Boundary Level order traversal of a Binary Tree

Given a Binary Tree, the task is to print all levels of this tree in Boundary Level order traversal.

Boundary Level order traversal: In this traversal, the first element of the level (starting boundary) is printed first, followed by last element (ending boundary). Then the process is repeated for the second and last-second element, till the complete level has been printed.

Examples:

Input: 
                   1
                /    \ 
              12       13 
             /  \     /   \ 
            11    6  4    11 
           /     /  \     / \
         23     7    9   2   4
Output:
1
12 13
11 11 6 4
23 4 7 2 9

Input: 
                  7
                /  \ 
              22     19
             /  \      \
            3     6     13 
           / \     \    / \
          1   5     8  1   4  
                   /
                  23 
Output:
7
22 19
3 13 6
1 4 5 1 8
23

Approach:

• In order to print level in Boundary Level order traversal, we need to first do the Level Order Traversal of the Binary tree to get the values at each level.
• Here a Queue data structure is used to store the levels of the Tree while doing the Level Order Traversal.
• Then for each level, the first element of the level (starting boundary) is printed first, followed by the last element (ending boundary). Then the process is repeated for the second and last-second element, till the complete level has been printed.

Below is the implementation of the above approach: 

C++

// C++ program for printing a
// Levels of Binary Tree in a
// start end fashion

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

// A Tree node
struct Node {
    int key;
    struct Node *left, *right;
};

// Utility function to create a new node
Node* newNode(int key)
{
    Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return (temp);
}

// Utility function to print level in
// start end fashion
void printLevelUtil(struct Node* queue[],
                    int index, int size)
{
    while (index < size) {
        cout << queue[index++]->key << " "
             << queue[size--]->key << " ";
    }
    if (index == size) {
        cout << queue[index]->key << " ";
    }

    cout << endl;
}

// Utility function to print level in  start
// end fashion in a given Binary tree
void printLevel(struct Node* node,
                struct Node* queue[],
                int index, int size)
{

    // Print root node value
    // as a single value in a
    // binary tree
    cout << queue[index]->key << endl;

    // Level order traversal of Tree
    while (index < size) {
        int curr_size = size;
        while (index < curr_size) {
            struct Node* temp = queue[index];

            if (temp->left != NULL) {
                queue[size++] = temp->left;
            }

            if (temp->right != NULL) {
                queue[size++] = temp->right;
            }

            index++;
        }

        // Print level in a desire fashion
        printLevelUtil(queue, index, size - 1);
    }
}

// Function to find total no of nodes
int findSize(struct Node* node)
{

    if (node == NULL)
        return 0;

    return 1
           + findSize(node->left)
           + findSize(node->right);
}

// Function to print level in start end
// fashion in a given binary tree
void printLevelInStartEndFashion(
    struct Node* node)
{
    int t_size = findSize(node);
    struct Node* queue[t_size];
    queue[0] = node;
    printLevel(node, queue, 0, 1);
}

// Driver Code
int main()
{
    /*     10
           / \
         13   13
          /     \
        14       15
        / \     / \
       21 22   22 21
                  /
                 8 */

    // Create Binary Tree as shown
    Node* root = newNode(10);
    root->left = newNode(13);
    root->right = newNode(13);

    root->right->left = newNode(14);
    root->right->right = newNode(15);

    root->right->left->left = newNode(21);
    root->right->left->right = newNode(22);
    root->right->right->left = newNode(22);
    root->right->right->right = newNode(21);
    root->right->right->right->left = newNode(8);

    // Print Levels In Start End Fashion
    printLevelInStartEndFashion(root);

    return 0;
}

Java

// Java program for printing a
// Levels of Binary Tree in a
// start end fashion
class GFG{

// A Tree node
static class Node {
    int key;
    Node left, right;
};

// Utility function to create a new node
static Node newNode(int key)
{
    Node temp = new Node();
    temp.key = key;
    temp.left = temp.right = null;
    return (temp);
}

// Utility function to print level in
// start end fashion
static void printLevelUtil(Node queue[],
                    int index, int size)
{
    while (index < size) {
        System.out.print(queue[index++].key+ " "
             + queue[size--].key+ " ");
    }
    if (index == size) {
        System.out.print(queue[index].key+ " ");
    }

    System.out.println();
}

// Utility function to print level in  start
// end fashion in a given Binary tree
static void printLevel(Node node,
                Node queue[],
                int index, int size)
{

    // Print root node value
    // as a single value in a
    // binary tree
    System.out.print(queue[index].key +"\n");

