Foldable Binary Trees

Given a binary tree, find out if the tree can be folded or not. A tree can be folded if the left and right subtrees of the tree are structure-wise mirror images of each other. An empty tree is considered foldable. 

Examples:

Input:
       10
     /     \
   7      15
     \     /
    9  11
Output: Can be folded      

Input:
        10
       /  \
     7   15
   /    /
5   11
Output: Cannot be folded    

Foldable Binary Trees by Changing Left Subtree to its Mirror:

The idea is to change the left subtree to its mirror then check that left subtree with its right subtree.

Follow the steps below to solve the problem:

1. If tree is empty, then return true.
2. Convert the left subtree to its mirror image
3. Check if the structure of left subtree and right subtree is same and store the result.
   • res = isStructSame(root->left, root->right). isStructSame() recursively compares structures of two subtrees and returns true if structures are same
4. Revert the changes made in step (2) to get the original tree.
5. Return result res stored in step 3.

Below is the implementation of the above approach.

C++

// C++ program to check foldable binary tree
#include <bits/stdc++.h>
using namespace std;

/* You would want to remove below
3 lines if your compiler supports
bool, true and false */

/* A binary tree node has data,
pointer to left child and a
pointer to right child */
class node {
public:
    int data;
    node* left;
    node* right;
};

/* converts a tree to its mirror image */
void mirror(node* node);

/* returns true if structure of
two trees a and b is same only
structure is considered for comparison, not data! */
bool isStructSame(node* a, node* b);

/* Returns true if the given tree is foldable */
bool isFoldable(node* root)
{
    bool res;

    /* base case */
    if (root == NULL)
        return true;

    /* convert left subtree to its mirror */
    mirror(root->left);

    /* Compare the structures of the
    right subtree and mirrored
    left subtree */
    res = isStructSame(root->left, root->right);

    /* Get the original tree back */
    mirror(root->left);

    return res;
}

bool isStructSame(node* a, node* b)
{
    if (a == NULL && b == NULL) {
        return true;
    }
    if (a != NULL && b != NULL
        && isStructSame(a->left, b->left)
        && isStructSame(a->right, b->right)) {
        return true;
    }

    return false;
}

/* UTILITY FUNCTIONS */
/* Change a tree so that the roles of the left and
    right pointers are swapped at every node.
    See https:// www.geeksforgeeks.org/?p=662 for details */
void mirror(node* Node)
{
    if (Node == NULL)
        return;
    else {
        node* temp;

        /* do the subtrees */
        mirror(Node->left);
        mirror(Node->right);

        /* swap the pointers in this node */
        temp = Node->left;
        Node->left = Node->right;
        Node->right = temp;
    }
}

/* Helper function that allocates a new node with the
given data and NULL left and right pointers. */
node* newNode(int data)
{
    node* Node = new node();
    Node->data = data;
    Node->left = NULL;
    Node->right = NULL;

    return (Node);
}

/* Driver program to test mirror() */
int main(void)
{
    /* The constructed binary tree is
            1
        / \
        2 3
        \ /
        4 5
    */
    node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->right = newNode(4);
    root->right->left = newNode(5);

    if (isFoldable(root) == 1) {
        cout << "tree is foldable";
    }
    else {
        cout << "\ntree is not foldable";
    }
    return 0;
}

// This code is contributed by rathbhupendra

C

#include <stdio.h>
#include <stdlib.h>

/* You would want to remove below 3 lines if your compiler
   supports bool, true and false */
#define bool int
#define true 1
#define false 0

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
struct node {
    int data;
    struct node* left;
    struct node* right;
};

/* converts a tree to its mirror image */
void mirror(struct node* node);

/* returns true if structure of two trees a and b is same
   Only structure is considered for comparison, not data! */
bool isStructSame(struct node* a, struct node* b);

/* Returns true if the given tree is foldable */
bool isFoldable(struct node* root)
{
    bool res;

    /* base case */
    if (root == NULL)
        return true;

    /* convert left subtree to its mirror */
    mirror(root->left);

    /* Compare the structures of the right subtree and
    mirrored left subtree */
    res = isStructSame(root->left, root->right);

