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Reverse zigzag Traversal of a Binary Tree

  • Difficulty Level : Hard
  • Last Updated : 11 Aug, 2021

Given a Binary Tree, the task is to print the Reverse zigzag Order of the tree.
Examples: 
 

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

Input:
      5
     / \
    9   3
   /     \
  6       4
 / \
8   7
Output: 7 8 6 4 3 9 5

 

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Approach: The idea is to traverse the tree in a Reverse Level Order manner but with a slight modification. We will use a variable flag and initially set it’s value to one. As we complete the reverse level order traversal of the tree, from right to left we will set the value of flag to zero, so that next time we traverse the Tree from left to right and as we complete the traversal we set it’s value back to one. We will repeat this whole step until we have traversed the Binary Tree completely.
Below is the implementation of the above approach: 
 

C++




// C++ program to print reverse
// zigzag order of binary tree
#include <bits/stdc++.h>
using namespace std;
 
// Binary tree node
struct node {
    struct node* left;
    struct node* right;
    int data;
};
 
// Function to create a new
// Binary node
struct node* newNode(int data)
{
    struct node* temp = new node;
 
    temp->data = data;
    temp->left = NULL;
    temp->right = NULL;
 
    return temp;
}
 
// Recursive Function to find height
// of binary tree
int HeightOfTree(struct node* root)
{
    if (root == NULL)
        return 0;
 
    // Compute the height of each subtree
    int lheight = HeightOfTree(root->left);
    int rheight = HeightOfTree(root->right);
 
    // Return the maximum of two
    return max(lheight + 1, rheight + 1);
}
 
// Function to Print nodes from right to left
void Print_Level_Right_To_Left(struct node* root, int level)
{
    if (root == NULL)
        return;
 
    if (level == 1)
        cout << root->data << " ";
 
    else if (level > 1) {
        Print_Level_Right_To_Left(root->right, level - 1);
        Print_Level_Right_To_Left(root->left, level - 1);
    }
}
 
// Function to Print nodes from left to right
void Print_Level_Left_To_Right(struct node* root, int level)
{
    if (root == NULL)
        return;
 
    if (level == 1)
        cout << root->data << " ";
 
    else if (level > 1) {
        Print_Level_Left_To_Right(root->left, level - 1);
        Print_Level_Left_To_Right(root->right, level - 1);
    }
}
 
// Function to print Reverse zigzag of
// a Binary tree
void PrintReverseZigZag(struct node* root)
{
    // Flag is used to mark the change
    // in level
    int flag = 1;
 
    // Height of tree
    int height = HeightOfTree(root);
 
    for (int i = height; i >= 1; i--) {
 
        // If flag value is one print nodes
        // from right to left
        if (flag == 1) {
            Print_Level_Right_To_Left(root, i);
 
            // Mark flag as zero so that next time
            // tree is traversed from left to right
            flag = 0;
        }
 
        // If flag is zero print nodes
        // from left to right
        else if (flag == 0) {
            Print_Level_Left_To_Right(root, i);
 
            // Mark flag as one so that next time
            // nodes are printed from right to left
            flag = 1;
        }
    }
}
 
// Driver code
int main()
{
    struct node* root = newNode(5);
    root->left = newNode(9);
    root->right = newNode(3);
    root->left->left = newNode(6);
    root->right->right = newNode(4);
    root->left->left->left = newNode(8);
    root->left->left->right = newNode(7);
 
    PrintReverseZigZag(root);
 
    return 0;
}

Java




// Java program to print reverse
// zigzag order of binary tree
class GfG
{
 
// Binary tree node
static class node
{
    node left;
    node right;
    int data;
}
 
// Function to create a new
// Binary node
static node newNode(int data)
{
    node temp = new node();
 
    temp.data = data;
    temp.left = null;
    temp.right = null;
 
    return temp;
}
 
// Recursive Function to find height
// of binary tree
static int HeightOfTree(node root)
{
    if (root == null)
        return 0;
 
    // Compute the height of each subtree
    int lheight = HeightOfTree(root.left);
    int rheight = HeightOfTree(root.right);
 
    // Return the maximum of two
    return Math.max(lheight + 1, rheight + 1);
}
 
// Function to Print nodes from right to left
static void Print_Level_Right_To_Left(node root, int level)
{
    if (root == null)
        return;
 
    if (level == 1)
        System.out.print(root.data + " ");
 
    else if (level > 1)
    {
        Print_Level_Right_To_Left(root.right, level - 1);
        Print_Level_Right_To_Left(root.left, level - 1);
    }
}
 
