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K distance from root

In this article, we are going to see how to find the nodes at K distance from the root? This problem has been featured in coding round of Amazon.
Submitted by Radib Kar, on February 08, 2019

Problem statement:

Given a Binary Tree and a number K. Print all nodes that are at distance K from root (root is considered at distance 0 from itself). Nodes should be printed from left to right. If K is more that height of tree, nothing should be printed.

Example:

K distance from root?
    For the above tree:
    
    K=3
    Output:
    5, 11, 4

    K=4
    Output:
    No output

Solution

The above problem can be solved using level order traversal. For every level traversed, keep decrementing K.

Algorithm

Pre-requisite:

A Queue, input binary tree, input K

FUNCTION printKdistance(root, k)
1.  Declare a queueqto store tree nodes.
	EnQueue(q, root);
	EnQueue(q, NULL);
	NULL is EnQueued after end of each level. Root determines level-0  
	While (q is not empty)
		temp=DeQueue(q)
		IF(temp==NULL)
			IF (q is not empty)
				Decrement K
				IF (K<0)
				Return;
				END IF
				EnQueue(q, NULL);
			END IF
		ELSE
			IF(k==0) //K-th distance reached
				Print temp->data //print all nodes at K-th level
			END IF
			IF(temp->left is not NULL)
			EnQueue (q, temp->left);
			IF(temp->right is not NULL)
			EnQueue (q, temp->right);
		END IF-ELSE
	END WHILE
END FUNCTION

C++ implementation:

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

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

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

	return(node); 
} 

//to print nodes at Kth distance
void printKdistance(TreeNode *root, int k) 
{
	queue<TreeNode*> q;
	TreeNode* temp;
	
	q.push(root);
	q.push(NULL);
	
	while(!q.empty()){ //level order traversal
		temp=q.front();
		q.pop();

		if(temp==NULL){
			if(!q.empty()){
				k--;
				if(k<0){ //when k<0 return
					return;
				}
				q.push(NULL);
			}
		}
		else{
			if(k==0) //print at K-th distance
				cout<<temp->data<<" ";
			if(temp->left)
				q.push(temp->left);
			if(temp->right)
				q.push(temp->right);
		}
	}
}

int main() { 
	//**same tree is builted as shown in example**
	int k;
	cout<<"same tree is built as shown in example\n";
	
	TreeNode *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<<"enter K\n";
	cin>>k;
	cout<<"Output is:\n";
	printKdistance(root,k);

	return 0; 
} 

Output

same tree is built as shown in example
enter K
3
Output is:
5 11 4 

Example with explanation

For our example tree, K=3

Root=2;
EnQueue(root)
Queue status: 2
EnQueue(NULL)
Queue status: 2, NULL
K=3
----------------------------------------------------

1st iteration
Queue not empty
Queue front is 2
Pop 2
Push: 2->left(7) & 2->right(5)
Queue status: NULL, 7, 5
K=3
----------------------------------------------------

2nd iteration
Queue not empty
Queue front is NULL
Pop NULL
Decrement K
K=2
Push: NULL
Queue status: 7, 5, NULL
----------------------------------------------------

3rd iteration
Queue not empty
Queue front is 7
Pop 7
Push: 7->left (2) and 7->right (6) only
Queue status: 5, NULL, 2, 6
----------------------------------------------------

4th iteration
Queue not empty
Queue front is 5
Pop 5
Push: 5->right (9)(5->left is NULL)
Queue status: NULL, 2, 6, 9 
----------------------------------------------------

5th iteration
Queue not empty
Queue front is NULL
Pop NULL
Decrement K
K=1
Push: NULL
Queue status: 2, 6, 9, NULL
----------------------------------------------------

6th iteration
Queue not empty
Queue front is 2
Pop 2
Push: Nothing (2->left is NULL, 2->right is NULL)
Queue status: 6, 9, NULL
----------------------------------------------------

7th iteration
Queue not empty
Queue front is 6
Pop 6
Push: 6->left (5) & 6->right (11)
Queue status: 9, NULL, 5, 11
----------------------------------------------------

8th iteration
Queue not empty
Queue front is 9
Pop 9
Push: 9->left (4) (9->right is NULL)
Queue status: NULL, 5, 11, 4
----------------------------------------------------

9th iteration
Queue not empty
Queue front is NULL
Pop NULL
Decrement K
K=0
Push: NULL
Queue status: 5, 11, 4, NULL
----------------------------------------------------

10th iteration
Queue not empty
Queue front is 5
Pop 5
K=0
So print 5
Push: Nothing (9->left NULL, 9->right is NULL)
Queue status: 11, 4, NULL

----------------------------------------------------

11th iteration
Queue not empty
Queue front is 11
Pop 11
K=0
So print 11
Push: Nothing (11->left NULL, 11->right is NULL)
Queue status: 4, NULL
----------------------------------------------------

11th iteration
Queue not empty
Queue front is 11
Pop 11
K=0
So print 11
Push: Nothing (11->left NULL, 11->right is NULL)
Queue status: 4, NULL
----------------------------------------------------

12th iteration
Queue not empty
Queue front is 4
Pop 4
K=0
So print 4
Push: Nothing (11->left NULL, 11->right is NULL)
Queue status: NULL
----------------------------------------------------

13th iteration
Queue not empty
Queue front is NULL
Pop NULL
K=0
Now Queue is empty
Push: Nothing (11->left NULL, 11->right is NULL)
Queue status: empty Queue

Exit from program

Hence Output;
5 11 4






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