Iterative Approach to check if two Binary Trees are Isomorphic or not

Given two Binary Trees we have to detect if the two trees are Isomorphic. Two trees are called isomorphic if one of them can be obtained from another by a series of flips, i.e. by swapping left and right children of a number of nodes. Any number of nodes at any level can have their children swapped.

Note: Two empty trees are isomorphic.

For example, the following two trees are isomorphic with the following sub-trees flipped: 2 and 3, NULL and 6, 7, and 8.

Approach:



To solve the question mentioned above we traverse both the trees iteratively using level order traversal and store the levels in a queue data structure. There are following two conditions at each level:

  • Value of nodes has to be same.
  • Number of nodes at each level should be same.

Check the size of the queue to match the second condition mentioned above. Store the nodes of each level of the first tree as key with a value and for the second tree we will store all the nodes of a level in a vector. If the key is found we will decrease the value so as to keep track of how many nodes with the same value exists at a level. If value becomes zero that means the first tree has only this much number of nodes and we will remove it as a key. At the end of each level we will iterate through the array and check whether each value exists on the map or not. There will be three conditions:

  • If the key is not found then the first tree doesn’t contain a node found in the second tree at the same level.
  • If the key is found but the value becomes negative then the second tree has more nodes with the same value than first tree.
  • If map size is not zero, this means there are some keys still left which means the first tree has a node which doesn’t match with any node in the second tree.

Below is the implementation of the above approach:

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// C++ program to find two
// Binary Tree are Isomorphic or not
  
#include <bits/stdc++.h>
using namespace std;
  
/* A binary tree node has data,
pointer to left and right children */
struct node {
    int data;
    struct node* left;
    struct node* right;
};
  
/* function to retun if
   tree are isomorphic or not*/
bool isIsomorphic(node* root1, node* root2)
{
    // if Both roots are null
    // then tree is isomorphic
    if (root1 == NULL and root2 == NULL)
        return true;
  
    // check if one node is false
    else if (root1 == NULL or root2 == NULL)
        return false;
  
    queue<node *> q1, q2;
  
    // enqueue roots
    q1.push(root1);
    q2.push(root2);
  
    int level = 0;
    int size;
  
    vector<int> v2;
  
    unordered_map<int, int> mp;
  
    while (!q1.empty() and !q2.empty()) {
  
        // check if no. of nodes are
        // not same at a given level
        if (q1.size() != q2.size())
            return false;
  
        size = q1.size();
  
        level++;
  
        v2.clear();
        mp.clear();
  
        while (size--) {
  
            node* temp1 = q1.front();
            node* temp2 = q2.front();
  
            // dequeue the nodes
            q1.pop();
            q2.pop();
  
            // check if value
            // exists in the map
            if (mp.find(temp1->data) == mp.end())
                mp[temp1->data] = 1;
  
            else
                mp[temp1->data]++;
  
            v2.push_back(temp2->data);
  
            // enqueue the child nodes
            if (temp1->left)
                q1.push(temp1->left);
  
            if (temp1->right)
                q1.push(temp1->right);
  
            if (temp2->left)
                q2.push(temp2->left);
  
            if (temp2->right)
                q2.push(temp2->right);
        }
  
        // Iterate through each node at a level
        // to check whether it exists or not.
        for (auto i : v2) {
  
            if (mp.find(i) == mp.end())
                return false;
  
            else {
                mp[i]--;
  
                if (mp[i] < 0)
                    return false;
  
                else if (mp[i] == 0)
                    mp.erase(i);
            }
        }
  
        // check if the key remain
        if (mp.size() != 0)
            return false;
    }
    return true;
}
  
/* function that allocates a new node with the 
given data and NULL left and right pointers. */
node* newnode(int data)
{
    node* temp = new node;
    temp->data = data;
    temp->left = NULL;
    temp->right = NULL;
  
    return (temp);
}
  
/* Driver program*/
  
int main()
{
    // create tree
    struct node* n1 = newnode(1);
    n1->left = newnode(2);
    n1->right = newnode(3);
    n1->left->left = newnode(4);
    n1->left->right = newnode(5);
    n1->right->left = newnode(6);
    n1->left->right->left = newnode(7);
    n1->left->right->right = newnode(8);
  
    struct node* n2 = newnode(1);
    n2->left = newnode(3);
    n2->right = newnode(2);
    n2->right->left = newnode(4);
    n2->right->right = newnode(5);
    n2->left->right = newnode(6);
    n2->right->right->left = newnode(8);
    n2->right->right->right = newnode(7);
  
    if (isIsomorphic(n1, n2) == true)
        cout << "Yes";
    else
        cout << "No";
  
    return 0;
}

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Output:

Yes

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