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Boundary Root to Leaf Path traversal of a Binary Tree

  • Difficulty Level : Hard
  • Last Updated : 23 Jun, 2021

Given a Binary Tree, the task is to print all Root to Leaf path of this tree in Boundary Root to Leaf path traversal. 
 

Boundary Root to Leaf Path Traversal: In this traversal, the first Root to Leaf path(Left boundary) is printed first, followed by the last Root to Leaf path (Right boundary) in Reverse order. Then the process is repeated for the second and second-last Root to Leaf path, till the all Root to Leaf path has been printed. 
 

Examples: 
 

Input:  
                 1
                /  \ 
              15    13 
             /     /   \ 
            11    7     29 
                   \    / 
                   2   3  
Output:  1 15 11
         3 29 13 1
         1 13 7 2

Explanation:
First of all print first path from Root to the Leaf 
which is 1 15 11
Then, print the last path from the Leaf to Root
which is 3 29 13 1
Then, print the second path from Root to Leaf 
which is 1 13 7 2

Input:
                  7
                /  \ 
              23     41 
             /  \      \
            31   16     3 
           / \     \    / 
          2   5    17  11    
                   /
                  23 

Output:  7 23 31 2
         11 3 41 7
         7 23 31 5
         23 17 16 23 7

 

Approach: In order to print paths in Boundary Root to Leaf Path Traversal, 
 



  • We first need to make Preorder Traversal of the binary tree to get the all node values of particular path.
  • Here an array is used to store the path of the tree while doing the Preorder traversal then store this path into matrix.
  • Then for each path, print the matrix in first row (Left to Right) then last row (Right to Left) and so on.

Below is the implementation of the above approach: 
 

C++




// C++ implementation to print the
// path in Boundary Root to Leaf
// Path Traversal.
 
#include <bits/stdc++.h>
using namespace std;
 
// Structure of 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 length
// of longest path of the tree
int lengthOfLongestPath(struct Node* node)
{
    // Base Case
    if (node == NULL)
        return 0;
 
    // Recursive call to calculate the length
    // of longest path
    int left = lengthOfLongestPath(node->left);
    int right = lengthOfLongestPath(node->right);
 
    return 1 + (left > right ? left : right);
}
 
// Function to copy the complete
// path in a matrix
void copyPath(int* path, int index,
              int** mtrx, int row)
{
    // Loop to copy the path
    for (int i = 0; i < index; i++) {
        mtrx[row][i] = path[i];
    }
}
 
// Function to store all path
// one by one in matrix
void storePath(struct Node* node,
               int* path, int index,
               int** mtrx, int& row)
{
    // Base condition
    if (node == NULL) {
        return;
    }
 
    // Inserting the current node
    // into the current path
    path[index] = node->key;
 
    // Recursive call for
    // the left sub tree
    storePath(node->left, path,
              index + 1, mtrx, row);
 
    // Recursive call for
    // the right sub tree
    storePath(node->right, path,
              index + 1, mtrx, row);
 
    // Condition to check that current
    // node is a leaf node or not
    if (node->left == NULL
        && node->right == NULL) {
 
        // Increamentation for changing
        // row
        row = row + 1;
        // Function call for copying
        // the path
        copyPath(path, index + 1,
                 mtrx, row);
    }
}
 
// Function to calculate
// total path
int totalPath(Node* node)
{
    static int count = 0;
    if (node == NULL) {
        return count;
    }
    if (node->left == NULL
        && node->right == NULL) {
        return count + 1;
    }
    count = totalPath(node->left);
    return totalPath(node->right);
}
 
// Function for Clockwise Spiral Traversal
// of Binary Tree
void traverse_matrix(int** mtrx,
                     int height,
                     int width)
{
    int j = 0, k1 = 0, k2 = 0;
    int 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] << " ";
            }
        }
        cout << endl;
 
        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] << " ";
            }
        }
        cout << endl;
 
        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] << " ";
            }
        }
    }
}
 
