Connect nodes at same level

Write a function to connect all the adjacent nodes at the same level in a binary tree. Structure of the given Binary Tree node is like following.

filter_none

edit
close

play_arrow

link
brightness_4
code

struct node {
    int data;
    struct node* left;
    struct node* right;
    struct node* nextRight;
}

chevron_right


Initially, all the nextRight pointers point to garbage values. Your function should set these pointers to point next right for each node.

Example:

Input Tree
       A
      / \
     B   C
    / \   \
   D   E   F


Output Tree
       A--->NULL
      / \
     B-->C-->NULL
    / \   \
   D-->E-->F-->NULL

Method 1 (Extend Level Order Traversal or BFS)
Consider the method 2 of Level Order Traversal. The method 2 can easily be extended to connect nodes of same level. We can augment queue entries to contain level of nodes also which is 0 for root, 1 for root’s children and so on. So a queue node will now contain a pointer to a tree node and an integer level. When we enqueue a node, we make sure that correct level value for node is being set in queue. To set nextRight, for every node N, we dequeue the next node from queue, if the level number of next node is same, we set the nextRight of N as address of the dequeued node, otherwise we set nextRight of N as NULL.

We initialize a node Prev which points at the previous node. While traversing the nodes in the same level we keep track of the previous node and point the nextRight pointer to the current node in every iteration.



Java

filter_none

edit
close

play_arrow

link
brightness_4
code

import java.util.*;
import java.io.*;
class Node {
    int data;
    Node left, right, nextRight;
  
    Node(int item)
    {
        data = item;
        left = right = nextRight = null;
    }
}
  
public class BinaryTree {
    Node root;
    void connect(Node p)
    {
        // initialize queue to hold nodes at same level 
        Queue<Node> q = new LinkedList<>();
  
        q.add(root); // adding nodes to tehe queue
  
        Node temp = null; // initializing prev to null
        while (!q.isEmpty()) {
            int n = q.size();
            for (int i = 0; i < n; i++) {
                Node prev = temp;
                temp = q.poll();
  
                // i > 0 because when i is 0 prev points
                // the last node of previous level, 
                // so we skip it
                if (i > 0)
                    prev.nextRight = temp; 
  
                if (temp.left != null)
                    q.add(temp.left);
  
                if (temp.right != null)
                    q.add(temp.right);
            }
  
            // pointing last node of the nth level to null
            temp.nextRight = null
        }
    }
  
    // Driver program to test above functions
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();
  
        /* Constructed binary tree is 
             10 
            /  \ 
          8     2 
         
        
        */
        tree.root = new Node(10);
        tree.root.left = new Node(8);
        tree.root.right = new Node(2);
        tree.root.left.left = new Node(3);
  
        // Populates nextRight pointer in all nodes
        tree.connect(tree.root);
  
        // Let us check the values of nextRight pointers
        System.out.println("Following are populated nextRight pointers in "
                           + "the tree"
                           + "(-1 is printed if there is no nextRight)");
        int a = tree.root.nextRight != null ? tree.root.nextRight.data : -1;
        System.out.println("nextRight of " + tree.root.data + " is "
                           + a);
        int b = tree.root.left.nextRight != null ? tree.root.left.nextRight.data : -1;
        System.out.println("nextRight of " + tree.root.left.data + " is "
                           + b);
        int c = tree.root.right.nextRight != null ? tree.root.right.nextRight.data : -1;
        System.out.println("nextRight of " + tree.root.right.data + " is "
                           + c);
        int d = tree.root.left.left.nextRight != null ? tree.root.left.left.nextRight.data : -1;
        System.out.println("nextRight of " + tree.root.left.left.data + " is "
                           + d);
    }
}
// This code has been contributed by Rahul Shakya

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to connect nodes 
// at same level 
using System;
using System.Collections.Generic;
  
class Node
{
    public int data;
    public Node left, right, nextRight;
  
    public Node(int item)
    {
        data = item;
        left = right = nextRight = null;
    }
}
  
public class BinaryTree
{
    Node root;
    void connect(Node p)
    {
        // initialize queue to hold nodes at same level 
        Queue<Node> q = new Queue<Node>();
  
        q.Enqueue(root); // adding nodes to tehe queue 
  
        Node temp = null; // initializing prev to null 
        while (q.Count > 0)
        {
            int n = q.Count;
            for (int i = 0; i < n; i++)
            {
                Node prev = temp;
                temp = q.Dequeue();
  
