# Check if leaf traversal of two Binary Trees is same?

Leaf traversal is sequence of leaves traversed from left to right. The problem is to check if leaf traversals of two given Binary Trees are same or not.
Expected time complexity O(n). Expected auxiliary space O(h1 + h2) where h1 and h2 are heights of two Binary Trees.

Examples:

Input: Roots of below Binary Trees
1
/ \
2   3
/   / \
4   6   7

0
/   \
5     8
\   / \
4   6  7
Output: same
Leaf order traversal of both trees is 4 6 7

Input: Roots of below Binary Trees
0
/ \
1   2
/ \
8   9

1
/ \
4   3
\ / \
8 2  9

Output: Not Same
Leaf traversals of two trees are different.
For first, it is 8 9 2 and for second it is
8 2 9

We strongly recommend you to minimize your browser and try this yourself first.
A Simple Solution is traverse first tree and store leaves from left and right in an array. Then traverse other tree and store leaves in another array. Finally compare two arrays. If both arrays are same, then return true.
The above solution requires O(m+n) extra space where m and n are nodes in first and second tree respectively.
How to check with O(h1 + h2) space?
The idea is use iterative traversal. Traverse both trees simultaneously, look for a leaf node in both trees and compare the found leaves. All leaves must match.

Algorithm:

1. Create empty stacks stack1 and stack2
for iterative traversals of tree1 and tree2

2. insert (root of tree1) in stack1
insert (root of tree2) in stack2

3. Stores current leaf nodes of tree1 and tree2
temp1 = (root of tree1)
temp2 = (root of tree2)

4. Traverse both trees using stacks
while (stack1 and stack2 parent empty)
{
// Means excess leaves in one tree
if (if one of the stacks are empty)
return false

// get next leaf node in tree1
temp1 = stack1.pop()
while (temp1 is not leaf node)
{
push right child to stack1
push left child to stack1
}

// get next leaf node in tree2
temp2 = stack2.pop()
while (temp2 is not leaf node)
{
push right child to stack2
push left child to stack2
}

// If leaves do not match return false
if (temp1 != temp2)
return false
}

5. If all leaves matched, return true

Below is Java implementation of the above algorithm.

 // C++ code to check if leaf traversals // of two Binary Trees are same or not. #include using namespace std;    // Binary Tree Node struct Node {     int data;     Node* left;     Node* right; };    // Returns new Node with data as // input to below function. Node* newNode(int d) {     Node* temp = new Node;     temp->data = d;     temp->left = NULL;     temp->right = NULL;        return temp; }    // checks if a given node is leaf or not. bool isLeaf(Node* root) {     if (root == NULL)         return false;     if (!root->left && !root->right)         return true;     return false; }    // iterative function. // returns true if leaf traversals // are same, else false. bool isSame(Node* root1, Node* root2) {     stack s1;     stack s2;        // push root1 to empty stack s1.     s1.push(root1);        // push root2 to empty stack s2.     s2.push(root2);        // loop until either of stacks are non-empty.     while (!s1.empty() || !s2.empty())      {         // this means one of the stacks has         // extra leaves, hence return false.         if (s1.empty() || s2.empty())             return false;            Node* temp1 = s1.top();         s1.pop();         while (temp1 != NULL && !isLeaf(temp1))         {             // Push right child if exists             if (temp1->right)                 s1.push(temp1->right);                // Push left child if exists             if (temp1->left)                 s1.push(temp1->left);                // Note that right child(if exists)             // is pushed before left child(if exists).             temp1 = s1.top();             s1.pop();         }            Node* temp2 = s2.top();         s2.pop();         while (temp2 != NULL && !isLeaf(temp2))          {             // Push right child if exists             if (temp2->right)                 s2.push(temp2->right);                // Push left child if exists             if (temp2->left)                 s2.push(temp2->left);             temp2 = s2.top();             s2.pop();         }            if (!temp1 && temp2)             return false;         if (temp1 && !temp2)             return false;         if (temp1 && temp2) {             return temp1->data == temp2->data;         }     }        // all leaves are matched     return true; }    // Driver Code int main() {     Node* root1 = newNode(1);     root1->left = newNode(2);     root1->right = newNode(3);     root1->left->left = newNode(4);     root1->right->left = newNode(6);     root1->right->right = newNode(7);        Node* root2 = newNode(0);     root2->left = newNode(1);     root2->right = newNode(5);     root2->left->right = newNode(4);     root2->right->left = newNode(6);     root2->right->right = newNode(7);        if (isSame(root1, root2))         cout << "Same";     else         cout << "Not Same";     return 0; }    // This code is contributed // by AASTHA VARMA