// Function to Print nodes from left to right
static void Print_Level_Left_To_Right(node root, int level)
{
    if (root == null)
        return;
 
    if (level == 1)
        System.out.print(root.data + " ");
 
    else if (level > 1)
    {
        Print_Level_Left_To_Right(root.left, level - 1);
        Print_Level_Left_To_Right(root.right, level - 1);
    }
}
 
// Function to print Reverse zigzag of
// a Binary tree
static void PrintReverseZigZag(node root)
{
    // Flag is used to mark the change
    // in level
    int flag = 1;
 
    // Height of tree
    int height = HeightOfTree(root);
 
    for (int i = height; i >= 1; i--)
    {
 
        // If flag value is one print nodes
        // from right to left
        if (flag == 1)
        {
            Print_Level_Right_To_Left(root, i);
 
            // Mark flag as zero so that next time
            // tree is traversed from left to right
            flag = 0;
        }
 
        // If flag is zero print nodes
        // from left to right
        else if (flag == 0)
        {
            Print_Level_Left_To_Right(root, i);
 
            // Mark flag as one so that next time
            // nodes are printed from right to left
            flag = 1;
        }
    }
}
 
// Driver code
public static void main(String[] args)
{
    node root = newNode(5);
    root.left = newNode(9);
    root.right = newNode(3);
    root.left.left = newNode(6);
    root.right.right = newNode(4);
    root.left.left.left = newNode(8);
    root.left.left.right = newNode(7);
 
    PrintReverseZigZag(root);
}
}
 
// This code is contributed by Prerna Saini.

Python3




# Python3 program to print reverse
# zigzag order of binary tree
 
# Binary tree node
class Node:
     
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
     
# Recursive Function to find
# height of binary tree
def HeightOfTree(root):
 
    if root == None:
        return 0
 
    # Compute the height of each subtree
    lheight = HeightOfTree(root.left)
    rheight = HeightOfTree(root.right)
 
    # Return the maximum of two
    return max(lheight + 1, rheight + 1)
 
# Function to Print nodes from right to left
def Print_Level_Right_To_Left(root, level):
 
    if root == None:
        return
 
    if level == 1:
        print(root.data, end = " ")
 
    elif level > 1:
        Print_Level_Right_To_Left(root.right,
                                  level - 1)
        Print_Level_Right_To_Left(root.left,
                                  level - 1)
 
# Function to Print nodes from left to right
def Print_Level_Left_To_Right(root, level):
 
    if root == None:
        return
 
    if level == 1:
        print(root.data, end = " ")
 
    elif level > 1:
        Print_Level_Left_To_Right(root.left,   
                                  level - 1)
        Print_Level_Left_To_Right(root.right,
                                  level - 1)
     
# Function to print Reverse
# zigzag of a Binary tree
def PrintReverseZigZag(root):
 
    # Flag is used to mark the
    # change in level
    flag = 1
 
    # Height of tree
    height = HeightOfTree(root)
 
    for i in range(height, 0, -1):
 
        # If flag value is one print
        # nodes from right to left
        if flag == 1:
            Print_Level_Right_To_Left(root, i)
 
            # Mark flag as zero so that next time
            # tree is traversed from left to right
            flag = 0
         
        # If flag is zero print nodes
        # from left to right
        elif flag == 0:
            Print_Level_Left_To_Right(root, i)
 
            # Mark flag as one so that next time
            # nodes are printed from right to left
            flag = 1
 
# Driver code
if __name__ == "__main__":
 
    root = Node(5)
    root.left = Node(9)
    root.right = Node(3)
    root.left.left = Node(6)
    root.right.right = Node(4)
    root.left.left.left = Node(8)
    root.left.left.right = Node(7)
 
    PrintReverseZigZag(root)
 
# This code is contributed by Rituraj Jain

C#




// C# program to print reverse
// zigzag order of binary tree
using System;
 
class GfG
{
 
// Binary tree node
public class node
{
    public node left;
    public node right;
    public int data;
}
 
// Function to create a new
// Binary node
static node newNode(int data)
{
    node temp = new node();
 
    temp.data = data;
    temp.left = null;
    temp.right = null;
 
    return temp;
}
 
// Recursive Function to find height
// of binary tree
static int HeightOfTree(node root)
{
    if (root == null)
        return 0;
 
    // Compute the height of each subtree
    int lheight = HeightOfTree(root.left);
    int rheight = HeightOfTree(root.right);
 
