#include <iostream>
using namespace std;

// Structure to represent an interval
struct Interval
{
	int low, high;
};

// Structure to represent a node in Interval Search Tree
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;
	return temp;
};

// 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 *overlapSearch(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 overlapSearch(root->left, i);

	// Else interval can only overlap with right subtree
	return overlapSearch(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()
{

	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 << "Inorder traversal of constructed Interval Tree is\n";
	inorder(root);

	Interval x = {6, 7};

	cout << "\nSearching for interval [" << x.low << "," << x.high << "]";
	Interval *res = overlapSearch(root, x);
	if (res == NULL)
		cout << "\nNo Overlapping Interval";
	else
		cout << "\nOverlaps with [" << res->low << ", " << res->high << "]";
	return 0;
}