// Function to print all the paths
// in Boundary Root to Leaf
// Path Traversal
void PrintPath(Node* node)
{
    // Calculate the length of
    // longest path of the tree
    int max_len = lengthOfLongestPath(node);
     
    // Calculate total path
    int total_path = totalPath(node);
     
    // Array to store path
    int* path = new int[max_len];
    memset(path, 0, sizeof(path));
 
    // Use double pointer to create
    // 2D array which will contain
    // all path of the tree
    int** mtrx = new int*[total_path];
 
    // Initialize width for each row
    // of matrix
    for (int i = 0; i < total_path; i++)
    {
        mtrx[i] = new int[max_len];
    }
 
    // Initialize complete matrix with
    // MAX INTEGER(purpose garbage)
    for (int i = 0; i < total_path; i++)
    {
        for (int j = 0; j < max_len; j++)
        {
            mtrx[i][j] = INT_MAX;
        }
    }
 
    int row = -1;
    storePath(node, path, 0, mtrx, row);
 
    // Print the circular clockwise spiral
    // traversal of the tree
    traverse_matrix(mtrx, total_path,
                    max_len);
 
    // Release extra memory
    // allocated for matrix
    free(mtrx);
}
 
// Driver Code
int main()
{
    /*      10 
           /  \ 
         13    11 
              /  \ 
            19    23 
           / \    / \ 
          21 29 43  15
                   /
                  7 */
 
    // Create Binary Tree as shown
 
    Node* root = newNode(10);
    root->left = newNode(13);
    root->right = newNode(11);
 
    root->right->left = newNode(19);
    root->right->right = newNode(23);
 
    root->right->left->left = newNode(21);
    root->right->left->right = newNode(29);
    root->right->right->left = newNode(43);
    root->right->right->right = newNode(15);
    root->right->right->right->left = newNode(7);
 
    // Function Call
    PrintPath(root);
    return 0;
}

Java




// Java implementation to print the 
// path in Boundary Root to Leaf 
// Path Traversal.
import java.util.*;
 
class GFG{
 
static int row;
static int count = 0;
 
// Structure of 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);
}
 
// Function to calculate the length
// of longest path of the tree
static int lengthOfLongestPath(Node node)
{
     
    // Base Case
    if (node == null)
        return 0;
 
    // Recursive call to calculate the
    // length of longest path
    int left = lengthOfLongestPath(node.left);
    int right = lengthOfLongestPath(node.right);
 
    return 1 + (left > right ? left : right);
}
 
// Function to copy the complete
// path in a matrix
static void copyPath(int[] path, int index,
                     int[][] mtrx, int r)
{
     
    // Loop to copy the path
    for(int i = 0; i < index; i++)
    {
        mtrx[r][i] = path[i];
    }
}
 
// Function to store all path
// one by one in matrix
static void storePath(Node node, int[] path,
                      int index, int[][] mtrx)
{
     
    // Base condition
    if (node == null)
    {
        return;
    }
 
    // Inserting the current node
    // into the current path
    path[index] = node.key;
 
    // Recursive call for
    // the left sub tree
    storePath(node.left, path,
              index + 1, mtrx);
 
    // Recursive call for
    // the right sub tree
    storePath(node.right, path,
              index + 1, mtrx);
 
    // Condition to check that current
    // node is a leaf node or not
    if (node.left == null &&
        node.right == null)
    {
 
        // Increamentation for changing
        // row
        row = row + 1;
         
        // Function call for copying
        // the path
        copyPath(path, index + 1, mtrx, row);
    }
}
 
// Function to calculate
// total path
static int totalPath(Node node)
{
    if (node == null)
    {
        return count;
    }
    if (node.left == null &&
        node.right == null)
    {
        return count + 1;
    }
    count = totalPath(node.left);
    return totalPath(node.right);
}
 
