# C++ Program to Find Size of the Largest Independent Set(LIS) in a Given a Binary Tree

This is a C++ Program to Find Size of the Largest Independent Set (LIS) in a Given a Binary Tree.

## Algorithm

Begin.
Create a structure n to declare data d, a left child pointer l and a right child pointer r.
Call a function max() to return maximum between two integers. Create a function LIS() to return the
size of the largest independent set in a given binary tree.
Calculate size excluding the current node
int size_excl = LIS(root->l) + LIS(root->r)
Calculate size including the current node
int size_incl = 1;
if (root->l)
size_incl += LIS(root->l->l) + LIS(root->l->r)
if (root->right)
size_incl += LIS(root->r->l) + LIS(root->r->r)
Return the maximum of two sizes
Create a function to create newnode.
End.

## Example Code

Live Demo

#include <iostream>
using namespace std;
struct n {
int d;
int lis;
struct n *l, *r;
};
int max(int x, int y) {
return (x > y) ? x : y;
}
int LIS(struct n *root) {
if (root == NULL)
return 0;
if (root->lis)
return root->lis;
if (root->l == NULL && root->r == NULL)
return (root->lis = 1);
int lis_excl = LIS(root->l) + LIS(root->r);
int lis_incl = 1;
if (root->l)
lis_incl += LIS(root->l->l) + LIS(root->l->r);
if (root->r)
lis_incl += LIS(root->r->l) + LIS(root->r->r);
root->lis = max(lis_incl, lis_excl);
return root->lis;
}
struct n* newnode(int d) {
struct n* t = (struct n *) malloc(sizeof(struct n));
t->d = d;
t->l = t->r = NULL;
t->lis = 0;
return t;
}
int main() {
struct n *root = newnode(30);
root->l= newnode(20);
root->l->l = newnode(10);
root->l->r = newnode(7);
root->l->r->l = newnode(9);
root->l->r->r = newnode(6);
root->r = newnode(50);
root->r->r = newnode(26);
cout<<"Size of the Largest Independent Set is "<< LIS(root);
return 0;
}

## Output

Size of the Largest Independent Set is 5
Samual Sam

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