else If Ladder in C++
if (condition) statement 1; else if (condition) statement 2; . . else statement;
Working of the if-else-if ladder: 1. Control falls into the if block. 2. The flow jumps to Condition 1. 3. Condition is tested. If Condition yields true, goto Step 4. If Condition yields false, goto Step 5. 4. The present block is executed. Goto Step 7. 5. The flow jumps to Condition 2. If Condition yields true, goto step 4. If Condition yields false, goto Step 6. 6. The flow jumps to Condition 3. If Condition yields true, goto step 4. If Condition yields false, execute else block. Goto Step 7. 7. Exits the if-else-if ladder. • The if else ladder statement in C++ programming language is used to check set of conditions in sequence. • This is useful when we want to selectively executes one code block(out of many) based on certain conditions. • It allows us to check for multiple condition expressions and execute different code blocks for more than two conditions. • A condition expression is tested only when all previous if conditions in if-else ladder is false. • If any of the conditional expression evaluates to true, then it will execute the corresponding code block and exits whole if-else ladder.
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/* If Else Statement in C++ Language */ #include <iostream> using namespace std; int main () { // local variable declaration: int a = 100; // check the boolean condition if( a < 20 ) { // if condition is true then print the following cout << "a is less than 20;" << endl; } else { // if condition is false then print the following cout << "a is not less than 20;" << endl; } cout << "value of a is : " << a << endl; return 0; }
If Else If Ladder in C/C++
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.
Syntax of if...else Ladder in C++
if (Condition1) { Statement1; } else if(Condition2) { Statement2; } . . . else if(ConditionN) { StatementN; } else { Default_Statement; }
In the above syntax of if-else-if, if the Condition1 is TRUE then the Statement1 will be executed and control goes to next statement in the program following if-else-if ladder. If Condition1 is FALSE then Condition2 will be checked, if Condition2 is TRUE then Statement2 will be executed and control goes to next statement in the program following if-else-if ladder. Similarly, if Condition2 is FALSE then next condition will be checked and the process continues. If all the conditions in the if-else-if ladder are evaluated to FALSE, then Default_Statement will be executed.
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/* write a C program which demonstrate use of if-else-if ladder statement */ /* Program to Print Day Names using Else If Ladder in C++*/ #include <iostream> using namespace std; int main() { int day; cout << "Enter Day Number: "; cin >> day; cout << "Day is "; if (day == 1) cout << "Sunday" << endl; else if (day == 2) cout << "Monday" << endl; else if (day == 3) cout << "Tuesday" << endl; else if (day == 4) cout << "Wednesday" << endl; else if (day == 5) cout << "Thursday" << endl; else if (day == 6) cout << "Friday" << endl; else cout << "Saturday" << endl; return 0; }
What is an Multi-Dimensional Array
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.
Declaring Two-Dimensional Arrays
An array of arrays is known as 2D array. The two dimensional (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). General form of declaring N-dimensional arrays is:
datatype arrayname[size1][size2]....[sizeN]; example: int 2d-array[8][16]; char letters[4][9]; float numbers[10][25];
Initializing Two-Dimensional Arrays
In the 1D array, we don't need to specify the size of the array if the declaration and initialization are being done simultaneously. However, this will not work with 2D arrays. We will have to define at least the second dimension of the array. The two-dimensional array can be declared and defined in the following way. Multidimensional arrays may be initialized by specifying bracketed values for each row. Following is an array with 3 rows and each row has 4 columns.
int numbers[3][4] = {{0, 1, 2, 3}, {4, 5, 6, 7}, {8, 9, 10, 11}};
Accessing Two-Dimensional Array Elements
Just like one-dimensional arrays, two-dimensional arrays also require indices to access the required elements. A row and a column index are needed to access a particular element; for nested loops, two indices (one to traverse the rows and the other to traverse the columns in each row) are required to print a two-dimensional array.
// an array with 3 rows and 2 columns. int x[3][2] = {{0,1}, {2,3}, {4,5}}; // output each array element's value for (int i = 0; i < 3; i++) { for (int j = 0; j < 2; j++) { cout << "Element at x[" << i << "][" << j << "]: "; cout << x[i][j]<<endl; } }
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/* multi-dimensional arrays in C++ language */ /* taking input for two dimensional array */ #include <iostream> using namespace std; int main() { int numbers[2][3]; cout << "Enter 6 numbers: " << endl; // Storing user input in the array for (int i = 0; i < 2; ++i) { for (int j = 0; j < 3; ++j) { cin >> numbers[i][j]; } } cout << "The numbers are: " << endl; // Printing array elements for (int i = 0; i < 2; ++i) { for (int j = 0; j < 3; ++j) { cout << "numbers[" << i << "][" << j << "]: " << numbers[i][j] << 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; }
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; }
Standard Input Stream (cin) in C++
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.
Syntax for Standard Input Stream (cin) in C++
cin >> var_name;
>>
is the extraction operator.
var_name
is usually a variable, but can also be an element of containers like arrays, vectors, lists, etc. 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. The >> operator can also be used more than once in the same statement to accept multiple inputs. The cin object can also be used with other member functions such as getline(), read(), etc. Some of the commonly used member functions are: • cin.get(char &ch): Reads an input character and stores it in ch. • cin.getline(char *buffer, int length): Reads a stream of characters into the string buffer, It stops when: it has read length-1 characters or when it finds an end-of-line character '\n' or the end of the file eof. • cin.read(char *buffer, int n): Reads n bytes (or until the end of the file) from the stream into the buffer. • cin.ignore(int n): Ignores the next n characters from the input stream. • cin.eof(): Returns a non-zero value if the end of file (eof) is reached. The prototype of cin as defined in the iostream header file is: extern istream cin; The cin object in C++ is an object of class istream. It is associated with the standard C input stream stdin. The cin object is ensured to be initialized during or before the first time an object of type ios_base::Init is constructed. After the cin object is constructed, cin.tie() returns &cout. This means that any formatted input operation on cin forces a call to cout.flush() if any characters are pending for output.
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/* Standard Input Stream (cin) in C++ language */ // cin with Member Functions #include <iostream> using namespace std; int main() { char name[20], address[20]; cout << "Name: "; // use cin with getline() cin.getline(name, 20); cout << "Address: "; cin.getline(address, 20); cout << endl << "You entered " << endl; cout << "Name = " << name << endl; cout << "Address = " << address; 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
Base value
exponent
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; }


To calculate "area and perimeter" of a square and rectangle in C++ Programming, you have to ask to the user to enter length and breadth of the rectangle and side length of the square
Program to solve a matching problem. Given N men and N women, where each person has ranked all members of the opposite gender in order of preference, marry the men & women