 // Java program to check if two Leaf Traversal of // Two Binary Trees is same or not import java.util.*; import java.lang.*; import java.io.*;    // Binary Tree node class Node  {     int data;     Node left, right;     public Node(int x)     {         data = x;         left = right = null;     }     public boolean isLeaf()     {         return (left == null && right == null);     } }    class LeafOrderTraversal {     // Returns true of leaf traversal of two trees is     // same, else false     public static boolean isSame(Node root1, Node root2)     {         // Create empty stacks.  These stacks are going         // to be used for iterative traversals.         Stack s1 = new Stack();         Stack s2 = new Stack();            s1.push(root1);         s2.push(root2);            // Loop until either of two stacks is not empty         while (!s1.empty() || !s2.empty())         {             // If one of the stacks is empty means other             // stack has extra leaves so return false             if (s1.empty() || s2.empty())                 return false;                Node temp1 = s1.pop();             while (temp1 != null && !temp1.isLeaf())              {                 // Push right and left children of temp1.                 // Note that right child is inserted                 // before left                 if (temp1.right != null)                     s1.push(temp1.right);                 if (temp1.left != null)                     s1.push(temp1.left);                 temp1 = s1.pop();             }                // same for tree2             Node temp2 = s2.pop();             while (temp2 != null && !temp2.isLeaf())              {                 if (temp2.right != null)                     s2.push(temp2.right);                 if (temp2.left != null)                     s2.push(temp2.left);                 temp2 = s2.pop();             }                // If one is null and other is not, then             // return false             if (temp1 == null && temp2 != null)                 return false;             if (temp1 != null && temp2 == null)                 return false;                // If both are not null and data is not             // same return false             if (temp1 != null && temp2 != null)              {                 if (temp1.data != temp2.data)                     return false;             }         }            // If control reaches this point, all leaves         // are matched         return true;     }        // Driver code     public static void main(String[] args)     {         // Let us create trees in above example 1         Node root1 = new Node(1);         root1.left = new Node(2);         root1.right = new Node(3);         root1.left.left = new Node(4);         root1.right.left = new Node(6);         root1.right.right = new Node(7);            Node root2 = new Node(0);         root2.left = new Node(1);         root2.right = new Node(5);         root2.left.right = new Node(4);         root2.right.left = new Node(6);         root2.right.right = new Node(7);            if (isSame(root1, root2))             System.out.println("Same");         else             System.out.println("Not Same");     } }