    /* Get the original tree back */
    mirror(root->left);

    return res;
}

bool isStructSame(struct node* a, struct node* b)
{
    if (a == NULL && b == NULL) {
        return true;
    }
    if (a != NULL && b != NULL
        && isStructSame(a->left, b->left)
        && isStructSame(a->right, b->right)) {
        return true;
    }

    return false;
}

/* UTILITY FUNCTIONS */
/* Change a tree so that the roles of the  left and
    right pointers are swapped at every node.
    See https:// www.geeksforgeeks.org/?p=662 for details */
void mirror(struct node* node)
{
    if (node == NULL)
        return;
    else {
        struct node* temp;

        /* do the subtrees */
        mirror(node->left);
        mirror(node->right);

        /* swap the pointers in this node */
        temp = node->left;
        node->left = node->right;
        node->right = temp;
    }
}

/* Helper function that allocates a new node with the
   given data and NULL left and right pointers. */
struct node* newNode(int data)
{
    struct node* node
        = (struct node*)malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;

    return (node);
}

/* Driver program to test mirror() */
int main(void)
{
    /* The constructed binary tree is
         1
       /   \
      2     3
      \    /
       4  5
  */
    struct node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->right->left = newNode(4);
    root->left->right = newNode(5);

    if (isFoldable(root) == 1) {
        printf("\n tree is foldable");
    }
    else {
        printf("\n tree is not foldable");
    }

    getchar();
    return 0;
}

Java

// Java program to check foldable binary tree

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
class Node {
    int data;
    Node left, right;

    Node(int item)
    {
        data = item;
        left = right = null;
    }
}

class BinaryTree {
    Node root;

    /* Returns true if the given tree is foldable */
    boolean isFoldable(Node node)
    {
        boolean res;

        /* base case */
        if (node == null)
            return true;

        /* convert left subtree to its mirror */
        mirror(node.left);

        /* Compare the structures of the right subtree and
         mirrored left subtree */
        res = isStructSame(node.left, node.right);

        /* Get the original tree back */
        mirror(node.left);

        return res;
    }

    boolean isStructSame(Node a, Node b)
    {
        if (a == null && b == null)
            return true;
        if (a != null && b != null
            && isStructSame(a.left, b.left)
            && isStructSame(a.right, b.right))
            return true;

        return false;
    }

    /* UTILITY FUNCTIONS */

    /* Change a tree so that the roles of the  left and
       right pointers are swapped at every node.
       See https:// www.geeksforgeeks.org/?p=662 for details
     */
    void mirror(Node node)
    {
        if (node == null)
            return;
        else {
            Node temp;

            /* do the subtrees */
            mirror(node.left);
            mirror(node.right);

            /* swap the pointers in this node */
            temp = node.left;
            node.left = node.right;
            node.right = temp;
        }
    }

    /* Driver program to test above functions */
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();

        /* The constructed binary tree is
             1
           /   \
          2     3
           \    /
            4  5
        */
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.right.left = new Node(4);
        tree.root.left.right = new Node(5);

        if (tree.isFoldable(tree.root))
            System.out.println("tree is foldable");
        else
            System.out.println("Tree is not foldable");
    }
}

// This code has been contributed by Mayank Jaiswal

Python3

# Python3 program to check foldable binary tree

#  A binary tree node has data,
# pointer to left child and a
# pointer to right child


class newNode:
    def __init__(self, d):
        self.data = d
        self.left = None
        self.right = None

# Returns true if the given
# tree is foldable


def isFoldable(node):

    # base case
    if node == None:
        return true

    # convert left subtree to its mirror
    mirror(node.left)

    # Compare the structures of the right subtree and mirrored
    # left subtree
    res = isStructSame(node.left, node.right)

    # Get the original tree back
    mirror(node.left)

    return res


def isStructSame(a, b):

    if a == None and b == None:
        return True
    if a != None and b != None and isStructSame(a.left, b.left) and isStructSame(a.right, b.right):
        return True

    return False


def mirror(node):

    if node == None:
        return
    else:

        # do the subtrees
        mirror(node.left)
        mirror(node.right)

        # swap the pointers in this node
        temp = node.left
        node.left = node.right
        node.right = temp


# Driver Code
if __name__ == '__main__':

    '''
    The constructed binary tree is
             1
           /   \
          2     3
           \    /
            4  5
    '''
    root = newNode(1)
    root.left = newNode(2)
    root.right = newNode(3)
    root.right.left = newNode(4)
    root.left.right = newNode(5)

    if isFoldable(root):
        print("tree is foldable")
    else:
        print("Tree is not foldable")

