Clockwise Spiral Traversal of Binary Tree

Given a Binary Tree. The task is to print the circular clockwise spiral order traversal of the given binary tree. 

For the above binary tree, the circular clockwise spiral order traversal will be 1, 4, 5, 6, 7, 2, 3.

Examples:

Input : 

                       10

                     /     \

                   12       13

                          /     \

                       14       15

                      /   \     /  \

                     21   22   23   24

Output : 10, 24, 23, 22, 21, 12, 13, 15, 14

Approach:  

1. First, calculate the width of the given tree.
2. Create an auxiliary 2D array of order (width*width)
3. Do level order traversal of the binary tree and store levels in the newly created 2D matrix one by one in respective rows. That is, store nodes at level 0 at row indexed 0, nodes at level 1 at row indexed 1, and so on.
4. Finally, traverse the 2d array in the below fashion: 
   • Start from the first row from left to right and print elements.
   • Then traverse the last row from right to left and print elements.
   • Again traverse the second row from left to right and print.
   • The second last row from right to left and so on repeats the steps until the complete 2-D array is traversed.

Below is the implementation of the above approach: 

C++

// C++ program for Clockwise Spiral Traversal
// of Binary Tree

#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);
}
//function to calculate the height of the tree
int findHeight(struct Node* node)
{
    //Base condition
    if(node == NULL) return 0;
    int leftHeight = findHeight(node->left);
    int rightHeight = findHeight(node->right);
    //return maximum of left or right subtree height addition with one
    return 1+(leftHeight > rightHeight ? leftHeight : rightHeight );
}
// Function to find the width of tree
void findWidth(struct Node* node, int& maxValue,
            int& minValue, int hd)
{
    if (node == NULL)
        return;

    if (hd > maxValue) {
        maxValue = hd;
    }

    if (hd < minValue) {
        minValue = hd;
    }

    findWidth(node->left, maxValue, minValue, hd - 1);
    findWidth(node->right, maxValue, minValue, hd + 1);
}

// Function to traverse the tree and
// store level order traversal in a matrix
void BFS(int** mtrx, struct Node* node)
{
    // Create queue for storing
    // the addresses of nodes
    queue<struct Node*> qu;

    qu.push(node);

    int i = -1, j = -1;

    struct Node* poped_node = NULL;

    while (!qu.empty()) {

        i++;

        int qsize = qu.size();

        while (qsize--) {
            j++;

            poped_node = qu.front();

            // Store data of node into the matrix
            mtrx[i][j] = poped_node->key;
            qu.pop();

            if (poped_node->left != NULL) {
                qu.push(poped_node->left);
            }

            if (poped_node->right != NULL) {
                qu.push(poped_node->right);
            }
        }

        j = -1;
    }
}

// Function for Clockwise Spiral Traversal
// of Binary Tree
void traverse_matrix(int** mtrx, int height, int width)
{
    int j = 0, k1 = 0, k2 = 0, k3 = height - 1;
    int k4 = width - 1;

    for (int round = 0; round < height / 2; round++) {
        for (j = k2; j < width; j++) {

            // only print those values which
            // are not MAX_INTEGER
            if (mtrx[k1][j] != INT_MAX) {
                cout << mtrx[k1][j] << ", ";
            }
        }

        k2 = 0;
        k1++;

        for (j = k4; j >= 0; j--) {

            // only print those values which are
            // not MAX_INTEGER
            if (mtrx[k3][j] != INT_MAX) {
                cout << mtrx[k3][j] << ", ";
            }
        }

        k4 = width - 1;
        k3--;
    }

    // condition (one row may be left traversing)
    // if number of rows in matrix are odd
    if (height % 2 != 0) {
        for (j = k2; j < width; j++) {

            // only print those values which are
            // not MAX_INTEGER
            if (mtrx[k1][j] != INT_MAX) {
                cout << mtrx[k1][j] << ", ";
            }
        }
    }
}

// A utility function to print clockwise
// spiral traversal of tree
void printPattern(struct Node* node)
{
    // max, min has taken for
    // calculating width of tree
    int max_value = INT_MIN;
    int min_value = INT_MAX;
    int hd = 0;

    // calculate the width of a tree
    findWidth(node, max_value, min_value, hd);
    int width = max_value + abs(min_value);

    //calculate the height of the tree
    int height = findHeight(node);

