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C++ Program to Implement Interval Tree

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/* C++ Program to Implement Interval Tree This is a C++ Program to implement interval tree. In computer science, an interval tree is an ordered tree data structure to hold intervals. Specifically, it allows one to efficiently find all intervals that overlap with any given interval or point. It is often used for windowing queries, for instance, to find all roads on a computerized map inside a rectangular viewport, or to find all visible elements inside a three-dimensional scene. A similar data structure is the segment tree. */ #include <iostream> using namespace std; struct Interval { int low, high; }; struct ITNode { Interval *i; // 'i' could also be a normal variable int max; ITNode *left, *right; }; // A utility function to create a new Interval Search Tree Node ITNode * newNode(Interval i) { ITNode *temp = new ITNode; temp->i = new Interval(i); temp->max = i.high; temp->left = temp->right = NULL; }; // A utility function to insert a new Interval Search Tree Node // This is similar to BST Insert. Here the low value of interval is used tomaintain BST property ITNode *insert(ITNode *root, Interval i) { // Base case: Tree is empty, new node becomes root if (root == NULL) return newNode(i); // Get low value of interval at root int l = root->i->low; // If root's low value is smaller, then new interval goes to left subtree if (i.low < l) root->left = insert(root->left, i); // Else, new node goes to right subtree. else root->right = insert(root->right, i); // Update the max value of this ancestor if needed if (root->max < i.high) root->max = i.high; return root; } // A utility function to check if given two intervals overlap bool doOVerlap(Interval i1, Interval i2) { if (i1.low <= i2.high && i2.low <= i1.high) return true; return false; } // The main function that searches a given interval i in a given Interval Tree. Interval *intervalSearch(ITNode *root, Interval i) { // Base Case, tree is empty if (root == NULL) return NULL; // If given interval overlaps with root if (doOVerlap(*(root->i), i)) return root->i; // If left child of root is present and max of left child is greater than or equal to given interval, then i may overlap with an interval is left subtree if (root->left != NULL && root->left->max >= i.low) return intervalSearch(root->left, i); // Else interval can only overlap with right subtree return intervalSearch(root->right, i); } void inorder(ITNode *root) { if (root == NULL) return; inorder(root->left); cout << "[" << root->i->low << ", " << root->i->high << "]" << " max = " << root->max << endl; inorder(root->right); } int main(int argc, char **argv) { Interval ints[] = { { 15, 20 }, { 10, 30 }, { 17, 19 }, { 5, 20 }, { 12, 15 }, { 30, 40 } }; int n = sizeof(ints) / sizeof(ints[0]); ITNode *root = NULL; for (int i = 0; i < n; i++) root = insert(root, ints[i]); cout << "In-order traversal of constructed Interval Tree is\n"; inorder(root); Interval x = { 6, 7 }; cout << "\nSearching for interval [" << x.low << "," << x.high << "]"; Interval *res = intervalSearch(root, x); if (res == NULL) cout << "\nNo Overlapping Interval"; else cout << "\nOverlaps with [" << res->low << ", " << res->high << "]"; }

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.

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:

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 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.

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.

Search range for subsequence. Searches the range [first1,last1) for the first occurrence of the sequence defined by [first2,last2), and returns an iterator to its first element, or last1 if no occurrences are found. The elements in both ranges are compared sequentially using operator== (or pred, in version (2)): A subsequence of [first1,last1) is considered a match only when this is true for all the elements of [first2,last2). This function returns the first of such occurrences. For an algorithm that returns the last instead, see find_end. The function shall not modify any of its arguments.

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.

#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 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 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.

Allocate storage space. Default allocation functions (single-object form). A new operator is used to create the object while a delete operator is used to delete the object. When the object is created by using the new operator, then the object will exist until we explicitly use the delete operator to delete the object. Therefore, we can say that the lifetime of the object is not related to the block structure of the program.

Prints a 'subset' of the given array using coin flipping method. The time complexity of this algorithm is O(n). Takes the input of 'n' data element and prints a possible subset. that, it

This is a C++ Program to perform Fast Fourier Transform. A 'Fast Fourier transform' (FFT) is an algorithm to compute the discrete Fourier transform (DFT) & its inverse. Fourier analysis