C#

// C# program to check foldable
// binary tree
using System;

/* A binary tree node has data,
pointer to left child and
a pointer to right child */
class Node {
    public int data;
    public Node left, right;

    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}

class BinaryTree {
    Node root;

    /* Returns true if the given
   tree is foldable */
    Boolean isFoldable(Node node)
    {
        Boolean res;

        /* base case */
        if (node == null)
            return true;

        /* convert left subtree
       to its mirror */
        mirror(node.left);

        /* Compare the structures of the
       right subtree and mirrored
       left subtree */
        res = isStructSame(node.left, node.right);

        /* Get the original tree back */
        mirror(node.left);

        return res;
    }

    Boolean isStructSame(Node a, Node b)
    {
        if (a == null && b == null)
            return true;
        if (a != null && b != null
            && isStructSame(a.left, b.left)
            && isStructSame(a.right, b.right))
            return true;

        return false;
    }

    /* UTILITY FUNCTIONS */

    /* Change a tree so that the roles
of the left and right pointers are
swapped at every node.
See https:// www.geeksforgeeks.org/?p=662
for details */
    void mirror(Node node)
    {
        if (node == null)
            return;
        else {
            Node temp;

            /* do the subtrees */
            mirror(node.left);
            mirror(node.right);

            /* swap the pointers in this node */
            temp = node.left;
            node.left = node.right;
            node.right = temp;
        }
    }

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

        /* The constructed binary tree is
                    1
                 /     \
                2        3
                 \     /
                 4    5
    */
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.right.left = new Node(4);
        tree.root.left.right = new Node(5);

        if (tree.isFoldable(tree.root))
            Console.WriteLine("tree is foldable");
        else
            Console.WriteLine("Tree is not foldable");
    }
}

// This code is contributed by Arnab Kundu

Javascript

<script>

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

    }
}

function isFoldable(node)
{
    let res;

        /* base case */
        if (node == null)
            return true;

        /* convert left subtree to its mirror */
        mirror(node.left);

        /* Compare the structures of the right subtree and mirrored
         left subtree */
        res = isStructSame(node.left, node.right);

        /* Get the original tree back */
        mirror(node.left);

        return res;
}

function isStructSame(a,b)
{
    if (a == null && b == null)
            return true;
        if (a != null && b != null
            && isStructSame(a.left, b.left)
            && isStructSame(a.right, b.right))
            return true;

        return false;
}

function mirror(node)
{
    if (node == null)
            return;
        else {
            let temp;

            /* do the subtrees */
            mirror(node.left);
            mirror(node.right);

            /* swap the pointers in this node */
            temp = node.left;
            node.left = node.right;
            node.right = temp;
        }
}

/* The constructed binary tree is
             1
           /   \
          2     3
           \    /
            4  5
        */
let root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.right.left = new Node(4);
root.left.right = new Node(5);

if (isFoldable(root))
    document.write("tree is foldable");
else
    document.write("Tree is not foldable");



// This code is contributed by avanitrachhadiya2155

</script>

Output

tree is foldable

Time complexity: O(N), Visiting all the nodes of the tree of size N.
Auxiliary Space: O(N), If stack space is considered else O(1)

Thanks to ajaym for suggesting this approach. 

Foldable Binary Trees by Checking if Left and Right subtrees are Mirror:

The idea is to check the left and right subtree whether they are mirror or not.

Follow the steps below to solve the problem:

• If tree is empty then return true.
• Else check if left and right subtrees are structure wise mirrors of each other. Use utility function IsFoldableUtil(root->left, root->right) for this.
• Checks if n1 and n2 are mirror of each other.
  • If both trees are empty then return true. 
  • If one of them is empty and other is not then return false. 
  • Return true if following conditions are met
    • n1->left is mirror of n2->right
    • n1->right is mirror of n2->left

Below is the implementation of the above approach.