    // use double pointer to create 2D array
    int** mtrx = new int*[height];

    // initialize width for each row of matrix
    for (int i = 0; i < height; i++) {
        mtrx[i] = new int[width];
    }

    // initialize complete matrix with
    // MAX INTEGER(purpose garbage)
    for (int i = 0; i < height; i++) {
        for (int j = 0; j < width; j++) {
            mtrx[i][j] = INT_MAX;
        }
    }

    // Store the BFS traversal of the tree
    // into the 2-D matrix
    BFS(mtrx, node);

    // Print the circular clockwise spiral
    // traversal of the tree
    traverse_matrix(mtrx, height, width);

    // release extra memory
    // allocated for matrix
    free(mtrx);
}

// Driver Code
int main()
{
    /*     10
        /     \
    12     13
        /     \
        14     15
        / \     / \
        21 22 23 24

    Let us create Binary Tree as shown
    in above example */

    Node* root = newNode(10);
    root->left = newNode(12);
    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(23);
    root->right->right->right = newNode(24);

    cout << "Circular Clockwise Spiral Traversal : \n";

    printPattern(root);

    return 0;
}
// This code is contributed by MOHAMMAD MUDASSIR

Java

// Java program for above approach
import java.util.*;

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

  Node(int key)
  {
    this.key = key;
    left = right = null;
  }
}

class BinaryTree {
  // root of the binary tree
  Node root;

  // function to calculate the height of the tree
  int findHeight(Node node)
  {
    // Base condition
    if (node == null)
      return 0;
    int leftHeight = findHeight(node.left);
    int rightHeight = findHeight(node.right);
    // return maximum of left or right subtree height
    // addition with one
    return 1
      + (leftHeight > rightHeight ? leftHeight
         : rightHeight);
  }

  // Function to find the width of tree
  void findWidth(Node node, int[] maxValue,
                 int[] minValue, int hd)
  {
    if (node == null)
      return;

    if (hd > maxValue[0]) {
      maxValue[0] = hd;
    }

    if (hd < minValue[0]) {
      minValue[0] = hd;
    }

    findWidth(node.left, maxValue, minValue, hd - 1);
    findWidth(node.right, maxValue, minValue, hd + 1);
  }

  // Function to traverse the tree and
  // store level order traversal in a matrix
  void BFS(int[][] mtrx, Node node)
  {
    // Create queue for storing
    // the addresses of nodes
    Queue<Node> qu = new LinkedList<Node>();

    qu.add(node);

    int i = -1, j = -1;

    Node poped_node;

    while (!qu.isEmpty()) {

      i++;

      int qsize = qu.size();

      while (qsize-- > 0) {
        j++;

        poped_node = qu.remove();

        // Store data of node into the matrix
        mtrx[i][j] = poped_node.key;

        if (poped_node.left != null) {
          qu.add(poped_node.left);
        }

        if (poped_node.right != null) {
          qu.add(poped_node.right);
        }
      }

      j = -1;
    }
  }

  // Function for Clockwise Spiral Traversal
  // of Binary Tree
  void traverse_matrix(int[][] mtrx, int height,
                       int width)
  {
    int j = 0, k1 = 0, k2 = 0, k3 = height - 1;
    int k4 = width - 1;

    for (int round = 0; round < height / 2; round++) {
      for (j = k2; j < width; j++) {

        // only print those values which
        // are not MAX_INTEGER
        if (mtrx[k1][j] != Integer.MAX_VALUE) {
          System.out.print(mtrx[k1][j] + ", ");
        }
      }

      k2 = 0;
      k1++;

      for (j = k4; j >= 0; j--) {

        // only print those values which are
        // not MAX_INTEGER
        if (mtrx[k3][j] != Integer.MAX_VALUE) {
          System.out.print(mtrx[k3][j] + ", ");
        }
      }

      k4 = width - 1;
      k3--;
    }

    // condition (one row may be left traversing)
    // if number of rows in matrix are odd
    if (height % 2 != 0) {
      for (j = k2; j < width; j++) {

        // only print those values which are
        // not MAX_INTEGER
        if (mtrx[k1][j] != Integer.MAX_VALUE) {
          System.out.print(mtrx[k1][j] + ", ");
        }
      }
    }
  }