    // Level order traversal of Tree
    while (index < size) {
        int curr_size = size;
        while (index < curr_size) {
            Node temp = queue[index];

            if (temp.left != null) {
                queue[size++] = temp.left;
            }

            if (temp.right != null) {
                queue[size++] = temp.right;
            }

            index++;
        }

        // Print level in a desire fashion
        printLevelUtil(queue, index, size - 1);
    }
}

// Function to find total no of nodes
static int findSize(Node node)
{

    if (node == null)
        return 0;

    return 1
           + findSize(node.left)
           + findSize(node.right);
}

// Function to print level in start end
// fashion in a given binary tree
static void printLevelInStartEndFashion(
    Node node)
{
    int t_size = findSize(node);
    Node []queue = new Node[t_size];
    queue[0] = node;
    printLevel(node, queue, 0, 1);
}

// Driver Code
public static void main(String[] args)
{
    /*     10
           / \
         13   13
          /     \
        14       15
        / \     / \
       21 22   22 21
                  /
                 8 */

    // Create Binary Tree as shown
    Node root = newNode(10);
    root.left = newNode(13);
    root.right = newNode(13);

    root.right.left = newNode(14);
    root.right.right = newNode(15);

    root.right.left.left = newNode(21);
    root.right.left.right = newNode(22);
    root.right.right.left = newNode(22);
    root.right.right.right = newNode(21);
    root.right.right.right.left = newNode(8);

    // Print Levels In Start End Fashion
    printLevelInStartEndFashion(root);

}
}

// This code is contributed by Princi Singh

Python3

# Python3 program for printing a
# Levels of Binary Tree in a
# start end fashion

# A Tree node
class Node:

    def __init__(self, key):

        self.key = key
        self.left = None
        self.right = None

# function to create a
# new node
def newNode(key):

    temp = Node(key);
    return temp;


# Utility function to print
# level in start end fashion
def printLevelUtil(queue,
                   index, size):

    while (index < size):
        print(str(queue[index].key) + ' ' +
              str(queue[size].key), end = ' ')
        size -= 1
        index += 1

    if (index == size):
        print(queue[index].key,
              end = ' ')
    print()

# Utility function to print
# level in  start end fashion
# in a given Binary tree
def printLevel(node, queue,
               index, size):

    # Print root node value
    # as a single value in a
    # binary tree
    print(queue[index].key)

    # Level order traversal
    # of Tree
    while (index < size):
        curr_size = size;
        while (index < curr_size):
            temp = queue[index];
            if (temp.left != None):
                queue[size] = temp.left;
                size += 1
            if (temp.right != None):
                queue[size] = temp.right;
                size += 1

            index += 1

        # Print level in a desire
        # fashion
        printLevelUtil(queue, index,
                       size - 1);

# Function to find total
# no of nodes
def findSize(node):

    if (node == None):
        return 0;

    return (1 + findSize(node.left) +
                findSize(node.right));

# Function to print level in start
# end fashion in a given binary tree
def printLevelInStartEndFashion(node):

    t_size = findSize(node);
    queue=[0 for i in range(t_size)];
    queue[0] = node;
    printLevel(node, queue, 0, 1);

# Driver code
if __name__=="__main__":

    '''     10
           / \
         13   13
          /     \
        14       15
        / \     / \
       21 22   22 21
                  /
                 8 '''

    # Create Binary Tree as shown
    root = newNode(10);
    root.left = newNode(13);
    root.right = newNode(13);

    root.right.left = newNode(14);
    root.right.right = newNode(15);

    root.right.left.left = newNode(21);
    root.right.left.right = newNode(22);
    root.right.right.left = newNode(22);
    root.right.right.right = newNode(21);
    root.right.right.right.left = newNode(8);

    # Print Levels In Start End Fashion
    printLevelInStartEndFashion(root);

# This code is contributed by Rutvik_56

C#

// C# program for printing a
// Levels of Binary Tree in a
// start end fashion
using System;

class GFG{

// A Tree node
class Node {
    public int key;
    public Node left, right;
};

// Utility function to create a new node
static Node newNode(int key)
{
    Node temp = new Node();
    temp.key = key;
    temp.left = temp.right = null;
    return (temp);
}

// Utility function to print level in
// start end fashion
static void printLevelUtil(Node []queue,
                    int index, int size)
{
    while (index < size) {
        Console.Write(queue[index++].key+ " "
             + queue[size--].key+ " ");
    }
    if (index == size) {
        Console.Write(queue[index].key+ " ");
    }

