C++ Program to Implement Interval Tree

An interval tree is an ordered tree data structure to hold intervals. It specifically allows one to efficiently find all intervals that overlap with any given interval or point. Here is a C++ Program to implement an interval tree.

Algorithm

Begin
   function insert() is used to insert new nodes into the tree:
      If Tree is empty, new node becomes root.
         Get low value of interval at root.
      If root's low value is smaller, then new interval goes to left subtree.
      Else, new node goes to right subtree.
      If needed, update the max value of this ancestor.
End

Begin
   function intervalFind() searches a given interval i in a given interval Tree:
      If tree is empty return null.
      If given interval overlaps with root
      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
      Else
         interval can only overlap with right subtree.
End

Example Code

#include <iostream>
using namespace std;

struct Interval//interval variables declaration {
   int l, h;
};
struct ITNod//node declaration {
   Interval *i;
   int max;
   ITNod *l, *r;
};
ITNod * newNode(Interval i)//to create new node {
   ITNod *t = new ITNod;
   t->i = new Interval(i);
   t->max = i.h;
   t->l = t->r = NULL;
};
ITNod *insert(ITNod *r, Interval i) {
   if (r== NULL)
      return newNode(i);
      int l = r->i->l;
   if (i.l< l)
      r->l = insert(r->l, i);
   else
      r->r = insert(r->r, i);
   if (r->max < i.h)
      r->max = i.h;
      return r;
}
bool Overlap(Interval i1, Interval i2)// check if two intervals overlap or not. {
   if (i1.l <= i2.h && i2.l<= i1.h)
      return true;
      return false;
}
Interval *intervalFind(ITNod *root, Interval i) {
   if (root == NULL)
      return NULL;
   if (Overlap(*(root->i), i))
      return root->i;
   if (root->l!= NULL && root->l->max >= i.l)
      return intervalFind(root->l, i);
      return intervalFind(root->r, i);
}

void inorder(ITNod *root)//perform inorder traversal {
   if (root == NULL)
      return;
      inorder(root->l);
      cout << "[" << root->i->l<< ", " << root->i->h << "]" << " max = "<< root->max << endl;
      inorder(root->r);
}
int main(int argc, char **argv) {
   Interval ints[] = { { 5, 20 }, { 6, 7 }, { 3, 4 }, { 67, 26 }, { 3, 4 } };
   int n = sizeof(ints) / sizeof(ints[0]);
   ITNod *root = NULL;
   for (int i = 0; i < n; i++)
      root = insert(root, ints[i]);
      cout << "In-order traversal of the constructed Interval Tree is\n";
      inorder(root);
      Interval x = { 7, 6 };
      cout << "\nSearching for interval [" << x.l << "," << x.h << "]";
      Interval *res = intervalFind(root, x);
      if (res == NULL)
         cout << "\nNo Overlapping Interval";
      else
         cout << "\nOverlaps with [" << res->l << ", " << res->h << "]";
}

Output

In-order traversal of the constructed Interval Tree is
[3, 4] max = 4
[3, 4] max = 4
[5, 20] max = 26
[6, 7] max = 26
[67, 26] max = 26

Searching for interval [7,6]
Overlaps with [5, 20]