                // i > 0 because when i is 0 prev points 
                // the last node of previous level, 
                // so we skip it 
                if (i > 0)
                    prev.nextRight = temp;
  
                if (temp.left != null)
                    q.Enqueue(temp.left);
  
                if (temp.right != null)
                    q.Enqueue(temp.right);
            }
  
            // pointing last node of the nth level to null 
            temp.nextRight = null;
        }
    }
  
    // Driver code
    public static void Main(String[] args)
    {
        BinaryTree tree = new BinaryTree();
  
        /* Constructed binary tree is 
            10 
            / \ 
        8     2 
        
        
        */
        tree.root = new Node(10);
        tree.root.left = new Node(8);
        tree.root.right = new Node(2);
        tree.root.left.left = new Node(3);
  
        // Populates nextRight pointer in all nodes 
        tree.connect(tree.root);
  
        // Let us check the values of nextRight pointers 
        Console.WriteLine("Following are populated nextRight pointers in "
                        + "the tree"
                        + "(-1 is printed if there is no nextRight)");
        int a = tree.root.nextRight != null ? tree.root.nextRight.data : -1;
        Console.WriteLine("nextRight of " + tree.root.data + " is "
                        + a);
        int b = tree.root.left.nextRight != null ? tree.root.left.nextRight.data : -1;
        Console.WriteLine("nextRight of " + tree.root.left.data + " is "
                        + b);
        int c = tree.root.right.nextRight != null ? tree.root.right.nextRight.data : -1;
        Console.WriteLine("nextRight of " + tree.root.right.data + " is "
                        + c);
        int d = tree.root.left.left.nextRight != null ? tree.root.left.left.nextRight.data : -1;
        Console.WriteLine("nextRight of " + tree.root.left.left.data + " is "
                        + d);
  
        Console.ReadKey();
    }
}
  
// This code has been contributed by techno2mahi 

chevron_right


Output:

Following are populated nextRight pointers in the tree(-1 is printed if there is no nextRight)
nextRight of 10 is -1
nextRight of 8 is 2
nextRight of 2 is -1
nextRight of 3 is -1

Please refer connect Nodes at same Level (Level Order Traversal) for implementation.

Time Complexity: O(n)


Method 2 (Extend Pre Order Traversal)
This approach works only for Complete Binary Trees. In this method we set nextRight in Pre Order fashion to make sure that the nextRight of parent is set before its children. When we are at node p, we set the nextRight of its left and right children. Since the tree is complete tree, nextRight of p’s left child (p->left->nextRight) will always be p’s right child, and nextRight of p’s right child (p->right->nextRight) will always be left child of p’s nextRight (if p is not the rightmost node at its level). If p is the rightmost node, then nextRight of p’s right child will be NULL.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to connect nodes
// at same level using extended
// pre-order traversal
#include <bits/stdc++.h>
#include <iostream>
using namespace std;
  
class node {
public:
    int data;
    node* left;
    node* right;
    node* nextRight;
  
    /* Constructor that allocates a new node with the 
    given data and NULL left and right pointers. */
    node(int data)
    {
        this->data = data;
        this->left = NULL;
        this->right = NULL;
        this->nextRight = NULL;
    }
};
  
void connectRecur(node* p);
  
// Sets the nextRight of
// root and calls connectRecur()
// for other nodes
void connect(node* p)
{
    // Set the nextRight for root
    p->nextRight = NULL;
  
    // Set the next right for rest of the nodes
    // (other than root)
    connectRecur(p);
}
  
/* Set next right of all descendents of p. 
Assumption: p is a compete binary tree */
void connectRecur(node* p)
{
    // Base case
    if (!p)
        return;
  
    // Set the nextRight pointer for p's left child
    if (p->left)
        p->left->nextRight = p->right;
  
