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# 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 ``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

 ``

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.

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