# Anti Clockwise spiral traversal of a binary tree

• Difficulty Level : Hard
• Last Updated : 22 Aug, 2022

Given a binary tree, the task is to print the nodes of the tree in an anti-clockwise spiral manner.

Examples:

```Input:
1
/  \
2    3
/ \  / \
4   5 6  7
Output: 1 4 5 6 7 3 2

Input:
1
/  \
2    3
/    / \
4    5   6
/ \  /   / \
7   8 9  10  11
Output: 1 7 8 9 10 11 3 2 4 5 6```

Approach: The idea is to use two variables i initialized to 1 and j initialized to the height of tree and run a while loop which wont break until i becomes greater than j. We will use another variable flag and initialize it to 0. Now in the while loop we will check a condition that if flag is equal to 0 we will traverse the tree from right to left and mark flag as 1 so that next time we traverse the tree from left to right and then increment the value of i so that next time we visit the level just below the current level. Also when we will traverse the level from bottom we will mark flag as 0 so that next time we traverse the tree from left to right and then decrement the value of j so that next time we visit the level just above the current level. Repeat the whole process until the binary tree is completely traversed.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Binary tree node``struct` `Node {``    ``struct` `Node* left;``    ``struct` `Node* right;``    ``int` `data;` `    ``Node(``int` `data)``    ``{``        ``this``->data = data;``        ``this``->left = NULL;``        ``this``->right = NULL;``    ``}``};` `// Recursive Function to find height``// of binary tree``int` `height(``struct` `Node* root)``{``    ``// Base condition``    ``if` `(root == NULL)``        ``return` `0;` `    ``// Compute the height of each subtree``    ``int` `lheight = height(root->left);``    ``int` `rheight = height(root->right);` `    ``// Return the maximum of two``    ``return` `max(1 + lheight, 1 + rheight);``}` `// Function to Print Nodes from left to right``void` `leftToRight(``struct` `Node* root, ``int` `level)``{``    ``if` `(root == NULL)``        ``return``;` `    ``if` `(level == 1)``        ``cout << root->data << ``" "``;` `    ``else` `if` `(level > 1) {``        ``leftToRight(root->left, level - 1);``        ``leftToRight(root->right, level - 1);``    ``}``}` `// Function to Print Nodes from right to left``void` `rightToLeft(``struct` `Node* root, ``int` `level)``{``    ``if` `(root == NULL)``        ``return``;` `    ``if` `(level == 1)``        ``cout << root->data << ``" "``;` `    ``else` `if` `(level > 1) {``        ``rightToLeft(root->right, level - 1);``        ``rightToLeft(root->left, level - 1);``    ``}``}` `// Function to print anti clockwise spiral``// traversal of a binary tree``void` `antiClockWiseSpiral(``struct` `Node* root)``{``    ``int` `i = 1;``    ``int` `j = height(root);` `    ``// Flag to mark a change in the direction``    ``// of printing nodes``    ``int` `flag = 0;``    ``while` `(i <= j) {` `        ``// If flag is zero print nodes``        ``// from right to left``        ``if` `(flag == 0) {``            ``rightToLeft(root, i);` `            ``// Set the value of flag as zero``            ``// so that nodes are next time``            ``// printed from left to right``            ``flag = 1;` `            ``// Increment i``            ``i++;``        ``}` `        ``// If flag is one print nodes``        ``// from left to right``        ``else` `{``            ``leftToRight(root, j);` `            ``// Set the value of flag as zero``            ``// so that nodes are next time``            ``// printed from right to left``            ``flag = 0;` `            ``// Decrement j``            ``j--;``        ``}``    ``}``}` `// Driver code``int` `main()``{``    ``struct` `Node* root = ``new` `Node(1);``    ``root->left = ``new` `Node(2);``    ``root->right = ``new` `Node(3);``    ``root->left->left = ``new` `Node(4);``    ``root->right->left = ``new` `Node(5);``    ``root->right->right = ``new` `Node(7);``    ``root->left->left->left = ``new` `Node(10);``    ``root->left->left->right = ``new` `Node(11);``    ``root->right->right->left = ``new` `Node(8);` `    ``antiClockWiseSpiral(root);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GfG``{` `// Binary tree node``static` `class` `Node``{``    ``Node left;``    ``Node right;``    ``int` `data;` `    ``Node(``int` `data)``    ``{``        ``this``.data = data;``        ``this``.left = ``null``;``        ``this``.right = ``null``;``    ``}``}` `// Recursive Function to find height``// of binary tree``static` `int` `height(Node root)``{``    ``// Base condition``    ``if` `(root == ``null``)``        ``return` `0``;` `    ``// Compute the height of each subtree``    ``int` `lheight = height(root.left);``    ``int` `rheight = height(root.right);` `    ``// Return the maximum of two``    ``return` `Math.max(``1` `+ lheight, ``1` `+ rheight);``}` `// Function to Print Nodes from left to right``static` `void` `leftToRight(Node root, ``int` `level)``{``    ``if` `(root == ``null``)``        ``return``;` `    ``if` `(level == ``1``)``        ``System.out.print(root.data + ``" "``);` `    ``else` `if` `(level > ``1``)``    ``{``        ``leftToRight(root.left, level - ``1``);``        ``leftToRight(root.right, level - ``1``);``    ``}``}` `// Function to Print Nodes from right to left``static` `void` `rightToLeft(Node root, ``int` `level)``{``    ``if` `(root == ``null``)``        ``return``;` `    ``if` `(level == ``1``)``        ``System.out.print(root.data + ``" "``);` `    ``else` `if` `(level > ``1``)``    ``{``        ``rightToLeft(root.right, level - ``1``);``        ``rightToLeft(root.left, level - ``1``);``    ``}``}` `// Function to print anti clockwise spiral``// traversal of a binary tree``static` `void` `antiClockWiseSpiral(Node root)``{``    ``int` `i = ``1``;``    ``int` `j = height(root);` `    ``// Flag to mark a change in the direction``    ``// of printing nodes``    ``int` `flag = ``0``;``    ``while` `(i <= j)``    ``{` `        ``// If flag is zero print nodes``        ``// from right to left``        ``if` `(flag == ``0``)``        ``{``            ``rightToLeft(root, i);` `            ``// Set the value of flag as zero``            ``// so that nodes are next time``            ``// printed from left to right``            ``flag = ``1``;` `            ``// Increment i``            ``i++;``        ``}` `        ``// If flag is one print nodes``        ``// from left to right``        ``else` `{``            ``leftToRight(root, j);` `            ``// Set the value of flag as zero``            ``// so that nodes are next time``            ``// printed from right to left``            ``flag = ``0``;` `            ``// Decrement j``            ``j--;``        ``}``    ``}``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``Node root = ``new` `Node(``1``);``    ``root.left = ``new` `Node(``2``);``    ``root.right = ``new` `Node(``3``);``    ``root.left.left = ``new` `Node(``4``);``    ``root.right.left = ``new` `Node(``5``);``    ``root.right.right = ``new` `Node(``7``);``    ``root.left.left.left = ``new` `Node(``10``);``    ``root.left.left.right = ``new` `Node(``11``);``    ``root.right.right.left = ``new` `Node(``8``);` `    ``antiClockWiseSpiral(root);``}``}` `// This code is contributed by Prerna Saini.`

## Python3

 `# Python3 implementation of the approach` `# Binary tree node``class` `newNode:` `    ``# Constructor to create a newNode``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.left ``=` `None``        ``self``.right ``=` `None``        ``self``.visited ``=` `False``        ` `# Recursive Function to find height``# of binary tree``def` `height(root):` `    ``# Base condition``    ``if` `(root ``=``=` `None``):``        ``return` `0` `    ``# Compute the height of each subtree``    ``lheight ``=` `height(root.left)``    ``rheight ``=` `height(root.right)` `    ``# Return the