    // Set the nextRight pointer
    // for p's right child p->nextRight
    // will be NULL if p is the right
    // most child at its level
    if (p->right)
        p->right->nextRight = (p->nextRight) ? p->nextRight->left : NULL;
  
    // Set nextRight for other
    // nodes in pre order fashion
    connectRecur(p->left);
    connectRecur(p->right);
}
  
/* Driver code*/
int main()
{
  
    /* Constructed binary tree is 
                10 
            / \ 
            8 2 
        
        
    */
    node* root = new node(10);
    root->left = new node(8);
    root->right = new node(2);
    root->left->left = new node(3);
  
    // Populates nextRight pointer in all nodes
    connect(root);
  
    // Let us check the values
    // of nextRight pointers
    cout << "Following are populated nextRight pointers in the tree"
            " (-1 is printed if there is no nextRight)\n";
    cout << "nextRight of " << root->data << " is "
         << (root->nextRight ? root->nextRight->data : -1) << endl;
    cout << "nextRight of " << root->left->data << " is "
         << (root->left->nextRight ? root->left->nextRight->data : -1) << endl;
    cout << "nextRight of " << root->right->data << " is "
         << (root->right->nextRight ? root->right->nextRight->data : -1) << endl;
    cout << "nextRight of " << root->left->left->data << " is "
         << (root->left->left->nextRight ? root->left->left->nextRight->data : -1) << endl;
    return 0;
}
  
// This code is contributed by rathbhupendra

chevron_right


C

filter_none

edit
close

play_arrow

link
brightness_4
code

// C program to connect nodes at same level using extended
// pre-order traversal
#include <stdio.h>
#include <stdlib.h>
  
struct node {
    int data;
    struct node* left;
    struct node* right;
    struct node* nextRight;
};
  
void connectRecur(struct node* p);
  
// Sets the nextRight of root and calls connectRecur()
// for other nodes
void connect(struct node* p)
{
    // Set the nextRight for root
    p->nextRight = NULL;
  
    // Set the next right for rest of the nodes
    // (other than root)
    connectRecur(p);
}
  
/* Set next right of all descendents of p.
   Assumption:  p is a compete binary tree */
void connectRecur(struct node* p)
{
    // Base case
    if (!p)
        return;
  
    // Set the nextRight pointer for p's left child
    if (p->left)
        p->left->nextRight = p->right;
  
    // Set the nextRight pointer for p's right child
    // p->nextRight will be NULL if p is the right
    // most child at its level
    if (p->right)
        p->right->nextRight = (p->nextRight) ? p->nextRight->left : NULL;
  
    // Set nextRight for other nodes in pre order fashion
    connectRecur(p->left);
    connectRecur(p->right);
}
  
/* UTILITY FUNCTIONS */
/* Helper function that allocates a new node with the
   given data and NULL left and right pointers. */
struct node* newnode(int data)
{
    struct node* node = (struct node*)
        malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    node->nextRight = NULL;
  
    return (node);
}
  
/* Driver program to test above functions*/
int main()
{
  
    /* Constructed binary tree is
            10
          /   \
        8      2
      /
    3
  */
    struct node* root = newnode(10);
    root->left = newnode(8);
    root->right = newnode(2);
    root->left->left = newnode(3);
  
    // Populates nextRight pointer in all nodes
    connect(root);
  
    // Let us check the values of nextRight pointers
    printf("Following are populated nextRight pointers in the tree "
           "(-1 is printed if there is no nextRight) \n");
    printf("nextRight of %d is %d \n", root->data,
           root->nextRight ? root->nextRight->data : -1);
    printf("nextRight of %d is %d \n", root->left->data,
           root->left->nextRight ? root->left->nextRight->data : -1);
    printf("nextRight of %d is %d \n", root->right->data,
           root->right->nextRight ? root->right->nextRight->data : -1);
    printf("nextRight of %d is %d \n", root->left->left->data,
           root->left->left->nextRight ? root->left->left->nextRight->data : -1);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to connect nodes at same level using extended
// pre-order traversal
  
// A binary tree node
class Node {
    int data;
    Node left, right, nextRight;
  
    Node(int item)
    {
        data = item;
        left = right = nextRight = null;
    }
}
  
class BinaryTree {
    Node root;
  