    Console.WriteLine();
}

// Utility function to print level in  start
// end fashion in a given Binary tree
static void printLevel(Node node,
                Node []queue,
                int index, int size)
{

    // Print root node value
    // as a single value in a
    // binary tree
    Console.Write(queue[index].key +"\n");

    // Level order traversal of Tree
    while (index < size) {
        int curr_size = size;
        while (index < curr_size) {
            Node temp = queue[index];

            if (temp.left != null) {
                queue[size++] = temp.left;
            }

            if (temp.right != null) {
                queue[size++] = temp.right;
            }

            index++;
        }

        // Print level in a desire fashion
        printLevelUtil(queue, index, size - 1);
    }
}

// Function to find total no of nodes
static int findSize(Node node)
{

    if (node == null)
        return 0;

    return 1
           + findSize(node.left)
           + findSize(node.right);
}

// Function to print level in start end
// fashion in a given binary tree
static void printLevelInStartEndFashion(
    Node node)
{
    int t_size = findSize(node);
    Node []queue = new Node[t_size];
    queue[0] = node;
    printLevel(node, queue, 0, 1);
}

// Driver Code
public static void Main(String[] args)
{
    /*     10
           / \
         13   13
          /     \
        14       15
        / \     / \
       21 22   22 21
                  /
                 8 */

    // Create Binary Tree as shown
    Node root = newNode(10);
    root.left = newNode(13);
    root.right = newNode(13);

    root.right.left = newNode(14);
    root.right.right = newNode(15);

    root.right.left.left = newNode(21);
    root.right.left.right = newNode(22);
    root.right.right.left = newNode(22);
    root.right.right.right = newNode(21);
    root.right.right.right.left = newNode(8);

    // Print Levels In Start End Fashion
    printLevelInStartEndFashion(root);
}
}

// This code is contributed by PrinciRaj1992

Javascript

<script>

// JavaScript program for printing a
// Levels of Binary Tree in a
// start end fashion

// A Tree node
class Node {
    constructor()
    {
        this.key = 0;
        this.left = null;
        this.right = null;
    }
};

// Utility function to create a new node
function newNode(key)
{
    var temp = new Node();
    temp.key = key;
    temp.left = temp.right = null;
    return (temp);
}

// Utility function to print level in
// start end fashion
function printLevelUtil(queue, index, size)
{
    while (index < size) {
        document.write(queue[index++].key+ " "
             + queue[size--].key+ " ");
    }
    if (index == size) {
        document.write(queue[index].key+ " ");
    }

    document.write("<br>");
}

// Utility function to print level in  start
// end fashion in a given Binary tree
function printLevel(node, queue, index, size)
{

    // Print root node value
    // as a single value in a
    // binary tree
    document.write(queue[index].key +"<br>");

    // Level order traversal of Tree
    while (index < size) {
        var curr_size = size;
        while (index < curr_size) {
            var temp = queue[index];

            if (temp.left != null) {
                queue[size++] = temp.left;
            }

            if (temp.right != null) {
                queue[size++] = temp.right;
            }

            index++;
        }

        // Print level in a desire fashion
        printLevelUtil(queue, index, size - 1);
    }
}

// Function to find total no of nodes
function findSize(node)
{

    if (node == null)
        return 0;

    return 1
           + findSize(node.left)
           + findSize(node.right);
}

// Function to print level in start end
// fashion in a given binary tree
function printLevelInStartEndFashion( node)
{
    var t_size = findSize(node);
    var queue = Array(t_size);
    queue[0] = node;
    printLevel(node, queue, 0, 1);
}

// Driver Code
/*     10
       / \
     13   13
      /     \
    14       15
    / \     / \
   21 22   22 21
              /
             8 */

// Create Binary Tree as shown
var root = newNode(10);
root.left = newNode(13);
root.right = newNode(13);

root.right.left = newNode(14);
root.right.right = newNode(15);

root.right.left.left = newNode(21);
root.right.left.right = newNode(22);
root.right.right.left = newNode(22);
root.right.right.right = newNode(21);
root.right.right.right.left = newNode(8);

// Print Levels In Start End Fashion
printLevelInStartEndFashion(root);

</script>

Output:

10
13 13 
14 15 
21 21 22 22 
8

 Time complexity: The time complexity of this implementation is also O(N), as the printLevel function visits each node in the tree exactly once and performs a constant amount of work for each node.

Auxiliary Space:  The Auxiliary Space of this implementation is O(N), where N is the number of nodes in the tree. This is because the printLevel function uses an array of size N to store the nodes at each level of the tree as it performs a level order traversal.