C++

#include <bits/stdc++.h>
using namespace std;

/* You would want to remove below 3 lines if your compiler
supports bool, true and false */

/* A binary tree node has data, pointer to left child
and a pointer to right child */
class node {
public:
    int data;
    node* left;
    node* right;
};

/* A utility function that checks
if trees with roots as n1 and n2
are mirror of each other */
bool IsFoldableUtil(node* n1, node* n2);

/* Returns true if the given tree can be folded */
bool IsFoldable(node* root)
{
    if (root == NULL) {
        return true;
    }

    return IsFoldableUtil(root->left, root->right);
}

/* A utility function that checks
if trees with roots as n1 and n2
are mirror of each other */
bool IsFoldableUtil(node* n1, node* n2)
{
    /* If both left and right subtrees are NULL,
    then return true */
    if (n1 == NULL && n2 == NULL) {
        return true;
    }

    /* If one of the trees is NULL and other is not,
    then return false */
    if (n1 == NULL || n2 == NULL) {
        return false;
    }

    /* Otherwise check if left and right subtrees are
    mirrors of their counterparts */
    return IsFoldableUtil(n1->left, n2->right)
           && IsFoldableUtil(n1->right, n2->left);
}

/*UTILITY FUNCTIONS */
/* Helper function that allocates a new node with the
given data and NULL left and right pointers. */
node* newNode(int data)
{
    node* Node = new node();
    Node->data = data;
    Node->left = NULL;
    Node->right = NULL;

    return (Node);
}

/* Driver code */
int main(void)
{
    /* The constructed binary tree is
        1
        / \
        2 3
        \ /
        4 5
    */
    node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->right = newNode(4);
    root->right->left = newNode(5);

    if (IsFoldable(root) == true) {
        cout << "tree is foldable";
    }
    else {
        cout << "tree is not foldable";
    }

    return 0;
}

// This is code is contributed by rathbhupendra

C

#include <stdio.h>
#include <stdlib.h>

/* You would want to remove below 3 lines if your compiler
   supports bool, true and false */
#define bool int
#define true 1
#define false 0

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
struct node {
    int data;
    struct node* left;
    struct node* right;
};

/* A utility function that checks if trees with roots as n1
  and n2 are mirror of each other */
bool IsFoldableUtil(struct node* n1, struct node* n2);

/* Returns true if the given tree can be folded */
bool IsFoldable(struct node* root)
{
    if (root == NULL) {
        return true;
    }

    return IsFoldableUtil(root->left, root->right);
}

/* A utility function that checks if trees with roots as n1
  and n2 are mirror of each other */
bool IsFoldableUtil(struct node* n1, struct node* n2)
{
    /* If both left and right subtrees are NULL,
      then return true */
    if (n1 == NULL && n2 == NULL) {
        return true;
    }

    /* If one of the trees is NULL and other is not,
      then return false */
    if (n1 == NULL || n2 == NULL) {
        return false;
    }

    /* Otherwise check if left and right subtrees are
       mirrors of their counterparts */
    return IsFoldableUtil(n1->left, n2->right)
           && IsFoldableUtil(n1->right, n2->left);
}

/*UTILITY FUNCTIONS */
/* Helper function that allocates a new node with the
   given data and NULL left and right pointers. */
struct node* newNode(int data)
{
    struct node* node
        = (struct node*)malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;

    return (node);
}

/* Driver program to test mirror() */
int main(void)
{
    /* The constructed binary tree is
         1
       /   \
      2     3
      \    /
       4  5
  */
    struct node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->right = newNode(4);
    root->right->left = newNode(5);

    if (IsFoldable(root) == true) {
        printf("\n tree is foldable");
    }
    else {
        printf("\n tree is not foldable");
    }

    getchar();
    return 0;
}

Java

// Java program to check foldable binary tree

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
class Node {
    int data;
    Node left, right;

    Node(int item)
    {
        data = item;
        left = right = null;
    }
}

class BinaryTree {
    Node root;

    /* Returns true if the given tree can be folded */
    boolean IsFoldable(Node node)
    {
        if (node == null)
            return true;

        return IsFoldableUtil(node.left, node.right);
    }

    /* A utility function that checks if trees with roots as
     n1 and n2 are mirror of each other */
    boolean IsFoldableUtil(Node n1, Node n2)
    {

        /* If both left and right subtrees are NULL,
         then return true */
        if (n1 == null && n2 == null)
            return true;

        /* If one of the trees is NULL and other is not,
         then return false */
        if (n1 == null || n2 == null)
            return false;