maximum of two``    ``return` `max``(``1` `+` `lheight, ``1` `+` `rheight)` `# Function to Print Nodes from left to right``def` `leftToRight(root, level):` `    ``if` `(root ``=``=` `None``):``        ``return` `    ``if` `(level ``=``=` `1``):``        ``print``(root.data, end ``=` `" "``)` `    ``elif` `(level > ``1``):``        ``leftToRight(root.left, level ``-` `1``)``        ``leftToRight(root.right, level ``-` `1``)``    ` `# Function to Print Nodes from right to left``def` `rightToLeft(root, level):` `    ``if` `(root ``=``=` `None``) :``        ``return` `    ``if` `(level ``=``=` `1``):``        ``print``(root.data, end ``=` `" "``)` `    ``elif` `(level > ``1``):``        ``rightToLeft(root.right, level ``-` `1``)``        ``rightToLeft(root.left, level ``-` `1``)``    ` `# Function to print anti clockwise spiral``# traversal of a binary tree``def` `antiClockWiseSpiral(root):` `    ``i ``=` `1``    ``j ``=` `height(root)` `    ``# Flag to mark a change in the``    ``# direction of printing nodes``    ``flag ``=` `0``    ``while` `(i <``=` `j):` `        ``# If flag is zero print nodes``        ``# from right to left``        ``if` `(flag ``=``=` `0``):``            ``rightToLeft(root, i)` `            ``# Set the value of flag as zero``            ``# so that nodes are next time``            ``# printed from left to right``            ``flag ``=` `1` `            ``# Increment i``            ``i ``+``=` `1``            ` `        ``# If flag is one print nodes``        ``# from left to right``        ``else``:``            ``leftToRight(root, j)` `            ``# Set the value of flag as zero``            ``# so that nodes are next time``            ``# printed from right to left``            ``flag ``=` `0` `            ``# Decrement j``            ``j``-``=``1``        ` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``root ``=` `newNode(``1``)``    ``root.left ``=` `newNode(``2``)``    ``root.right ``=` `newNode(``3``)``    ``root.left.left ``=` `newNode(``4``)``    ``root.right.left ``=` `newNode(``5``)``    ``root.right.right ``=` `newNode(``7``)``    ``root.left.left.left ``=` `newNode(``10``)``    ``root.left.left.right ``=` `newNode(``11``)``    ``root.right.right.left ``=` `newNode(``8``)` `    ``antiClockWiseSpiral(root)` `# This code is contributed by``# SHUBHAMSINGH10`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `// Binary tree node``public` `class` `Node``{``    ``public` `Node left;``    ``public` `Node right;``    ``public` `int` `data;` `    ``public` `Node(``int` `data)``    ``{``        ``this``.data = data;``        ``this``.left = ``null``;``        ``this``.right = ``null``;``    ``}``};` `// Recursive Function to find height``// of binary tree``static` `int` `height( Node root)``{``    ``// Base condition``    ``if` `(root == ``null``)``        ``return` `0;` `    ``// Compute the height of each subtree``    ``int` `lheight = height(root.left);``    ``int` `rheight = height(root.right);` `    ``// Return the maximum of two``    ``return` `Math.Max(1 + lheight, 1 + rheight);``}` `// Function to Print Nodes from left to right``static` `void` `leftToRight( Node root, ``int` `level)``{``    ``if` `(root == ``null``)``        ``return``;` `    ``if` `(level == 1)``        ``Console.Write( root.data + ``" "``);` `    ``else` `if` `(level > 1)``    ``{``        ``leftToRight(root.left, level - 1);``        ``leftToRight(root.right, level - 1);``    ``}``}` `// Function to Print Nodes from right to left``static` `void` `rightToLeft( Node root, ``int` `level)``{``    ``if` `(root == ``null``)``        ``return``;` `    ``if` `(level == 1)``        ``Console.Write( root.data + ``" "``);` `    ``else` `if` `(level > 1)``    ``{``        ``rightToLeft(root.right, level - 1);``        ``rightToLeft(root.left, level - 1);``    ``}``}` `// Function to print anti clockwise spiral``// traversal of a binary tree``static` `void` `antiClockWiseSpiral( Node root)``{``    ``int` `i = 1;``    ``int` `j = height(root);` `    ``// Flag to mark a change in the direction``    ``// of printing nodes``    ``int` `flag = 0;``    ``while` `(i <= j)``    ``{` `        ``// If flag is zero print nodes``        ``// from right to left``        ``if` `(flag == 0)``        ``{``            ``rightToLeft(root, i);` `            ``// Set the value of flag as zero``            ``// so that nodes are next time``            ``// printed from left to right``            ``flag = 1;` `            ``// Increment i``            ``i++;``        ``}` `        ``// If flag is one print nodes``        ``// from left to right``        ``else``        ``{``            ``leftToRight(root, j);` `            ``// Set the value of flag as zero``            ``// so that nodes are next time``            ``// printed from right to left``            ``flag = 0;` `            ``// Decrement j``            ``j--;``        ``}``    ``}``}` `// Driver code``public` `static` `void` `Main(String []args)``{``    ``Node root = ``new` `Node(1);``    ``root.left = ``new` `Node(2);``    ``root.right = ``new` `Node(3);``    ``root.left.left = ``new` `Node(4);``    ``root.right.left = ``new` `Node(5);``    ``root.right.right = ``new` `Node(7);``    ``root.left.left.left = ``new` `Node(10);``    ``root.left.left.right = ``new` `Node(11);``    ``root.right.right.left = ``new` `Node(8);` `    ``antiClockWiseSpiral(root);` `}``}` `//This code is contributed by Arnab Kundu`

## Javascript

 ``

Output:

`1 10 11 8 3 2 4 5 7 `

Another Approach:
The above approach have O(n^2) worst case complexity due to calling the print level everytime. An improvement over it can be storing the level wise nodes and use it to print.

## C++

 `// C++ implementation of the above approach` `#include ``using` `namespace` `std;` `struct` `Node {``    ``struct` `Node* left;``    ``struct` `Node* right;``    ``int` `data;``    ``Node(``int` `data)``    ``{``        ``this``->data = data;``        ``this``->left = NULL;``        ``this``->right = NULL;``    ``}``};` `void` `antiClockWiseSpiral(``struct` `Node* root)``{``    ``// Initialize the queue``    ``queue q;` `    ``// Add the root node``    ``q.push(root);` `    ``//  Initialize the vector``    ``vector topone;` `    ``// Until queue is not empty``    ``while` `(!q.empty()) {``        ``int` `len = q.size();` `        ``// len is greater than zero``        ``while` `(len > 0) {``            ``Node* nd = q.front();``            ``q.pop();``            ``if` `(nd != NULL) {``                ``topone.push_back(nd);``                ``if` `(nd->right != NULL)``                    ``q.push(nd->right);``                ``if` `(nd->left != NULL)``                    ``q.push(nd->left);``            ``}``            ``len--;``        ``}``        ``topone.push_back(NULL);``    ``}``    ``bool` `top = ``true``;``    ``int` `l = 0, r = (``int``)topone.size() - 2;` `    ``while` `(l < r) {``        ``if` `(top) {``            ``while` `(l < (``int``)topone.size()) {``                ``Node* nd = topone[l++];``                ``if` `(nd == NULL) {``                    ``break``;``                ``}``                ``cout << nd->data << ``" "``;``            ``}``        ``}``        ``else` `{``            ``while` `(r >= l) {``                ``Node* nd = topone[r--];``                ``if` `(nd == NULL)``                    ``break``;``                ``cout << nd->data << ``" "``;``            ``}``        ``}``        ``top = !top;``    ``}``}` `// Build Tree``int` `main()``{``    ``/*``               ``1``            ``2     3``          ``4     5   7``         ``10 11     8``   ``*/` `    ``struct` `Node* root = ``new` `Node(1);``    ``root->left = ``new` `Node(2);``    ``root->right = ``new` `Node(3);``    ``root->left->left = ``new` `Node(4);``    ``root->right->left = ``new` `Node(5);``    ``root->right->right = ``new` `Node(7);``    ``root->left->left->left = ``new` `Node(10);``    ``root->left->left->right = ``new` `Node(11);``    ``root->right->right->left = ``new` `Node(8);` `    ``antiClockWiseSpiral(root);` `    ``return` `0;``}`