// Function for Clockwise Spiral Traversal
// of Binary Tree
static void traverse_matrix(int[][] mtrx,
                            int height,
                            int width)
{
    int j = 0, k1 = 0, k2 = 0;
    int 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] + " ");
            }
        }
        System.out.println();
 
        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] + " ");
            }
        }
        System.out.println();
 
        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] + " ");
            }
        }
    }
}
 
// Function to print all the paths
// in Boundary Root to Leaf
// Path Traversal
static void PrintPath(Node node)
{
     
    // Calculate the length of
    // longest path of the tree
    int max_len = lengthOfLongestPath(node);
 
    // Calculate total path
    int total_path = totalPath(node);
 
    // Array to store path
    int[] path = new int[max_len];
    Arrays.fill(path, 0);
 
    // Use double pointer to create
    // 2D array which will contain
    // all path of the tree
    int[][] mtrx = new int[total_path][max_len];
 
    // Initialize complete matrix with
    // MAX INTEGER(purpose garbage)
    for(int i = 0; i < total_path; i++)
    {
        for(int j = 0; j < max_len; j++)
        {
            mtrx[i][j] = Integer.MAX_VALUE;
        }
    }
 
    row = -1;
    storePath(node, path, 0, mtrx);
 
    // Print the circular clockwise spiral
    // traversal of the tree
    traverse_matrix(mtrx, total_path, max_len);
}
 
// Driver Code
public static void main(String[] args)
{
 
    /* 10
      /  \
     13  11
        /  \
       19   23
      / \   / \
     21 29 43  15
              /
             7 */
              
    // Create Binary Tree as shown
    Node root = newNode(10);
    root.left = newNode(13);
    root.right = newNode(11);
 
    root.right.left = newNode(19);
    root.right.right = newNode(23);
 
    root.right.left.left = newNode(21);
    root.right.left.right = newNode(29);
    root.right.right.left = newNode(43);
    root.right.right.right = newNode(15);
    root.right.right.right.left = newNode(7);
 
    // Function Call
    PrintPath(root);
}
}
 
// This code is contributed by sanjeev2552

Python3




# Python3 implementation to prthe
# path in Boundary Root to Leaf
# Path Traversal.
  
# Structure of tree node
class Node:
     
    def __init__(self, key):
         
        self.key = key
        self.left = None
        self.right = None
 
row = 0
count = 0
  
# Utility function to
# create a new node
def newNode(key):
     
    temp = Node(key)
    return temp
   
# Function to calculate the length
# of longest path of the tree
def lengthOfLongestPath(node):
 
    # Base Case
    if (node == None):
        return 0;
  
    # Recursive call to calculate the length
    # of longest path
    left = lengthOfLongestPath(node.left);
    right = lengthOfLongestPath(node.right);
  
    return 1 + (left if left > right else right);
 
# Function to copy the complete
# path in a matrix
def copyPath(path, index, mtrx, r):
 
    # Loop to copy the path
    for i in range(index):
     
        mtrx[r][i] = path[i];
 
# Function to store all path
# one by one in matrix
def storePath(node, path, index, mtrx):
    global row
     
    # Base condition
    if (node == None):
        return;
  
    # Inserting the current node
    # into the current path
    path[index] = node.key;
  
    # Recursive call for
    # the left sub tree
    storePath(node.left, path,
              index + 1, mtrx);
  
    # Recursive call for
    # the right sub tree
    storePath(node.right, path,
              index + 1, mtrx);
  
    # Condition to check that current
    # node is a leaf node or not
    if (node.left == None and node.right == None):
  
        # Increamentation for changing
        # row
        row = row + 1;
       
        # Function call for copying
        # the path
        copyPath(path, index + 1,
                 mtrx, row);
      
# Function to calculate
# total path
def totalPath(node):
    global count
     
    if (node == None):
        return count;
     
    if (node.left == None and node.right == None):
        return count + 1;
     
    count = totalPath(node.left);
    return totalPath(node.right);
  
