Foldable Binary Trees
Question: Given a binary tree, find out if the tree can be folded or not.
A tree can be folded if left and right subtrees of the tree are structure wise mirror image of each other. An empty tree is considered as foldable.
Consider the below trees:
(a) and (b) can be folded.
(c) and (d) cannot be folded.
(a)
10
/ \
7 15
\ /
9 11
(b)
10
/ \
7 15
/ \
9 11
(c)
10
/ \
7 15
/ /
5 11
(d)
10
/ \
7 15
/ \ /
9 10 12Method 1 (Change Left subtree to its Mirror and compare it with Right subtree)
Algorithm: isFoldable(root)
1) If tree is empty, then return true.
2) Convert the left subtree to its mirror image
mirror(root->left); /* See this post */
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.
mirror(root->left);
5) Return result res stored in step 2.Thanks to ajaym for suggesting this approach.
C++
// C++ program to check foldable binary tree#include <bits/stdc++.h>using namespace std;/* You would want to remove below3 lines if your compiler supportsbool, true and false */#define bool int#define true 1#define false 0/* A binary tree node has data,pointer to left child and apointer to right child */class node {public: int data; node* left; node* right;};/* converts a tree to its mrror image */void mirror(node* node);/* returns true if structure oftwo trees a and b is same onlystructure 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 originial 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 thegiven 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->right->left = newNode(4); root->left->right = 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 mrror 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 originial 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 originial 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 |
C#
// C# program to check foldable// binary treeusing System;/* A binary tree node has data,pointer to left child anda 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 originial 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 rolesof the left and right pointers areswapped at every node.See https:// www.geeksforgeeks.org/?p=662for 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 |
Output
tree is foldable
Time complexity: O(n)
Method 2 (Check if Left and Right subtrees are Mirror)
There are mainly two functions:
// Checks if tree can be folded or not
IsFoldable(root)
1) If tree is empty then return true
2) 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.
IsFoldableUtil(n1, n2) 1) If both trees are empty then return true. 2) If one of them is empty and other is not then return false. 3) Return true if following conditions are met a) n1->left is mirror of n2->right b) n1->right is mirror of n2->left
C++
#include <bits/stdc++.h>using namespace std;/* You would want to remove below 3 lines if your compilersupports bool, true and false */#define bool int#define true 1#define false 0/* A binary tree node has data, pointer to left childand a pointer to right child */class node {public: int data; node* left; node* right;};/* A utility function that checksif trees with roots as n1 and n2are 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 checksif trees with roots as n1 and n2are 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 thegiven 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 nodeclass newNode: def __init__(self, data): self.data = data self.left = self.right = None# Returns true if the given tree can be foldeddef 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 otherdef 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 codeif __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 treeusing System;/* A binary tree node has data, pointer to left childand 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 */ |
Output
tree is foldable
Thanks to Dzmitry Huba for suggesting this approach.
Please write comments if you find the above code/algorithm incorrect, or find other ways to solve the same problem.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