  // A utility function to print clockwise
  // spiral traversal of tree
  void printPattern(Node node)
  {
    // max, min has taken for
    // calculating width of tree
    int[] max_value = new int[1];
    max_value[0] = Integer.MIN_VALUE;
    int[] min_value = new int[1];
    min_value[0] = Integer.MAX_VALUE;
    int hd = 0;

    // calculate the width of a tree
    findWidth(node, max_value, min_value, hd);
    int width = max_value[0] + Math.abs(min_value[0]);

    // calculate the height of the tree
    int height = findHeight(node);

    // use double pointer to create 2D array
    int[][] mtrx = new int[height][width];

    // initialize complete matrix with
    // MAX INTEGER(purpose garbage)
    for (int i = 0; i < height; i++) {
      for (int j = 0; j < width; j++) {
        mtrx[i][j] = Integer.MAX_VALUE;
      }
    }

    // Store the BFS traversal of the tree
    // into the 2-D matrix
    BFS(mtrx, node);

    // Print the circular clockwise spiral
    // traversal of the tree
    traverse_matrix(mtrx, height, width);
  }

  // Driver Code
  public static void main(String[] args)
  {
    /*     10
                /     \
        12     13
                /     \
                14     15
                / \     / \
                21 22 23 24

        Let us create Binary Tree as shown
        in above example */

    BinaryTree tree = new BinaryTree();
    tree.root = new Node(10);
    tree.root.left = new Node(12);
    tree.root.right = new Node(13);

    tree.root.right.left = new Node(14);
    tree.root.right.right = new Node(15);

    tree.root.right.left.left = new Node(21);
    tree.root.right.left.right = new Node(22);
    tree.root.right.right.left = new Node(23);
    tree.root.right.right.right = new Node(24);

    System.out.println(
      "Circular Clockwise Spiral Traversal : ");

    tree.printPattern(tree.root);
  }
}

// This code is contributed by adityamaharshi21

Python3

# Python3 program for Clockwise Spiral
# Traversal of Binary Tree
INT_MAX = 2**31
INT_MIN = -2**31

# Binary tree node
class newNode:

    # Constructor to create a newNode
    def __init__(self, data):
        self.key = data
        self.left = None
        self.right = None

# Function to find the width of tree
def findWidth(node, maxValue, minValue, hd):

    if (node == None):
        return

    if (hd > maxValue[0]):
        maxValue[0] = hd

    if (hd < minValue[0]):
        minValue[0] = hd

    findWidth(node.left, maxValue,
                         minValue, hd - 1)
    findWidth(node.right, maxValue,
                          minValue, hd + 1)

# Function to traverse the tree and
# store level order traversal in a matrix
def BFS(mtrx,node):

    # Create queue for storing
    # the addresses of nodes
    qu = []

    qu.append(node)

    i = -1
    j = -1

    poped_node = None

    while (len(qu)):
        i += 1

        qsize = len(qu)

        while (qsize > 0):
            qsize -= 1
            j += 1

            poped_node = qu[0]

            # Store data of node into the matrix
            mtrx[i][j] = poped_node.key
            qu.pop(0)

            if (poped_node.left != None):
                qu.append(poped_node.left)

            if (poped_node.right != None):
                qu.append(poped_node.right)

        j = -1

# Function for Clockwise Spiral
# Traversal of Binary Tree
def traverse_matrix(mtrx, width):

    j = 0
    k1 = 0
    k2 = 0
    k3 = width - 1
    k4 = width - 1

    for round in range(width // 2):
        for j in range(k2, width):

            # only print those values which
            # are not MAX_INTEGER
            if (mtrx[k1][j] != INT_MAX):
                print(mtrx[k1][j], ", ", end = "")
        k2 = 0
        k1 += 1

        for j in range(k4, -1, -1):

            # only print those values which are
            # not MAX_INTEGER
            if (mtrx[k3][j] != INT_MAX):
                print(mtrx[k3][j], ", ", end = "")

        k4 = width - 1
        k3 -= 1

    # condition (one row may be left traversing)
    # if number of rows in matrix are odd
    if (width % 2 != 0):
        for j in range(k2, width):

            # only print those values which
            # are not MAX_INTEGER
            if (mtrx[k1][j] != INT_MAX):
                print(mtrx[k1][j], ", ", end = "")

