Reverse Level Order traversal in spiral form

Given a binary tree, the task is to print the reverse level order in spiral form.

Examples:

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

Input:
     5
   /   \
  6     4
 / \   / 
7   1 8
 \     \
  3     10
Output: 3 10 8 1 7 6 4 5

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 left to right we will set the value of flag to zero, so that next time we traverse the Tree from right to left 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 level order  
// traversal of a binary tree in spiral form 
#include <bits/stdc++.h> 
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) 
{ 
    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(lheight + 1, rheight + 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 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 Reverse level order traversal 
// of a Binary tree in spiral form 
void reverseSpiral(struct Node* root) 
{ 
    // Flag is used to mark the change 
    // in level 
    int flag = 1; 
  
    // Height of tree 
    int h = height(root); 
  
    for (int i = h; i >= 1; i--) { 
  
        // If flag value is one print Nodes 
        // from left to right 
        if (flag == 1) { 
            leftToRight(root, i); 
  
            // Mark flag as zero so that next time 
            // tree is traversed from right to left 
            flag = 0; 
        } 
  
        // If flag is zero print Nodes 
        // from right to left 
        else if (flag == 0) { 
            rightToLeft(root, i); 
  
            // Mark flag as one so that next time 
            // Nodes are printed from left to right 
            flag = 1; 
        } 
    } 
} 
  
// Driver code 
int main() 
{ 
    struct Node* root = new Node(5); 
    root->left = new Node(9); 
    root->right = new Node(3); 
    root->left->left = new Node(6); 
    root->right->right = new Node(4); 
    root->left->left->left = new Node(8); 
    root->left->left->right = new Node(7); 
  
    reverseSpiral(root); 
  
    return 0; 
} 

Java

// Java program to print reverse level order  
// traversal of a binary tree in spiral form 
class Solution 
{ 
      
// 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) 
{ 
    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(lheight + 1, rheight + 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 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 Reverse level order traversal 
// of a Binary tree in spiral form 
static void reverseSpiral( Node root) 
{ 
    // Flag is used to mark the change 
    // in level 
    int flag = 1; 
  
    // Height of tree 
    int h = height(root); 
  
    for (int i = h; i >= 1; i--)  
    { 
  
        // If flag value is one print Nodes 
        // from left to right 
        if (flag == 1)  
        { 
            leftToRight(root, i); 
  
            // Mark flag as zero so that next time 
            // tree is traversed from right to left 
            flag = 0; 
        } 
  
        // If flag is zero print Nodes 
        // from right to left 
        else if (flag == 0)  
        { 
            rightToLeft(root, i); 
  
            // Mark flag as one so that next time 
            // Nodes are printed from left to right 
            flag = 1; 
        } 
    } 
} 
  
// Driver code 
public static void main(String args[]) 
{ 
    Node root = new Node(5); 
    root.left = new Node(9); 
    root.right = new Node(3); 
    root.left.left = new Node(6); 
    root.right.right = new Node(4); 
    root.left.left.left = new Node(8); 
    root.left.left.right = new Node(7); 
  
    reverseSpiral(root); 
} 
} 
  
// This code is contributed by Arnab Kundu 

Python3

# Python3 program to prreverse level order  
# traversal of a binary tree in spiral form 
  
class newNode:  
  
    # Construct to create a newNode  
    def __init__(self, key):  
        self.data = key  
        self.left = None
        self.right = None
  
# Recursive Function to find height  
# of binary tree  
def height(root): 
  
    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(lheight + 1, rheight + 1)  
  
# Function to PrNodes 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 PrNodes 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 prReverse level order traversal  
# of a Binary tree in spiral form  
def reverseSpiral(root): 
  
    # Flag is used to mark the  
    # change in level  
    flag = 1
  
    # Height of tree  
    h = height(root)  
  
    for i in range(h, 0, -1):  
  
        # If flag value is one prNodes  
        # from left to right  
        if (flag == 1): 
            leftToRight(root, i)  
  
            # Mark flag as zero so that next time  
            # tree is traversed from right to left  
            flag = 0
          
        # If flag is zero prNodes  
        # from right to left  
        elif (flag == 0): 
            rightToLeft(root, i)  
  
            # Mark flag as one so that next time  
            # Nodes are printed from left to right  
            flag = 1
      
# Driver Code 
if __name__ == '__main__': 
    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)  
  
    reverseSpiral(root)  
      
# This code is contributed  
# by SHUBHAMSINGH10 

C#

// C# program to print reverse level order  
// traversal of a binary tree in spiral form  
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)  
{  
    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(lheight + 1, rheight + 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 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 Reverse level order traversal  
// of a Binary tree in spiral form  
static void reverseSpiral( Node root)  
{  
    // Flag is used to mark the change  
    // in level  
    int flag = 1;  
  
    // Height of tree  
    int h = height(root);  
  
    for (int i = h; i >= 1; i--)  
    {  
  
        // If flag value is one print Nodes  
        // from left to right  
        if (flag == 1)  
        {  
            leftToRight(root, i);  
  
            // Mark flag as zero so that next time  
            // tree is traversed from right to left  
            flag = 0;  
        }  
  
        // If flag is zero print Nodes  
        // from right to left  
        else if (flag == 0)  
        {  
            rightToLeft(root, i);  
  
            // Mark flag as one so that next time  
            // Nodes are printed from left to right  
            flag = 1;  
        }  
    }  
}  
  
// Driver code  
public static void Main(String []args)  
{  
    Node root = new Node(5);  
    root.left = new Node(9);  
    root.right = new Node(3);  
    root.left.left = new Node(6);  
    root.right.right = new Node(4);  
    root.left.left.left = new Node(8);  
    root.left.left.right = new Node(7);  
  
    reverseSpiral(root);  
}  
}  
  
/* This code is contributed by PrinciRaj1992 */

Output:

8 7 4 6 9 3 5

Time Complexity Analysis : The best case time complexity of reverseSpiral() is O(n+n/2+n/4…) = O(n) in case of a perfect binary tree. And the worst case time complexity is O(n**2) [O((n)+(n-1)+(n-2)+…] in case of a skewed tree taken as input.

Improved by :HarendraSingh22

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Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

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