        /* Otherwise check if left and right subtrees are
         mirrors of their counterparts */
        return IsFoldableUtil(n1.left, n2.right)
            && IsFoldableUtil(n1.right, n2.left);
    }

    /* Driver program to test above functions */
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();

        /* The constructed binary tree is
             1
           /   \
          2     3
           \    /
            4  5
        */
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.right.left = new Node(4);
        tree.root.left.right = new Node(5);

        if (tree.IsFoldable(tree.root))
            System.out.println("tree is foldable");
        else
            System.out.println("Tree is not foldable");
    }
}

// This code has been contributed by Mayank Jaiswal

Python3

# Python3 program to check
# foldable binary tree

# Utility function to create a new
# tree node


class newNode:
    def __init__(self, data):
        self.data = data
        self.left = self.right = None

# Returns true if the given tree can be folded


def IsFoldable(root):
    if (root == None):
        return True
    return IsFoldableUtil(root.left, root.right)


# A utility function that checks
# if trees with roots as n1 and n2
# are mirror of each other
def IsFoldableUtil(n1, n2):
    # If both left and right subtrees are NULL,
    # then return true
    if n1 == None and n2 == None:
        return True

    # If one of the trees is NULL and other is not,
    # then return false
    if n1 == None or n2 == None:
        return False

    # Otherwise check if left and
    # right subtrees are mirrors of
    # their counterparts

    d1 = IsFoldableUtil(n1.left, n2.right)
    d2 = IsFoldableUtil(n1.right, n2.left)
    return d1 and d2


# Driver code
if __name__ == "__main__":

    """ The constructed binary tree is
    1
    / \
    2 3
    \ /
    4 5
"""
    root = newNode(1)
    root.left = newNode(2)
    root.right = newNode(3)
    root.left.right = newNode(4)
    root.right.left = newNode(5)

    if IsFoldable(root):
        print("tree is foldable")
    else:
        print("tree is not foldable")

# This code is contributed by
# Anupam Baranwal(anupambaranwal)

C#

// C# program to check foldable binary tree
using System;

/* A binary tree node has data, pointer to left child
and a pointer to right child */
public class Node {
    public int data;
    public Node left, right;

    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}

public class BinaryTree {
    Node root;

    /* Returns true if the given tree can be folded */
    bool IsFoldable(Node node)
    {
        if (node == null)
            return true;

        return IsFoldableUtil(node.left, node.right);
    }

    /* A utility function that checks if
    trees with roots as n1 and n2
    are mirror of each other */
    bool IsFoldableUtil(Node n1, Node n2)
    {

        /* If both left and right subtrees are NULL,
        then return true */
        if (n1 == null && n2 == null)
            return true;

        /* If one of the trees is NULL and other is not,
        then return false */
        if (n1 == null || n2 == null)
            return false;

        /* Otherwise check if left and right subtrees are
        mirrors of their counterparts */
        return IsFoldableUtil(n1.left, n2.right)
            && IsFoldableUtil(n1.right, n2.left);
    }

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

        /* The constructed binary tree is
            1
        / \
        2     3
        \ /
            4 5
        */
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.right.left = new Node(4);
        tree.root.left.right = new Node(5);

        if (tree.IsFoldable(tree.root))
            Console.WriteLine("tree is foldable");
        else
            Console.WriteLine("Tree is not foldable");
    }
}

/* This code contributed by PrinciRaj1992 */

Javascript

<script>

    // JavaScript program to check foldable binary tree

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

    let root;

    /* Returns true if the given tree can be folded */
    function IsFoldable(node)
    {
        if (node == null)
            return true;

        return IsFoldableUtil(node.left, node.right);
    }

    /* A utility function that checks if trees with roots as
     n1 and n2 are mirror of each other */
    function IsFoldableUtil(n1, n2)
    {

        /* If both left and right subtrees are NULL,
         then return true */
        if (n1 == null && n2 == null)
            return true;

        /* If one of the trees is NULL and other is not,
         then return false */
        if (n1 == null || n2 == null)
            return false;

        /* Otherwise check if left and right subtrees are
         mirrors of their counterparts */
        return IsFoldableUtil(n1.left, n2.right)
            && IsFoldableUtil(n1.right, n2.left);
    }

    /* The constructed binary tree is
             1
           /   \
          2     3
           \    /
            4  5
        */
    root = new Node(1);
    root.left = new Node(2);
    root.right = new Node(3);
    root.right.left = new Node(4);
    root.left.right = new Node(5);

    if (IsFoldable(root))
      document.write("tree is foldable");
    else
      document.write("Tree is not foldable");

</script>

Output

tree is foldable

Time Complexity: O(N), Visiting every node of the tree of size N.
Auxiliary Space: O(N), If stack space is considered 

Foldable Binary Trees using Breadth first Search:

The idea is to use Queue for traversing the tree and using the BFS approach. 