# A utility function to prclockwise
# spiral traversal of tree
def printPattern(node):

    # max, min has taken for
    # calculating width of tree
    max_value = [INT_MIN]
    min_value = [INT_MAX ]
    hd = 0

    # calculate the width of a tree
    findWidth(node, max_value, min_value, hd)
    width = max_value[0] + abs(min_value[0])

    # use double pointer to
    # create 2D array
    mtrx = [0]*width

    # initialize width for each
    # row of matrix
    for i in range(width):
        mtrx[i] = [0] * width

    # initialize complete matrix with
    # MAX INTEGER(purpose garbage)
    for i in range(width):
        for j in range(width):
            mtrx[i][j] = INT_MAX

    # Store the BFS traversal of the
    # tree into the 2-D matrix
    BFS(mtrx, node)

    # Print the circular clockwise spiral
    # traversal of the tree
    traverse_matrix(mtrx, width)

# Driver Code
if __name__ == '__main__':

    """     10
        /     \
    12     13
        /     \
        14     15
        / \     / \
        21 22 23 24

    Let us create Binary Tree as shown
    in above example """

    root = newNode(10)
    root.left = newNode(12)
    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(23)
    root.right.right.right = newNode(24)

    print("Circular Clockwise Spiral Traversal :")

    printPattern(root)

# This code is contributed by
# SHUBHAMSINGH10

C#

using System;
using System.Collections.Generic;

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

    public Node(int key)
    {
        this.key = key;
        left = right = null;
    }
}

class BinaryTree {
    // root of the binary tree
    public Node root;

    // function to calculate the height of the tree
    public int findHeight(Node node)
    {
        // Base condition
        if (node == null)
            return 0;
        int leftHeight = findHeight(node.left);
        int rightHeight = findHeight(node.right);
        // return maximum of left or right subtree height
        // addition with one
        return 1
            + (leftHeight > rightHeight ? leftHeight
                                        : rightHeight);
    }

    // Function to find the width of tree
    public void findWidth(Node node, int[] maxValue,
                          int[] minValue, int hd)
    {
        if (node == null)
            return;

        if (hd > maxValue[0]) {
            maxValue[0] = hd;
        }

        if (hd < minValue[0]) {
            minValue[0] = hd;
        }

        findWidth(node.left, maxValue, minValue, hd - 1);
        findWidth(node.right, maxValue, minValue, hd + 1);
    }

    // Function to traverse the tree and
    // store level order traversal in a matrix
    public void BFS(int[, ] mtrx, Node node)
    {
        // Create queue for storing
        // the addresses of nodes
        Queue<Node> qu = new Queue<Node>();

        qu.Enqueue(node);

        int i = -1, j = -1;

        Node poped_node;

        while (qu.Count != 0) {

            i++;

            int qsize = qu.Count;

            while (qsize-- > 0) {
                j++;

                poped_node = qu.Dequeue();

                // Store data of node into the matrix
                mtrx[i, j] = poped_node.key;

                if (poped_node.left != null) {
                    qu.Enqueue(poped_node.left);
                }

                if (poped_node.right != null) {
                    qu.Enqueue(poped_node.right);
                }
            }

            j = -1;
        }
    }

    // Function for Clockwise Spiral Traversal
    // of Binary Tree
    public void traverse_matrix(int[, ] mtrx, int height,
                                int width)
    {
        int j = 0, k1 = 0, k2 = 0, k3 = height - 1;
        int k4 = width - 1;

        for (int round = 0; round < height / 2; round++) {
            for (j = k2; j < width; j++) {

                // only print those values which
                // are not MAX_INTEGER
                if (mtrx[k1, j] != int.MaxValue) {
                    Console.Write(mtrx[k1, j] + ", ");
                }
            }
            k2 = 0;
            k1++;

            for (j = k4; j >= 0; j--) {

                // only print those values which are
                // not MAX_INTEGER
                if (mtrx[k3, j] != int.MaxValue) {
                    Console.Write(mtrx[k3, j] + ", ");
                }
            }

            k4 = width - 1;
            k3--;
        }

        // condition (one row may be left traversing)
        // if number of rows in matrix are odd
        if (height % 2 != 0) {
            for (j = k2; j < width; j++) {

