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Find the level in a binary tree with given sum K



Here, we are going to learn how to find the level in a binary tree with given sum K – its an interview coding problem came in Samsung, Microsoft?
Submitted by Radib Kar, on November 25, 2018

Description:

The article describes how to find the level in a binary tree with given sum K? This is an interview coding problem came in Samsung, Microsoft.

Problem statement:

Given a binary tree and an integer K, output the level no of the tree which sums to K. Assume root level is level 0.

Solution

Algorithm:

One of the popular traversal techniques to solve this kind of problems is level order tree traversal (Read more: Level Order Traversal on a Binary Tree) where we use the concept of BFS with some modifications.

1. Set a variable level=0 & declare a variable of type tree* named temp. level is a flag for the current level & temp stores tree node to be processed.

2. Set cur_sum=0

3. if(!root) // root is NULL
return -1; //no such level exists

4. q=createQueue() //to store pointers to tree node

5. EnQueue(q,root);

6. EnQueue(q,NULL);

Every time, we EnQueue a NULL to reflect the end of current level. Same way while processing when NULL is found, it reveals that end of current level.

7. while( q is not empty)
    temp=DeQueue(q);
    if(temp==NULL){ //end of current level
        if (cur_sum==K) // current level sum is equal to K
            Return level; //return level no (root is at 0 level)
        else {
            Set cur_sum =0; // for next level
            If(q is not empty)
                // to reflect end of next level which 
                // will be processed in next iteration
                EnQueue(q,NULL)
            Increase level //increase level count
        }
    }
    Else{
        cur_sum+=temp->data; //sum the level
        //do level order traversal
        If(temp->left)
            EnQueue(temp->left);
        If(temp->right)
            EnQueue (temp->right);
        }
End while loop

8. If program control comes out of while loop then surely no level has a sum K. Thus print no level has sum K

tree image 1

Example:

Here the level sums are:
For level 0: 2
For level 1: 12
For level 2: 17
For level 3: 20
Thus if K is 12 our program will print level 1



C++ code to find the level in a binary tree with given sum K

#include <bits/stdc++.h>
using namespace std;

// tree node is defined
class tree{
	public:
		int data;
		tree *left;
		tree *right;
};

int findLevel( tree *root,int K){
	queue<tree*> q;  // using stl
	tree* temp;
	//counting level no & initializing cur_sum
	int level=0,cur_sum=0; 
	//EnQueue root
	q.push(root); 
	//EnQueue NULL to inticate end of 0 level
	q.push(NULL);
	while(!q.empty()){
		//DeQueueing using STL
		temp=q.front(); 
		q.pop();
		if(temp==NULL){
			//if current level sum equals to K
			if(cur_sum==K) 
				return level;//return level no
			//ifn't then set cur_sum to 0 for further levels
			cur_sum=0; 
			if(!q.empty())
				q.push(NULL);
			level++;
		}
		else{
		//level order traversal
		cur_sum+=temp->data; //sum thd level
		if(temp->left)
			q.push(temp->left); //EnQueue
		if(temp->right)
			q.push(temp->right); //EnQueue
		}
	}
	return -1;
}

// creating new node
tree* newnode(int data)  
{ 
	tree* node = (tree*)malloc(sizeof(tree)); 
	node->data = data; 
	node->left = NULL; 
	node->right = NULL; 

	return(node); 
} 

int main() 
{ 
	//**same tree is builted as shown in example**
	int c,K;
	cout<<"Tree is built like the example aforesaid"<<endl;
	cout<<"input K....."<<endl;
	cin>>K;

	tree *root=newnode(2); 
	root->left= newnode(7); 
	root->right= newnode(5); 
	root->right->right=newnode(9);
	root->right->right->left=newnode(4);
	root->left->left=newnode(2); 
	root->left->right=newnode(6);
	root->left->right->left=newnode(5);
	root->left->right->right=newnode(11);

	cout<<"finding if any level exists......"<<endl; 
	c=findLevel(root,K);
	if(c>=0)
		cout<<"level is found and it is level "<<c<<endl;
	else
		cout<<"level not found, no such tree level exists";

	return 0; 
} 

Output

First run:
Tree is built like the example aforesaid 
input K..... 
20 
finding if any level exists......
level is found and it is level 3 

Second run:
Tree is built like the example aforesaid 
input K..... 
25 
finding if any level exists......
level not found, no such tree level exists





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