# Function for Clockwise Spiral Traversal
# of Binary Tree
def traverse_matrix( mtrx, height, width):
 
    j = 0
    k1 = 0
    k2 = 0;
    k3 = height - 1;
    k4 = width - 1;
     
    for round in range(height//2):
        for j in range(k2, width):
  
            # Only prthose values which
            # are not MAX_INTEGER
            if (mtrx[k1][j] != 1000000):
                print(mtrx[k1][j], end=' ')
         
        print()       
        k2 = 0;
        k1 += 1
         
        for j in range(k4, -1, -1):
  
            # Only prthose values which
            # are not MAX_INTEGER
            if (mtrx[k3][j] != 1000000):
                print(mtrx[k3][j], end=' ')
         
        print()
        k4 = width - 1;
        k3 -= 1
  
    # Condition (one row may be left
    # traversing)
    # If number of rows in matrix are odd
    if (height % 2 != 0):
         
        for j in range(k2, width):
  
            # Only prthose values which are
            # not MAX_INTEGER
            if (mtrx[k1][j] != 1000000):
                print(mtrx[k1][j], end=' ')
              
# Function to prall the paths
# in Boundary Root to Leaf
# Path Traversal
def PrintPath(node):   
    global row
     
    # Calculate the length of
    # longest path of the tree
    max_len = lengthOfLongestPath(node);
      
    # Calculate total path
    total_path = totalPath(node);
      
    # Array to store path
    path = [0 for i in range(max_len)]
  
    # Use double pointer to create
    # 2D array which will contain
    # all path of the tree
    mtrx = [[1000000 for j in range(max_len)]
                for i in range(total_path)]
      
    row = -1;
    storePath(node, path, 0, mtrx);
  
    # Print the circular clockwise spiral
    # traversal of the tree
    traverse_matrix(mtrx, total_path,
                    max_len);
  
# Driver Code
if __name__=='__main__':
     
    '''      10 
           /  \ 
         13    11 
              /  \ 
            19    23 
           / \    / \ 
          21 29 43  15
                   /
                  7 '''
  
    # Create Binary Tree as shown
  
    root = newNode(10);
    root.left = newNode(13);
    root.right = newNode(11);
  
    root.right.left = newNode(19);
    root.right.right = newNode(23);
  
    root.right.left.left = newNode(21);
    root.right.left.right = newNode(29);
    root.right.right.left = newNode(43);
    root.right.right.right = newNode(15);
    root.right.right.right.left = newNode(7);
  
    # Function Call
    PrintPath(root);
     
    # This code is contributed by pratham76

C#




// C# implementation to print the 
// path in Boundary Root to Leaf 
// Path Traversal.
 
using System;
using System.Collections;
  
class GFG{
  
static int row;
static int count = 0;
  
// Structure of tree node
public 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);
}
  
// Function to calculate the length
// of longest path of the tree
static int lengthOfLongestPath(Node node)
{
      
    // Base Case
    if (node == null)
        return 0;
  
    // Recursive call to calculate the
    // length of longest path
    int left = lengthOfLongestPath(node.left);
    int right = lengthOfLongestPath(node.right);
  
    return 1 + (left > right ? left : right);
}
  
// Function to copy the complete
// path in a matrix
static void copyPath(int[] path, int index,
                     int[,] mtrx, int r)
{
      
    // Loop to copy the path
    for(int i = 0; i < index; i++)
    {
        mtrx[r, i] = path[i];
    }
}
  
// Function to store all path
// one by one in matrix
static void storePath(Node node, int[] path,
                      int index, int[,] mtrx)
{
      
    // Base condition
    if (node == null)
    {
        return;
    }
  
    // Inserting the current node
    // into the current path
    path[index] = node.key;
  
    // Recursive call for
    // the left sub tree
    storePath(node.left, path,
              index + 1, mtrx);
  
    // Recursive call for
    // the right sub tree
    storePath(node.right, path,
              index + 1, mtrx);
  
    // Condition to check that current
    // node is a leaf node or not
    if (node.left == null &&
        node.right == null)
    {
  