                // only print those values which are
                // not MAX_INTEGER
                if (mtrx[k1, j] != int.MaxValue) {
                    Console.Write(mtrx[k1, j] + ", ");
                }
            }
        }
    }
    // A utility function to print clockwise
    public void print_spiral_traversal(Node node)
    {
        int height = findHeight(node);
        int width = (int)Math.Pow(2, height - 1);

        int[, ] mtrx = new int[height, width];

        for (int i = 0; i < height; i++) {
            for (int j = 0; j < width; j++) {
                mtrx[i, j] = int.MaxValue;
            }
        }

        BFS(mtrx, node);

        traverse_matrix(mtrx, height, width);
    }

    // Driver code
    public static void Main(string[] args)
    {
        BinaryTree tree = new BinaryTree();

        // Let us create a binary tree shown
        // in above diagram
        tree.root = new Node(10);
        tree.root.left = new Node(12);
        tree.root.right = new Node(13);
        tree.root.left.left = new Node(14);
        tree.root.left.right = new Node(15);
        tree.root.right.left = new Node(21);
        tree.root.right.right = new Node(22);
        tree.root.right.right.left = new Node(23);
        tree.root.right.right.right = new Node(24);
      Console.WriteLine(
      "Circular Clockwise Spiral Traversal : ");
        tree.print_spiral_traversal(tree.root);
    }
}

Javascript

  <script>
    //JavaScript code for the above approach
    let INT_MAX = Math.pow(2, 31);
let INT_MIN = -Math.pow(2, 31);

class Node {
    constructor(data) {
        this.key = data;
        this.left = null;
        this.right = null;
    }
}

function findWidth(node, maxValue, minValue, hd) {
    if (!node) return;
    if (hd > maxValue[0]) maxValue[0] = hd;
    if (hd < minValue[0]) minValue[0] = hd;
    findWidth(node.left, maxValue, minValue, hd - 1);
    findWidth(node.right, maxValue, minValue, hd + 1);
}

function BFS(mtrx, node) {
        let qu = [];
        qu.push(node);

        let i = -1;
        let j = -1;
        let popedNode = null;

        while (qu.length) {
            i += 1;
            let qsize = qu.length;
            while (qsize > 0) {
                qsize -= 1;
                j += 1;

                popedNode = qu[0];
                mtrx[i][j] = popedNode.key;
                qu.shift();

                if (popedNode.left) qu.push(popedNode.left);
                if (popedNode.right) qu.push(popedNode.right);
            }
            j = -1;
        }
    }

    function traverseMatrix(mtrx, width) {
        let j = 0;
        let k1 = 0;
        let k2 = 0;
        let k3 = width - 1;
        let k4 = width - 1;

        for (let round = 0; round < width / 2; round++) {
            for (j = k2; j < width; j++) {
                if (mtrx[k1][j] !== INT_MAX) document.write(mtrx[k1][j] + ", ");
            }
            k2 = 0;
            k1 += 1;
            for (j = k4; j >= 0; j--) {
                if (mtrx[k3][j] !== INT_MAX) document.write(mtrx[k3][j] + ", ");
            }
            k4 = width - 1;
            k3 -= 1;
        }
        if (width % 2 !== 0) {
            for (j = k2; j < width; j++) {
                if (mtrx[k1][j] !== INT_MAX) document.write(mtrx[k1][j] + ", ");
            }
        }
    }

    function printPattern(node) {
        let maxValue = [INT_MIN];
        let minValue = [INT_MAX];
        let hd = 0;
        findWidth(node, maxValue, minValue, hd);
        let width = maxValue[0] + Math.abs(minValue[0]);
        let mtrx = new Array(width);
        for (let i = 0; i < width; i++) {
            mtrx[i] = new Array(width).fill(INT_MAX);
        }
        BFS(mtrx, node);
        traverseMatrix(mtrx, width);
    }


    let root = new Node(10);
    root.left = new Node(12);
    root.right = new Node(13);

    root.right.left = new Node(14);
    root.right.right = new Node(15);

    root.right.left.left = new Node(21);
    root.right.left.right = new Node(22);
    root.right.right.left = new Node(23);
    root.right.right.right = new Node(24);

    document.write("Circular Clockwise Spiral Traversal :"+"<br>");

    printPattern(root);

 // This code is contributed by Potta Lokesh

  </script>

Output:

Circular Clockwise Spiral Traversal : 
10, 24, 23, 22, 21, 12, 13, 15, 14,

Time Complexity: O(N), N is the number of nodes.
Auxiliary Space: O(N).