    // Sets the nextRight of root and calls connectRecur()
    // for other nodes
    void connect(Node p)
    {
  
        // Set the nextRight for root
        p.nextRight = null;
  
        // Set the next right for rest of the nodes (other
        // than root)
        connectRecur(p);
    }
  
    /* Set next right of all descendents of p.
       Assumption:  p is a compete binary tree */
    void connectRecur(Node p)
    {
        // Base case
        if (p == null)
            return;
  
        // Set the nextRight pointer for p's left child
        if (p.left != null)
            p.left.nextRight = p.right;
  
        // Set the nextRight pointer for p's right child
        // p->nextRight will be NULL if p is the right most child
        // at its level
        if (p.right != null)
            p.right.nextRight = (p.nextRight != null) ? p.nextRight.left : null;
  
        // Set nextRight for other nodes in pre order fashion
        connectRecur(p.left);
        connectRecur(p.right);
    }
  
    // Driver program to test above functions
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();
  
        /* Constructed binary tree is
             10
            /  \
          8     2
         /
        3
        */
        tree.root = new Node(10);
        tree.root.left = new Node(8);
        tree.root.right = new Node(2);
        tree.root.left.left = new Node(3);
  
        // Populates nextRight pointer in all nodes
        tree.connect(tree.root);
  
        // Let us check the values of nextRight pointers
        System.out.println("Following are populated nextRight pointers in "
                           + "the tree"
                           + "(-1 is printed if there is no nextRight)");
        int a = tree.root.nextRight != null ? tree.root.nextRight.data : -1;
        System.out.println("nextRight of " + tree.root.data + " is "
                           + a);
        int b = tree.root.left.nextRight != null ? tree.root.left.nextRight.data : -1;
        System.out.println("nextRight of " + tree.root.left.data + " is "
                           + b);
        int c = tree.root.right.nextRight != null ? tree.root.right.nextRight.data : -1;
        System.out.println("nextRight of " + tree.root.right.data + " is "
                           + c);
        int d = tree.root.left.left.nextRight != null ? tree.root.left.left.nextRight.data : -1;
        System.out.println("nextRight of " + tree.root.left.left.data + " is "
                           + d);
    }
}
  
// This code has been contributed by Mayank Jaiswal

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to connect nodes at same 
# level using extended pre-order traversal 
  
class newnode:
    def __init__(self, data):
        self.data = data
        self.left = self.right = self.nextRight = None
          
# Sets the nextRight of root and calls 
# connectRecur() for other nodes 
def connect (p):
      
    # Set the nextRight for root 
    p.nextRight = None
  
    # Set the next right for rest of
    # the nodes (other than root) 
    connectRecur(p)
  
# Set next right of all descendents of p. 
# Assumption: p is a compete binary tree 
def connectRecur(p):
      
    # Base case 
    if (not p):
        return
      
    # Set the nextRight pointer for p's 
    # left child 
    if (p.left): 
        p.left.nextRight = p.right 
      
    # Set the nextRight pointer for p's right
    # child p.nextRight will be None if p is 
    # the right most child at its level 
    if (p.right):
        if p.nextRight:
            p.right.nextRight = p.nextRight.left
        else:
            p.right.nextRight = None
      
    # Set nextRight for other nodes in
    # pre order fashion 
    connectRecur(p.left) 
    connectRecur(p.right)
  
# Driver Code
if __name__ == '__main__':
  
    # Constructed binary tree is 
    # 10 
    #     / \ 
    # 8     2 
    # / 
    # 3 
    root = newnode(10
    root.left = newnode(8
    root.right = newnode(2
    root.left.left = newnode(3
  
    # Populates nextRight pointer in all nodes 
    connect(root) 
  
    # Let us check the values of nextRight pointers 
    print("Following are populated nextRight"
          "pointers in the tree (-1 is printed",
                    "if there is no nextRight)")
    print("nextRight of", root.data, "is ", end = "")
    if root.nextRight:
        print(root.nextRight.data)
    else:
        print(-1)
    print("nextRight of", root.left.data, "is ", end = "") 
    if root.left.nextRight:
        print(root.left.nextRight.data)
    else:
        print(-1)
    print("nextRight of", root.right.data, "is ", end = "") 
    if root.right.nextRight:
        print(root.right.nextRight.data)
    else:
        print(-1)
    print("nextRight of", root.left.left.data, "is ", end = "") 
    if root.left.left.nextRight:
        print(root.left.left.nextRight.data)
    else:
        print(-1)
  