    // Return the maximum of two
    return Math.Max(lheight + 1, rheight + 1);
}
 
// Function to Print nodes from right to left
static void Print_Level_Right_To_Left(node root, int level)
{
    if (root == null)
        return;
 
    if (level == 1)
        Console.Write(root.data + " ");
 
    else if (level > 1)
    {
        Print_Level_Right_To_Left(root.right, level - 1);
        Print_Level_Right_To_Left(root.left, level - 1);
    }
}
 
// Function to Print nodes from left to right
static void Print_Level_Left_To_Right(node root, int level)
{
    if (root == null)
        return;
 
    if (level == 1)
        Console.Write(root.data + " ");
 
    else if (level > 1)
    {
        Print_Level_Left_To_Right(root.left, level - 1);
        Print_Level_Left_To_Right(root.right, level - 1);
    }
}
 
// Function to print Reverse zigzag of
// a Binary tree
static void PrintReverseZigZag(node root)
{
    // Flag is used to mark the change
    // in level
    int flag = 1;
 
    // Height of tree
    int height = HeightOfTree(root);
 
    for (int i = height; i >= 1; i--)
    {
 
        // If flag value is one print nodes
        // from right to left
        if (flag == 1)
        {
            Print_Level_Right_To_Left(root, i);
 
            // Mark flag as zero so that next time
            // tree is traversed from left to right
            flag = 0;
        }
 
        // If flag is zero print nodes
        // from left to right
        else if (flag == 0)
        {
            Print_Level_Left_To_Right(root, i);
 
            // Mark flag as one so that next time
            // nodes are printed from right to left
            flag = 1;
        }
    }
}
 
// Driver code
public static void Main(String[] args)
{
    node root = newNode(5);
    root.left = newNode(9);
    root.right = newNode(3);
    root.left.left = newNode(6);
    root.right.right = newNode(4);
    root.left.left.left = newNode(8);
    root.left.left.right = newNode(7);
 
    PrintReverseZigZag(root);
}
}
 
/* This code contributed by PrinciRaj1992 */

Javascript




<script>
 
    // JavaScript program to print reverse
    // zigzag order of binary tree
     
    // Binary tree node
    class node
    {
        constructor(data) {
           this.left = null;
           this.right = null;
           this.data = data;
        }
    }
     
    // Function to create a new
    // Binary node
    function newNode(data)
    {
        let temp = new node(data);
        return temp;
    }
 
    // Recursive Function to find height
    // of binary tree
    function HeightOfTree(root)
    {
        if (root == null)
            return 0;
 
        // Compute the height of each subtree
        let lheight = HeightOfTree(root.left);
        let rheight = HeightOfTree(root.right);
 
        // Return the maximum of two
        return Math.max(lheight + 1, rheight + 1);
    }
 
    // Function to Print nodes from right to left
    function Print_Level_Right_To_Left(root, level)
    {
        if (root == null)
            return;
 
        if (level == 1)
            document.write(root.data + " ");
 
        else if (level > 1)
        {
            Print_Level_Right_To_Left(root.right, level - 1);
            Print_Level_Right_To_Left(root.left, level - 1);
        }
    }
 
    // Function to Print nodes from left to right
    function Print_Level_Left_To_Right(root, level)
    {
        if (root == null)
            return;
 
        if (level == 1)
            document.write(root.data + " ");
 
        else if (level > 1)
        {
            Print_Level_Left_To_Right(root.left, level - 1);
            Print_Level_Left_To_Right(root.right, level - 1);
        }
    }
 
    // Function to print Reverse zigzag of
    // a Binary tree
    function PrintReverseZigZag(root)
    {
        // Flag is used to mark the change
        // in level
        let flag = 1;
 
        // Height of tree
        let height = HeightOfTree(root);
 
        for (let i = height; i >= 1; i--)
        {
 
            // If flag value is one print nodes
            // from right to left
            if (flag == 1)
            {
                Print_Level_Right_To_Left(root, i);
 
                // Mark flag as zero so that next time
                // tree is traversed from left to right
                flag = 0;
            }
 
            // If flag is zero print nodes
            // from left to right
            else if (flag == 0)
            {
                Print_Level_Left_To_Right(root, i);
 
                // Mark flag as one so that next time
                // nodes are printed from right to left
                flag = 1;
            }
        }
    }
     
    let root = newNode(5);
    root.left = newNode(9);
    root.right = newNode(3);
    root.left.left = newNode(6);
    root.right.right = newNode(4);
    root.left.left.left = newNode(8);
    root.left.left.right = newNode(7);
   
    PrintReverseZigZag(root);
 
</script>
Output: 
7 8 6 4 3 9 5

 

Time Complexity:O(N^2), where N is the number of nodes in a binary tree.
Auxiliary Space: O(N) 




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