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C++ Programming Code Examples

C++ > Data Structures and Algorithm Analysis in C++ Code Examples

Various maximum subsequence sum algorithms

/* Various maximum subsequence sum algorithms */ #include <iostream.h> #include "vector.h" /** * Cubic maximum contiguous subsequence sum algorithm. */ int maxSubSum1( const vector<int> & a ) { /* 1*/ int maxSum = 0; /* 2*/ for( int i = 0; i < a.size( ); i++ ) /* 3*/ for( int j = i; j < a.size( ); j++ ) { /* 4*/ int thisSum = 0; /* 5*/ for( int k = i; k <= j; k++ ) /* 6*/ thisSum += a[ k ]; /* 7*/ if( thisSum > maxSum ) /* 8*/ maxSum = thisSum; } /* 9*/ return maxSum; } /* END */ /** * Quadratic maximum contiguous subsequence sum algorithm. */ int maxSubSum2( const vector<int> & a ) { /* 1*/ int maxSum = 0; /* 2*/ for( int i = 0; i < a.size( ); i++ ) { /* 3*/ int thisSum = 0; /* 4*/ for( int j = i; j < a.size( ); j++ ) { /* 5*/ thisSum += a[ j ]; /* 6*/ if( thisSum > maxSum ) /* 7*/ maxSum = thisSum; } } /* 8*/ return maxSum; } /* END */ /** * Return maximum of three integers. */ int max3( int a, int b, int c ) { return a > b ? a > c ? a : c : b > c ? b : c; } /** * Recursive maximum contiguous subsequence sum algorithm. * Finds maximum sum in subarray spanning a[left..right]. * Does not attempt to maintain actual best sequence. */ int maxSumRec( const vector<int> & a, int left, int right ) { /* 1*/ if( left == right ) // Base case /* 2*/ if( a[ left ] > 0 ) /* 3*/ return a[ left ]; else /* 4*/ return 0; /* 5*/ int center = ( left + right ) / 2; /* 6*/ int maxLeftSum = maxSumRec( a, left, center ); /* 7*/ int maxRightSum = maxSumRec( a, center + 1, right ); /* 8*/ int maxLeftBorderSum = 0, leftBorderSum = 0; /* 9*/ for( int i = center; i >= left; i-- ) { /*10*/ leftBorderSum += a[ i ]; /*11*/ if( leftBorderSum > maxLeftBorderSum ) /*12*/ maxLeftBorderSum = leftBorderSum; } /*13*/ int maxRightBorderSum = 0, rightBorderSum = 0; /*14*/ for( int j = center + 1; j <= right; j++ ) { /*15*/ rightBorderSum += a[ j ]; /*16*/ if( rightBorderSum > maxRightBorderSum ) /*17*/ maxRightBorderSum = rightBorderSum; } /*18*/ return max3( maxLeftSum, maxRightSum, /*19*/ maxLeftBorderSum + maxRightBorderSum ); } /** * Driver for divide-and-conquer maximum contiguous * subsequence sum algorithm. */ int maxSubSum3( const vector<int> & a ) { return maxSumRec( a, 0, a.size( ) - 1 ); } /* END */ /** * Linear-time maximum contiguous subsequence sum algorithm. */ int maxSubSum4( const vector<int> & a ) { /* 1*/ int maxSum = 0, thisSum = 0; /* 2*/ for( int j = 0; j < a.size( ); j++ ) { /* 3*/ thisSum += a[ j ]; /* 4*/ if( thisSum > maxSum ) /* 5*/ maxSum = thisSum; /* 6*/ else if( thisSum < 0 ) /* 7*/ thisSum = 0; } /* 8*/ return maxSum; } /* END */ /** * Simple test program. */ int main( ) { vector<int> a( 8 ); a[ 0 ] = 4; a[ 1 ] = -3; a[ 2 ] = 5; a[ 3 ] = -2; a[ 4 ] = -1; a[ 5 ] = 2; a[ 6 ] = 6; a[ 7 ] = -2; int maxSum; maxSum = maxSubSum1( a ); cout << "Max sum is " << maxSum << endl; maxSum = maxSubSum2( a ); cout << "Max sum is " << maxSum << endl; maxSum = maxSubSum3( a ); cout << "Max sum is " << maxSum << endl; maxSum = maxSubSum4( a ); cout << "Max sum is " << maxSum << endl; return 0; }

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:

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.

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.

Return size. Returns the number of elements in the vector. This is the number of actual objects held in the vector, which is not necessarily equal to its storage capacity. vector::size() is a library function of "vector" header, it is used to get the size of a vector, it returns the total number of elements in the vector. The dynamic array can be created by using a vector in C++. One or more elements can be inserted into or removed from the vector at the run time that increases or decreases the size of the vector. The size or length of the vector can be counted using any loop or the built-in function named size(). This function does not accept any parameter.

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.

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++, vectors are used to store elements of similar data types. However, unlike arrays, the size of a vector can grow dynamically. That is, we can change the size of the vector during the execution of a program as per our requirements. Vectors are part of the C++ Standard Template Library. To use vectors, we need to include the vector header file in our program. The vector class provides various methods to perform different operations on vectors. Add Elements to a Vector: To add a single element into a vector, we use the push_back() function. It inserts an element into the end of the vector. Access Elements of a Vector: In C++, we use the index number to access the vector elements. Here, we use the at() function to access the element from the specified index.

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.

#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.

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.

Access element. Returns a reference to the element at position n in the vector container. A similar member function, vector::at, has the same behavior as this operator function, except that vector::at is bound-checked and signals if the requested position is out of range by throwing an out_of_range exception. Portable programs should never call this function with an argument n that is out of range, since this causes undefined behavior. Function returns the element at the specified position in the vector.

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