Interval Tree in C++

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.

Here is source code of the C++ Program to Implement Interval Tree. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
#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
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        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);

```
}
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```
 
```
```
void inorder(ITNode *root)
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```
{
```
```
    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 << "]";

```
}
```

Output:

$ g++ IntervalTree.cpp
$ a.out
 
In-order traversal of constructed Interval Tree is
[5, 20] max = 20
[10, 30] max = 30
[12, 15] max = 15
[15, 20] max = 40
[17, 19] max = 40
[30, 40] max = 40
 
Searching for interval [6,7]
Overlaps with [5, 20]
 
------------------
(program exited with code: 0)
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