 # Python3 program to check if two Leaf # Traversal of Two Binary Trees is same or not    # Binary Tree node       class Node:     def __init__(self, x):         self.data = x         self.left = self.right = None        def isLeaf(self):         return (self.left == None and                 self.right == None)    # Returns true of leaf traversal of # two trees is same, else false       def isSame(root1, root2):        # Create empty stacks. These stacks are going     # to be used for iterative traversals.     s1 = []     s2 = []        s1.append(root1)     s2.append(root2)        # Loop until either of two stacks     # is not empty     while (len(s1) != 0 or len(s2) != 0):            # If one of the stacks is empty means other         # stack has extra leaves so return false         if (len(s1) == 0 or len(s2) == 0):             return False            temp1 = s1.pop(-1)         while (temp1 != None and not temp1.isLeaf()):                # append right and left children of temp1.             # Note that right child is inserted             # before left             if (temp1.right != None):                 s1.append(temp1. right)             if (temp1.left != None):                 s1.append(temp1.left)                 temp1 = s1.pop(-1)            # same for tree2         temp2 = s2.pop(-1)         while (temp2 != None and not temp2.isLeaf()):             if (temp2.right != None):                 s2.append(temp2.right)             if (temp2.left != None):                 s2.append(temp2.left)             temp2 = s2.pop(-1)            # If one is None and other is not,         # then return false         if (temp1 == None and temp2 != None):             return False         if (temp1 != None and temp2 == None):             return False            # If both are not None and data is         # not same return false         if (temp1 != None and temp2 != None):             if (temp1.data != temp2.data):                 return False        # If control reaches this point,     # all leaves are matched     return True       # Driver Code if __name__ == '__main__':        # Let us create trees in above example 1     root1 = Node(1)     root1.left = Node(2)     root1.right = Node(3)     root1.left.left = Node(4)     root1.right.left = Node(6)     root1.right.right = Node(7)        root2 = Node(0)     root2.left = Node(1)     root2.right = Node(5)     root2.left.right = Node(4)     root2.right.left = Node(6)     root2.right.right = Node(7)        if (isSame(root1, root2)):         print("Same")     else:         print("Not Same")    # This code is contributed by pranchalK

 // C# program to check if two Leaf Traversal // of Two Binary Trees is same or not using System; using System.Collections.Generic;    // Binary Tree node public class Node {     public int data;     public Node left, right;     public Node(int x)     {         data = x;         left = right = null;     }     public virtual bool Leaf     {         get {            return (left == null && right == null);          }     } }    class GFG {     // Returns true of leaf traversal of     // two trees is same, else false     public static bool isSame(Node root1, Node root2)     {         // Create empty stacks. These stacks         // are going to be used for iterative         // traversals.         Stack s1 = new Stack();         Stack s2 = new Stack();            s1.Push(root1);         s2.Push(root2);            // Loop until either of two stacks         // is not empty         while (s1.Count > 0 || s2.Count > 0)         {             // If one of the stacks is empty means other             // stack has extra leaves so return false             if (s1.Count == 0 || s2.Count == 0)             {                 return false;             }                Node temp1 = s1.Pop();             while (temp1 != null && !temp1.Leaf)              {                 // Push right and left children of temp1.                 // Note that right child is inserted                 // before left                 if (temp1.right != null)                  {                     s1.Push(temp1.right);                 }                 if (temp1.left != null)                  {                     s1.Push(temp1.left);                 }                 temp1 = s1.Pop();             }                // same for tree2             Node temp2 = s2.Pop();             while (temp2 != null && !temp2.Leaf)              {                 if (temp2.right != null)                  {                     s2.Push(temp2.right);                 }                 if (temp2.left != null)                  {                     s2.Push(temp2.left);                 }                 temp2 = s2.Pop();             }                // If one is null and other is not,             // then return false             if (temp1 == null && temp2 != null)              {                 return false;             }             if (temp1 != null && temp2 == null)              {                 return false;             }                // If both are not null and data             // is not same return false             if (temp1 != null && temp2 != null)              {                 if (temp1.data != temp2.data)                  {                     return false;                 }             }         }            // If control reaches this point,         // all leaves are matched         return true;     }        // Driver Code     public static void Main(string[] args)     {         // Let us create trees in above example 1         Node root1 = new Node(1);         root1.left = new Node(2);         root1.right = new Node(3);         root1.left.left = new Node(4);         root1.right.left = new Node(6);         root1.right.right = new Node(7);            Node root2 = new Node(0);         root2.left = new Node(1);         root2.right = new Node(5);         root2.left.right = new Node(4);         root2.right.left = new Node(6);         root2.right.right = new Node(7);            if (isSame(root1, root2)) {             Console.WriteLine("Same");         }         else {             Console.WriteLine("Not Same");         }     } }    // This code is contributed by Shrikant13

Output
Same