## Java

 `// Java implementation of the above approach` `import` `java.io.*;``import` `java.util.*;` `class` `GFG {` `    ``// Structure of each node``    ``class` `Node {``        ``int` `val;``        ``Node left, right;``        ``Node(``int` `val)``        ``{``            ``this``.val = val;``            ``this``.left = ``this``.right = ``null``;``        ``}``    ``}` `    ``private` `void` `work(Node root)``    ``{``        ``// Initialize queue``        ``Queue q = ``new` `LinkedList<>();` `        ``// Add the root node``        ``q.add(root);` `        ``// Initialize the vector``        ``Vector topone = ``new` `Vector<>();` `        ``// Until queue is not empty``        ``while` `(!q.isEmpty()) {``            ``int` `len = q.size();` `            ``// len is greater than zero``            ``while` `(len > ``0``) {``                ``Node nd = q.poll();``                ``if` `(nd != ``null``) {``                    ``topone.add(nd);``                    ``if` `(nd.right != ``null``)``                        ``q.add(nd.right);``                    ``if` `(nd.left != ``null``)``                        ``q.add(nd.left);``                ``}``                ``len--;``            ``}``            ``topone.add(``null``);``        ``}``        ``boolean` `top = ``true``;``        ``int` `l = ``0``, r = topone.size() - ``2``;` `        ``while` `(l < r) {``            ``if` `(top) {``                ``while` `(l < topone.size()) {``                    ``Node nd = topone.get(l++);``                    ``if` `(nd == ``null``) {``                        ``break``;``                    ``}``                    ``System.out.print(nd.val + ``" "``);``                ``}``            ``}``            ``else` `{``                ``while` `(r >= l) {``                    ``Node nd = topone.get(r--);``                    ``if` `(nd == ``null``)``                        ``break``;``                    ``System.out.print(nd.val + ``" "``);``                ``}``            ``}``            ``top = !top;``        ``}``    ``}` `    ``// Build Tree``    ``public` `void` `solve()``    ``{``        ``/*``                            ``1``                         ``2     3``                       ``4     5   7``                      ``10 11     8``                    ``*/` `        ``Node root = ``new` `Node(``1``);``        ``root.left = ``new` `Node(``2``);``        ``root.right = ``new` `Node(``3``);``        ``root.left.left = ``new` `Node(``4``);``        ``root.right.left = ``new` `Node(``5``);``        ``root.right.right = ``new` `Node(``7``);``        ``root.left.left.left = ``new` `Node(``10``);``        ``root.left.left.right = ``new` `Node(``11``);``        ``root.right.right.left = ``new` `Node(``8``);` `        ``// Function call``        ``work(root);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``GFG t = ``new` `GFG();``        ``t.solve();``    ``}``}`

## Python3

 `# Python 3 implementation of the above approach` `from` `collections ``import`  `deque as dq` `class` `Node:``    ``def` `__init__(``self``, data):``    ` `        ``self``.data ``=` `data``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `def` `antiClockWiseSpiral(root):` `    ``# Initialize the queue``    ``q``=``dq([root])` `    ``# Initialize the list``    ``topone``=``[]` `    ``# Until queue is not empty``    ``while` `(q):``        ``l ``=` `len``(q)` `        ``# l is greater than zero``        ``while` `(l > ``0``):``            ``nd ``=` `q.popleft()``            ``if` `(nd !``=` `None``):``                ``topone.append(nd)``                ``if` `(nd.right !``=` `None``):``                    ``q.append(nd.right)``                ``if` `(nd.left !