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C++ Program to Implement Heap's Algorithm for Permutation of N Numbers

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/* C++ Program to Implement Heap's Algorithm for Permutation of N Numbers - This algorithm print the permutation using heap algorithm. - The time complexity of this algorithm is O(n!). - This algorithm takes the input of 'N' distinct numbers. - It fixes an element at the end of the array and permutes the remaining numbers. - Exit. */ #include<iostream> #include<iomanip> using namespace std; // A function swapping values using references. void swap(int *x, int *y) { int temp; temp = *x; *x = *y; *y = temp; } // A function to implement Heap's Algorithm for the permutation of N numbers. void print(const int *v) { int i; int size = sizeof(v)/sizeof(int)+1; // Loop to print the sequence. cout<<"\t"; for ( i = 0; i < size; i++) cout<<setw(4)<<v[i]; cout<<"\n"; } void HeapPermute(int v[], int n) { int i; // Print the sequence if the heap top reaches to the 1. if (n == 1) print(v); else { // Fix a number at the heap top until only two one element remaining and permute remaining. for (i = 0; i < n; i++) { HeapPermute(v, n-1); // If odd then swap the value at the start index with the n-1. if(n%2 == 1) swap(&v[0], &v[n-1]); // If even then swap the value at the 'i' index with the n-1. else swap(&v[i], &v[n-1]); } } } int main() { int i, n, count = 1; cout<<"How many numbers do you want to enter: "; cin>>n; int num[n]; // Take the input. cout<<"\nEnter the numbers: "; for (i = 0; i < n; i++) { cin>>num[i]; count *= (i+1); } // Print the permutation's count. cout<<"\nThe number of permutations possible is: "<<count<<"\n"; // Calling Function to print all the permutation. HeapPermute(num, n); return 0; }

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.

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.

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.

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, 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.

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.

Set field width. Sets the field width to be used on output operations. The C++ function std::setw behaves as if member width were called with n as argument on the stream on which it is inserted/extracted as a manipulator (it can be inserted/extracted on input streams or output streams). It is used to sets the field width to be used on output operations. This manipulator is declared in header <iomanip>. This method accepts n as a parameter which is the integer argument corresponding to which the field width is to be set. This function returns an object of unspecified type. The setw function should only be used as a stream manipulator.

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.

A relational operator is used to check the relationship between two operands. C++ Relational Operators are used to relate or compare given operands. Relational operations are like checking if two operands are equal or not equal, greater or lesser, etc. Relational Operators are also called Comparison Operators.

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.

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:

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.

#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.





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In this c++ program, user enter two numbers ('floating point numbers'). Then, the product of those two numbers is 'stored' in a variable and displayed on the screen. The 2 numbers