Follow the steps below to solve the problem:

• The left child of the left subtree = the right child of the right subtree. Both of them should be not null.
• The right child of the left subtree = left child of the right subtree. Both of them should be null or not null.

Below is the implementation of the above approach:

C++

// CPP code for above approach
#include <bits/stdc++.h>
using namespace std;

// Class Node to store the data and left and right
// pointers
class Node
{
public:
    int key;
    Node *left;
    Node *right;

    Node(int key)
    {
        this->key = key;
        left = right = NULL;
    }
};

class FoldableTrees
{
public:
    Node *root = NULL;

    // Function to find whether the tree is foldable
    bool isFoldable()
    {

        // Queue to store visited nodes
        queue<Node *> q;

        // Initially add the left and right nodes of root
        if (root != NULL)
        {
            q.push(root->left);
            q.push(root->right);
        }

        while (!q.empty())
        {

            // Remove the front 2 nodes to
            // check for null condition
            Node *p = q.front();
            q.pop();
            Node *r = q.front();
            q.pop();

            // If both are null, continue and check
            // the further elements
            if (p == NULL && r == NULL)
                continue;

            // If one of them is not null, then return false
            if ((p == NULL && r != NULL) || (p != NULL && r == NULL))
                return false;

            /* Insert in the same order:
            1. left of left subtree
            2. right of right subtree
            3.right of left subtree
            4.left of right subtree */
            q.push(p->left);
            q.push(r->right);
            q.push(p->right);
            q.push(r->left);
        }

        // Only if the tree is foldable
        return true;
    }

    // Driver code
};

int main()
{
    FoldableTrees tree = FoldableTrees();

    // Insert data into the tree
    tree.root = new Node(1);
    tree.root->left = new Node(2);
    tree.root->right = new Node(3);
    tree.root->right->left = new Node(4);
    tree.root->left->right = new Node(5);

    // Function call
    if (tree.isFoldable())
        cout << "tree is foldable" << endl;
    else
        cout << "tree is not foldable" << endl;
}

// This code is contributed by adityamaharshi21

Java

// Java code for the above approach

import java.util.LinkedList;
import java.util.Queue;

public class FoldableTrees {
    Node root = null;


    class Node {
        int key;
        Node left;
        Node right;

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

    // Function to find whether the tree is foldable
    boolean isFoldable()
    {

        // Queue to store visited nodes
        Queue<Node> q = new LinkedList<>();

        // Initially add the left and right nodes of root
        if (root != null) {
            q.add(root.left);
            q.add(root.right);
        }

        while (!q.isEmpty()) {

            // Remove the front 2 nodes to
            // check for null condition
            Node p = q.remove();
            Node r = q.remove();

            // If both are null, continue and check
            // the further elements
            if (p == null && r == null)
                continue;

            // If one of them is not null, then return false
            if ((p == null && r != null)
                || (p != null && r == null))
                return false;

            /* Insert in the same order:
              1. left of left subtree
              2. right of right subtree
              3.right of left subtree
              4.left of right subtree  */
            q.add(p.left);
            q.add(r.right);
            q.add(p.right);
            q.add(r.left);
        }

        // Only if the tree is foldable
        return true;
    }

    // Driver code
    public static void main(String args[])
    {
        FoldableTrees tree = new FoldableTrees();

        // Insert data into the tree
        tree.root = tree.new Node(1);
        tree.root.left = tree.new Node(2);
        tree.root.right = tree.new Node(3);
        tree.root.right.left = tree.new Node(4);
        tree.root.left.right = tree.new Node(5);

        // Function call
        if (tree.isFoldable())
            System.out.println("tree is foldable");
        else
            System.out.println("tree is not foldable");
    }
}

// This method is contributed by likhita AVL

Python3

# class to create a node with key, left child and right child.
class Node:
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None