``=` `None``):``                    ``q.append(nd.left)``            ``l``-``=``1``        ` `        ``topone.append(``None``)` `    ``top ``=` `True``    ``l ``=` `0``; r ``=` `len``(topone) ``-` `2` `    ``while` `(l < r):``        ``if` `(top):``            ``while` `(l < ``len``(topone)):``                ``nd ``=` `topone[l]``                ``l``+``=``1``                ``if` `(nd ``=``=` `None``):``                    ``break``                ``print``(nd.data,end``=``" "``)``        ``else``:``            ``while` `(r >``=` `l):``                ``nd ``=` `topone[r]``                ``r``-``=``1``                ``if` `(nd ``=``=` `None``):``                    ``break``                ``print``(nd.data,end``=``" "``)``            ` `        ` `        ``top ``=` `not` `top``    ``print``()` `# Build Tree``if` `__name__ ``=``=` `'__main__'``:`  `    ``#        1``    ``#     2     3``    ``#   4     5  7``    ``# 10 11     8`  `    ``root ``=` `Node(``1``)``    ``root.left ``=` `Node(``2``)``    ``root.right ``=`  `Node(``3``)``    ``root.left.left ``=` `Node(``4``)``    ``root.right.left ``=` `Node(``5``)``    ``root.right.right ``=` `Node(``7``)``    ``root.left.left.left ``=` `Node(``10``)``    ``root.left.left.right ``=` `Node(``11``)``    ``root.right.right.left ``=` `Node(``8``)` `    ``antiClockWiseSpiral(root)`

## C#

 `// C# implementation of the above approach``using` `System;``using` `System.Collections;``using` `System.Collections.Generic;` `public` `class` `GFG {` `  ``// Structure of each node``  ``class` `Node {``    ``public` `int` `val;``    ``public` `Node left, right;``    ``public` `Node(``int` `val)``    ``{``      ``this``.val = val;``      ``this``.left = ``this``.right = ``null``;``    ``}``  ``}` `  ``private` `void` `work(Node root)``  ``{``    ``// Initialize queue``    ``Queue q = ``new` `Queue();` `    ``// Add the root node``    ``q.Enqueue(root);` `    ``// Initialize the vector``    ``List topone = ``new` `List();` `    ``// Until queue is not empty``    ``while` `(q.Count != 0) {``      ``int` `len = q.Count;` `      ``// len is greater than zero``      ``while` `(len > 0) {``        ``Node nd = (Node)q.Dequeue();``        ``if` `(nd != ``null``) {``          ``topone.Add(nd);``          ``if` `(nd.right != ``null``)``            ``q.Enqueue(nd.right);``          ``if` `(nd.left != ``null``)``            ``q.Enqueue(nd.left);``        ``}``        ``len--;``      ``}``      ``topone.Add(``null``);``    ``}``    ``bool` `top = ``true``;``    ``int` `l = 0, r = topone.Count - 2;` `    ``while` `(l < r) {``      ``if` `(top) {``        ``while` `(l < topone.Count) {``          ``Node nd = topone[l++];``          ``if` `(nd == ``null``) {``            ``break``;``          ``}``          ``Console.Write(nd.val + ``" "``);``        ``}``      ``}``      ``else` `{``        ``while` `(r >= l) {``          ``Node nd = topone[r--];``          ``if` `(nd == ``null``)``            ``break``;``          ``Console.Write(nd.val + ``" "``);``        ``}``      ``}``      ``top = !top;``    ``}``  ``}` `  ``// Build Tree``  ``public` `void` `solve()``  ``{``    ``/*``                            ``1``                         ``2     3``                       ``4     5   7``                      ``10 11     8``                    ``*/` `    ``Node root = ``new` `Node(1);``    ``root.left = ``new` `Node(2);``    ``root.right = ``new` `Node(3);``    ``root.left.left = ``new` `Node(4);``    ``root.right.left = ``new` `Node(5);``    ``root.right.right = ``new` `Node(7);``    ``root.left.left.left = ``new` `Node(10);``    ``root.left.left.right = ``new` `Node(11);``    ``root.right.right.left = ``new` `Node(8);` `    ``// Function call``    ``work(root);``  ``}` `  ``static` `public` `void` `Main()``  ``{` `    ``// Code``    ``GFG t = ``new` `GFG();``    ``t.solve();``  ``}``}` `// This code is contributed by lokeshmvs21.`

## Javascript

 ``

Output:

`1 10 11 8 3 2 4 5 7 `

Time Complexity: O(N)
Auxiliary Space: O(N)

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