# C++ Programming Code Examples

## C++ > Mathematics Code Examples

### Program to Find Closest Pair of Points in an Array

/* Program to Find Closest Pair of Points in an Array */
#include <iostream>
#include <cfloat>
#include <cstdlib>
#include <cmath>
using namespace std;
/* Point Declaration */
struct Point
{
int x, y;
};
/* sort array of points according to X coordinate */
int compareX(const void* a, const void* b)
{
Point *p1 = (Point *)a, *p2 = (Point *)b;
return (p1->x - p2->x);
}
/* sort array of points according to Y coordinate */
int compareY(const void* a, const void* b)
{
Point *p1 = (Point *)a, *p2 = (Point *)b;
return (p1->y - p2->y);
}
/* find the distance between two points */
float dist(Point p1, Point p2)
{
return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
}
/* return the smallest distance between two points */
float small_dist(Point P[], int n)
{
float min = FLT_MAX;
for (int i = 0; i < n; ++i)
{
for (int j = i + 1; j < n; ++j)
{
if (dist(P[i], P[j]) < min)
min = dist(P[i], P[j]);
}
}
return min;
}
/* find the distance beween the closest points of strip of given size */
float stripClosest(Point strip[], int size, float d)
{
float min = d;
for (int i = 0; i < size; ++i)
{
for (int j = i + 1; j < size && (strip[j].y - strip[i].y) < min; ++j)
{
if (dist(strip[i],strip[j]) < min)
min = dist(strip[i], strip[j]);
}
}
return min;
}
/* find the smallest distance. */
float closestUtil(Point Px[], Point Py[], int n)
{
if (n <= 3)
return small_dist(Px, n);
int mid = n / 2;
Point midPoint = Px[mid];
Point Pyl[mid + 1];
Point Pyr[n - mid - 1];
int li = 0, ri = 0;
for (int i = 0; i < n; i++)
{
if (Py[i].x <= midPoint.x)
Pyl[li++] = Py[i];
else
Pyr[ri++] = Py[i];
}
float dl = closestUtil(Px, Pyl, mid);
float dr = closestUtil(Px + mid, Pyr, n-mid);
float d = min(dl, dr);
Point strip[n];
int j = 0;
for (int i = 0; i < n; i++)
{
if (abs(Py[i].x - midPoint.x) < d)
strip[j] = Py[i], j++;
}
return min(d, stripClosest(strip, j, d));
}
/* finds the smallest distance */
float closest(Point P[], int n)
{
Point Px[n];
Point Py[n];
for (int i = 0; i < n; i++)
{
Px[i] = P[i];
Py[i] = P[i];
}
qsort(Px, n, sizeof(Point), compareX);
qsort(Py, n, sizeof(Point), compareY);
return closestUtil(Px, Py, n);
}
/* Main */
int main()
{
Point P[] = {{4, 8}, {13, 38}, {44, 50}, {8, 3}, {14, 9}, {5, 8}};
int n = sizeof(P) / sizeof(P[0]);
cout << "The smallest distance is " << closest(P, n);
return 0;
}

The sizeof() is an operator that evaluates the size of data type, constants, variable. It is a compile-time operator as it returns the size of any variable or a constant at the compilation time. The size, which is calculated by the sizeof() operator, is the amount of RAM occupied in the computer. The sizeof is a keyword, but it is a compile-time operator that determines the size, in bytes, of a variable or data type. The sizeof operator can be used to get the size of classes, structures, unions and any other user defined data type. The data_type can be the data type of the data, variables, constants, unions, structures, or any other user-defined data type.

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.

Return the smallest. Returns the smallest of a and b. If both are equivalent, a is returned. min() function is a library function of algorithm header, it is used to find the smallest value from given two values, it accepts two values and returns the smallest value and if both the values are the same it returns the first value. The versions for initializer lists (3) return the smallest of all the elements in the list. Returning the first of them if these are more than one. The function uses operator< (or comp, if provided) to compare the values.

#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.

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, 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.

Absolute value. Returns the absolute value of parameter n ( /n/ ). In C++, this function is also overloaded in header <cmath> for floating-point types (see cmath abs), in header <complex> for complex numbers (see complex abs), and in header <valarray> for valarrays (see valarray abs). Basically the abs function evaluates the absolute value of the given value i.e. value after removing all the signs of negative and positive from the number. Which means it will always return a positive number. Function returns the absolute value of n. abs() function - In C the input is of type 'int' whereas in C++ input is of type 'int, long int or long long int'. In C the output is of 'int' type and in C++ the output has the same data type as input.

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 C++, classes and structs are blueprints that are used to create the instance of a class. Structs are used for lightweight objects such as Rectangle, color, Point, etc. Unlike class, structs in C++ are value type than reference type. It is useful if you have data that is not intended to be modified after creation of struct. C++ Structure is a collection of different data types. It is similar to the class that holds different types of data. A structure is declared by preceding the struct keyword followed by the identifier(structure name). Inside the curly braces, we can declare the member variables of different types.

Compute square root. Returns the square root of x. The sqrt() function in C++ returns the square root of a number. This function is defined in the cmath header file. There are various functions available in the C++ Library to calculate the square root of a number. Most prominently, sqrt is used. It takes double as an argument. The <cmath> header defines two more inbuilt functions for calculating the square root of a number (apart from sqrt) which has an argument of type float and long double. Therefore, all the functions used for calculating square root in C++ are. Mathematically, sqrt(x) = √x.

Check whether eofbit is set. Returns true if the eofbit error state flag is set for the stream. This flag is set by all standard input operations when the End-of-File is reached in the sequence associated with the stream. Note that the value returned by this function depends on the last operation performed on the stream (and not on the next). Operations that attempt to read at the End-of-File fail, and thus both the eofbit and the failbit end up set. This function can be used to check whether the failure is due to reaching the End-of-File or to some other reason.

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.

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.

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:

Sort elements of array. Sorts the num elements of the array pointed to by base, each element size bytes long, using the compar function to determine the order. The sorting algorithm used by this function compares pairs of elements by calling the specified compar function with pointers to them as argument. The function does not return any value, but modifies the content of the array pointed to by base reordering its elements as defined by compar. The order of equivalent elements is undefined.

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.

'boolalpha' turns on boolapha flag. 'dec' turns on dec flag. 'endl' output a newline character & flush the 'stream'. ends output a null. fixed Turns on fixed flag. flush Flush a stream. hex

For example 6 is Perfect Number since divisor of 6 are 1, 2 and 3. Sum of its divisor is 1 + 2+ 3 =6 and 28 is also a 'Perfect Number' since 1+ 2 + 4 + 7 + 14= 28. Other 'Perfect Numbers': 496

We create a queue for BFS. Mark the current node as visited and enqueue it. It will be used to get all adjacent vertices of a vertex. Get all adjacent vertices of the dequeued vertex s. If

To convert binary to octal in C++, you have to ask to the user to enter any number in binary to "convert it into octal" to display equivalent value in octal on the screen as shown in code