        // Increamentation for changing
        // row
        row = row + 1;
          
        // Function call for copying
        // the path
        copyPath(path, index + 1, mtrx, row);
    }
}
  
// Function to calculate
// total path
static int totalPath(Node node)
{
    if (node == null)
    {
        return count;
    }
    if (node.left == null &&
        node.right == null)
    {
        return count + 1;
    }
    count = totalPath(node.left);
    return totalPath(node.right);
}
  
// Function for Clockwise Spiral Traversal
// of Binary Tree
static void traverse_matrix(int[,] mtrx,
                            int height,
                            int width)
{
    int j = 0, k1 = 0, k2 = 0;
    int 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] != 10000000)
            {
                Console.Write(mtrx[k1, j] + " ");
            }
        }
        Console.WriteLine();
  
        k2 = 0;
        k1++;
  
        for(j = k4; j >= 0; j--)
        {
  
            // Only print those values which
            // are not MAX_INTEGER
            if (mtrx[k3, j] != 10000000)
            {
                Console.Write(mtrx[k3, j] + " ");
            }
        }
        Console.WriteLine();
  
        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] != 10000000)
            {
                Console.Write(mtrx[k1, j] + " ");
            }
        }
    }
}
  
// Function to print all the paths
// in Boundary Root to Leaf
// Path Traversal
static void PrintPath(Node node)
{
      
    // Calculate the length of
    // longest path of the tree
    int max_len = lengthOfLongestPath(node);
  
    // Calculate total path
    int total_path = totalPath(node);
  
    // Array to store path
    int[] path = new int[max_len];
    Array.Fill(path, 0);
  
    // Use double pointer to create
    // 2D array which will contain
    // all path of the tree
    int[,] mtrx = new int[total_path, max_len];
  
    // Initialize complete matrix with
    // MAX INTEGER(purpose garbage)
    for(int i = 0; i < total_path; i++)
    {
        for(int j = 0; j < max_len; j++)
        {
            mtrx[i, j] = 10000000;
        }
    }
  
    row = -1;
    storePath(node, path, 0, mtrx);
  
    // Print the circular clockwise spiral
    // traversal of the tree
    traverse_matrix(mtrx, total_path, max_len);
}
  
// Driver Code
public static void Main(string[] args)
{
  
    /* 10
      /  \
     13  11
        /  \
       19   23
      / \   / \
     21 29 43  15
              /
             7 */
               
    // Create Binary Tree as shown
    Node root = newNode(10);
    root.left = newNode(13);
    root.right = newNode(11);
  
    root.right.left = newNode(19);
    root.right.right = newNode(23);
  
    root.right.left.left = newNode(21);
    root.right.left.right = newNode(29);
    root.right.right.left = newNode(43);
    root.right.right.right = newNode(15);
    root.right.right.right.left = newNode(7);
  
    // Function Call
    PrintPath(root);
}
}
 
// This code is contributed by rutvik_56

Javascript




<script>
 
    // JavaScript implementation to print the
    // path in Boundary Root to Leaf
    // Path Traversal.
     
    let row;
    let count = 0;
 
    // Structure of tree node
    class Node
    {
        constructor(key) {
           this.left = null;
           this.right = null;
           this.key = key;
        }
    }
 
    // Utility function to
    // create a new node
    function newNode(key)
    {
        let temp = new Node(key);
        return (temp);
    }
 
    // Function to calculate the length
    // of longest path of the tree
    function lengthOfLongestPath(node)
    {
 
        // Base Case
        if (node == null)
            return 0;
 
        // Recursive call to calculate the
        // length of longest path
        let left = lengthOfLongestPath(node.left);
        let right = lengthOfLongestPath(node.right);
 
        return 1 + (left > right ? left : right);
    }
 
    // Function to copy the complete
    // path in a matrix
    function copyPath(path, index, mtrx, r)
    {
 
        // Loop to copy the path
        for(let i = 0; i < index; i++)
        {
            mtrx[r][i] = path[i];
        }
    }
 