# This code is contributed by PranchalK

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

using System;
  
// C# program to connect nodes at same level using extended
// pre-order traversal
  
// A binary tree node
public class Node {
    public int data;
    public Node left, right, nextRight;
  
    public Node(int item)
    {
        data = item;
        left = right = nextRight = null;
    }
}
  
public class BinaryTree {
    public Node root;
  
    // Sets the nextRight of root and calls connectRecur()
    // for other nodes
    public virtual void connect(Node p)
    {
  
        // Set the nextRight for root
        p.nextRight = null;
  
        // Set the next right for rest of the nodes (other
        // than root)
        connectRecur(p);
    }
  
    /* Set next right of all descendents of p. 
       Assumption:  p is a compete binary tree */
    public virtual void connectRecur(Node p)
    {
        // Base case
        if (p == null) {
            return;
        }
  
        // Set the nextRight pointer for p's left child
        if (p.left != null) {
            p.left.nextRight = p.right;
        }
  
        // Set the nextRight pointer for p's right child
        // p->nextRight will be NULL if p is the right most child
        // at its level
        if (p.right != null) {
            p.right.nextRight = (p.nextRight != null) ? p.nextRight.left : null;
        }
  
        // Set nextRight for other nodes in pre order fashion
        connectRecur(p.left);
        connectRecur(p.right);
    }
  
    // Driver program to test above functions
    public static void Main(string[] args)
    {
        BinaryTree tree = new BinaryTree();
  
        /* Constructed binary tree is 
             10 
            /  \ 
          8     2 
         
        
        */
        tree.root = new Node(10);
        tree.root.left = new Node(8);
        tree.root.right = new Node(2);
        tree.root.left.left = new Node(3);
  
        // Populates nextRight pointer in all nodes
        tree.connect(tree.root);
  
        // Let us check the values of nextRight pointers
        Console.WriteLine("Following are populated nextRight pointers in "
                          + "the tree"
                          + "(-1 is printed if there is no nextRight)");
        int a = tree.root.nextRight != null ? tree.root.nextRight.data : -1;
        Console.WriteLine("nextRight of " + tree.root.data + " is " + a);
        int b = tree.root.left.nextRight != null ? tree.root.left.nextRight.data : -1;
        Console.WriteLine("nextRight of " + tree.root.left.data + " is " + b);
        int c = tree.root.right.nextRight != null ? tree.root.right.nextRight.data : -1;
        Console.WriteLine("nextRight of " + tree.root.right.data + " is " + c);
        int d = tree.root.left.left.nextRight != null ? tree.root.left.left.nextRight.data : -1;
        Console.WriteLine("nextRight of " + tree.root.left.left.data + " is " + d);
    }
}
  
// This code is contributed by Shrikant13

chevron_right


Output:

Following are populated nextRight pointers in the tree (-1 is printed if there is no nextRight)
nextRight of 10 is -1
nextRight of 8 is 2
nextRight of 2 is -1
nextRight of 3 is -1

Thanks to Dhanya for suggesting this approach.

Time Complexity: O(n)

Why doesn’t method 2 work for trees which are not Complete Binary Trees?
Let us consider following tree as an example. In Method 2, we set the nextRight pointer in pre order fashion. When we are at node 4, we set the nextRight of its children which are 8 and 9 (the nextRight of 4 is already set as node 5). nextRight of 8 will simply be set as 9, but nextRight of 9 will be set as NULL which is incorrect. We can’t set the correct nextRight, because when we set nextRight of 9, we only have nextRight of node 4 and ancestors of node 4, we don’t have nextRight of nodes in right subtree of root.

            1
          /    \
        2        3
       / \      /  \
      4   5    6    7
     / \           / \  
    8   9        10   11

See Connect nodes at same level using constant extra space for more solutions.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.




My Personal Notes arrow_drop_up