इंटरवल ट्री अंतराल रखने के लिए एक आदेशित ट्री डेटा संरचना है। यह विशेष रूप से किसी भी अंतराल या बिंदु के साथ ओवरलैप होने वाले सभी अंतरालों को कुशलतापूर्वक खोजने की अनुमति देता है। यहाँ एक इंटरवल ट्री को लागू करने के लिए C++ प्रोग्राम है।
एल्गोरिदम
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
उदाहरण कोड
#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 << "]";
} के साथ ओवरलैप करता है आउटपुट
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]