    // Function to store all path
    // one by one in matrix
    function storePath(node, path, index, mtrx)
    {
 
        // Base condition
        if (node == null)
        {
            return;
        }
 
        // Inserting the current node
        // into the current path
        path[index] = node.key;
 
        // Recursive call for
        // the left sub tree
        storePath(node.left, path,
                  index + 1, mtrx);
 
        // Recursive call for
        // the right sub tree
        storePath(node.right, path,
                  index + 1, mtrx);
 
        // Condition to check that current
        // node is a leaf node or not
        if (node.left == null &&
            node.right == null)
        {
 
            // Increamentation for changing
            // row
            row = row + 1;
 
            // Function call for copying
            // the path
            copyPath(path, index + 1, mtrx, row);
        }
    }
 
    // Function to calculate
    // total path
    function totalPath(node)
    {
        if (node == null)
        {
            return count;
        }
        if (node.left == null &&
            node.right == null)
        {
            return count + 1;
        }
        count = totalPath(node.left);
        return totalPath(node.right);
    }
 
    // Function for Clockwise Spiral Traversal
    // of Binary Tree
    function traverse_matrix(mtrx, height, width)
    {
        let j = 0, k1 = 0, k2 = 0;
        let k3 = height - 1;
        let k4 = width - 1;
 
        for(let round = 0; round < parseInt(height / 2, 10);
        round++)
        {
            for(j = k2; j < width; j++)
            {
 
                // Only print those values which
                // are not MAX_INTEGER
                if (mtrx[k1][j] != Number.MAX_VALUE)
                {
                    document.write(mtrx[k1][j] + " ");
                }
            }
            document.write("</br>");
 
            k2 = 0;
            k1++;
 
            for(j = k4; j >= 0; j--)
            {
 
                // Only print those values which
                // are not MAX_INTEGER
                if (mtrx[k3][j] != Number.MAX_VALUE)
                {
                    document.write(mtrx[k3][j] + " ");
                }
            }
            document.write("</br>");
 
            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] != Number.MAX_VALUE)
                {
                    document.write(mtrx[k1][j] + " ");
                }
            }
        }
    }
 
    // Function to print all the paths
    // in Boundary Root to Leaf
    // Path Traversal
    function PrintPath(node)
    {
 
        // Calculate the length of
        // longest path of the tree
        let max_len = lengthOfLongestPath(node);
 
        // Calculate total path
        let total_path = totalPath(node);
 
        // Array to store path
        let path = new Array(max_len);
        path.fill(0);
 
        // Use double pointer to create
        // 2D array which will contain
        // all path of the tree
        let mtrx = new Array(total_path);
 
        // Initialize complete matrix with
        // MAX INTEGER(purpose garbage)
        for(let i = 0; i < total_path; i++)
        {
            mtrx[i] = new Array(max_len);
            for(let j = 0; j < max_len; j++)
            {
                mtrx[i][j] = Number.MAX_VALUE;
            }
        }
 
        row = -1;
        storePath(node, path, 0, mtrx);
 
        // Print the circular clockwise spiral
        // traversal of the tree
        traverse_matrix(mtrx, total_path, max_len);
    }
     
    /* 10
      /  \
     13  11
        /  \
       19   23
      / \   / \
     21 29 43  15
              /
             7 */
               
    // Create Binary Tree as shown
    let root = newNode(10);
    root.left = newNode(13);
    root.right = newNode(11);
  
    root.right.left = newNode(19);
    root.right.right = newNode(23);
  
    root.right.left.left = newNode(21);
    root.right.left.right = newNode(29);
    root.right.right.left = newNode(43);
    root.right.right.right = newNode(15);
    root.right.right.right.left = newNode(7);
  
    // Function Call
    PrintPath(root);
 
</script>
Output: 
10 13 
7 15 23 11 10 
10 11 19 21 
43 23 11 10 
10 11 19 29

 

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