# Function to find whether the tree is foldable
def isFoldable(root):

     # Queue to store visited nodes
    q = []

    # Initially add the left and right nodes of root
    if root != None:
        q.append(root.left)
        q.append(root.right)

    while (len(q) != 0):

        # Remove the front 2 nodes to
        # check for None condition
        p = q.pop(0)
        r = q.pop(0)

        # If both are None, continue and check
        # the further elements
        if (p == None and r == None):
            continue

        # If one of them is not None, then return False
        if ((p == None and r != None) or (p != None and r == None)):
            return False

        ''' Insert in the same order:
            1. left of left subtree
            2. right of right subtree
            3. right of left subtree
            4. left of right subtree
        '''
        q.append(p.left)
        q.append(r.right)
        q.append(p.right)
        q.append(r.left)

    # Only if the tree is foldable
    return True


# Driver code
# Insert data into the tree
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.right.left = Node(4)
root.left.right = Node(5)

# Function call
if isFoldable(root):
    print("tree is foldable")
else:
    print("tree is not foldable")

    # This code is contributed by mariuscristiancapatina

C#

using System;
using System.Collections.Generic;

public class Node {
    public int key;
    public Node left, right;

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

public class FoldableTrees {
    Node root = null;

    // Function to find whether the tree is foldable
    bool isFoldable()
    {

        // Queue to store visited nodes
        Queue<Node> q = new Queue<Node>();

        // Initially add the left and right nodes of root
        if (root != null) {
            q.Enqueue(root.left);
            q.Enqueue(root.right);
        }

        while (q.Count != 0) {

            // Remove the front 2 nodes to
            // check for null condition
            Node p = q.Dequeue();
            Node r = q.Dequeue();

            // If both are null, continue and check
            // the further elements
            if (p == null && r == null)
                continue;

            // If one of them is not null, then return false
            if ((p == null && r != null)
                || (p != null && r == null))
                return false;

            /* Insert in the same order:
              1. left of left subtree
              2. right of right subtree
              3.right of left subtree
              4.left of right subtree  */
            q.Enqueue(p.left);
            q.Enqueue(r.right);
            q.Enqueue(p.right);
            q.Enqueue(r.left);
        }

        // Only if the tree is foldable
        return true;
    }

    // Driver code
    static public void Main()
    {
        FoldableTrees tree = new FoldableTrees();

        // Insert data into the tree
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.right.left = new Node(4);
        tree.root.left.right = new Node(5);

        // Function call
        if (tree.isFoldable())
            Console.WriteLine("tree is foldable");
        else
            Console.WriteLine("tree is not foldable");
    }
}

// This code is contributed by patel2127.

Javascript

<script>
// Javascript code for the above approach

let root = null;

// Class Node to store the data and left and right pointers
class Node
{
    constructor(key)
    {
        this.key=key;
        this.left=this.right=null;
    }
}

// Function to find whether the tree is foldable
function isFoldable()
{
     // Queue to store visited nodes
        let q = [];

        // Initially add the left and right nodes of root
        if (root != null) {
            q.push(root.left);
            q.push(root.right);
        }

        while (q.length!=0) {

            // Remove the front 2 nodes to
            // check for null condition
            let p = q.shift();
            let r = q.shift();

            // If both are null, continue and check
            // the further elements
            if (p == null && r == null)
                continue;

            // If one of them is not null, then return false
            if ((p == null && r != null) || (p != null && r == null))
                return false;

              /* Insert in the same order:
                1. left of left subtree
                2. right of right subtree
                3.right of left subtree
                4.left of right subtree  */
            q.push(p.left);
            q.push(r.right);
            q.push(p.right);
            q.push(r.left);
        }

        // Only if the tree is foldable
        return true;
}

// Driver code
// Insert data into the tree
root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.right.left = new Node(4);
root.left.right = new Node(5);

// Function call
if(isFoldable())
    document.write("Tree is foldable");
else
    document.write("Tree is not foldable");


// This code is contributed by avanitrachhadiya2155
</script>

Output

tree is foldable

Time complexity: O(N), Visiting all the nodes of the tree of size N.
Auxiliary Space: O(N), Using queue for storing nodes

Please write comments if you find the above code/algorithm incorrect, or find other ways to solve the same problem.