Merge Two Binary Trees by doing Node Sum (Recursive and Iterative) - GeeksforGeeks

17 Apr, 2022
Given two binary trees. We need to merge them into a new binary tree. The merge rule is that if two nodes overlap, then sum node values up as the new value of the merged node. Otherwise, the non-null node will be used as the node of new tree.
Example:  
Input: 
     Tree 1            Tree 2                  
       2                 3                             
      / \               / \                            
     1   4             6   1                        
    /                   \   \                      
   5                     2   7                  

Output: Merged tree:
         5
        / \
       7   5
      / \   \ 
     5   2   7
Note: The merging process must start from the root nodes of both trees.  
Recursive Algorithm: 
Traverse the tree in Pre-order fashionCheck if both the tree nodes are NULL If not, then update the valueRecur for left subtreesRecur for right subtreesReturn root of updated Tree
Traverse the tree in Pre-order fashion
Check if both the tree nodes are NULL If not, then update the value
If not, then update the value
If not, then update the value
Recur for left subtrees
Recur for right subtrees
Return root of updated Tree
C++
C
Java
Python3
C#
Javascript
// C++ program to Merge Two Binary Trees#include <bits/stdc++.h>using namespace std; /* A binary tree node has data, pointer to left child   and a pointer to right child */struct Node{    int data;    struct Node *left, *right;}; /* Helper function that allocates a new node with the   given data and NULL left and right pointers. */Node *newNode(int data){    Node *new_node = new Node;    new_node->data = data;    new_node->left = new_node->right = NULL;    return new_node;} /* Given a binary tree, print its nodes in inorder*/void inorder(Node * node){    if (!node)        return;    /* first recur on left child */    inorder(node->left);    /* then print the data of node */    cout<<node->data<<" ";    /* now recur on right child */    inorder(node->right);} /* Function to merge given two binary trees*/Node *MergeTrees(Node * t1, Node * t2){    if (!t1)        return t2;    if (!t2)        return t1;    t1->data += t2->data;    t1->left = MergeTrees(t1->left, t2->left);    t1->right = MergeTrees(t1->right, t2->right);    return t1;} // Driver codeint main(){    /* Let us construct the first Binary Tree            1          /   \         2     3        / \     \       4   5     6    */     Node *root1 = newNode(1);    root1->left = newNode(2);    root1->right = newNode(3);    root1->left->left = newNode(4);    root1->left->right = newNode(5);    root1->right->right = newNode(6);     /* Let us construct the second Binary Tree           4         /   \        1     7       /     /  \      3     2    6   */    Node *root2 = newNode(4);    root2->left = newNode(1);    root2->right = newNode(7);    root2->left->left = newNode(3);    root2->right->left = newNode(2);    root2->right->right = newNode(6);     Node *root3 = MergeTrees(root1, root2);    printf("The Merged Binary Tree is:\n");    inorder(root3);    return 0;} // This code is contributed by Aditya Kumar (adityakumar129)
// C program to Merge Two Binary Trees #include<stdio.h>#include<stdlib.h> /* A binary tree node has data, pointer to left child   and a pointer to right child */typedef struct Node{    int data;    struct Node *left, *right;}Node; /* Helper function that allocates a new node with the   given data and NULL left and right pointers. */Node *newNode(int data){    Node *new_node = (Node *)malloc(sizeof(Node));    new_node->data = data;    new_node->left = new_node->right = NULL;    return new_node;} /* Given a binary tree, print its nodes in inorder*/void inorder(Node * node){    if (!node)        return;    /* first recur on left child */    inorder(node->left);    /* then print the data of node */    printf("%d ", node->data);    /* now recur on right child */    inorder(node->right);} /* Function to merge given two binary trees*/Node *MergeTrees(Node * t1, Node * t2){    if (!t1)        return t2;    if (!t2)        return t1;    t1->data += t2->data;    t1->left = MergeTrees(t1->left, t2->left);    t1->right = MergeTrees(t1->right, t2->right);    return t1;} // Driver codeint main(){    /* Let us construct the first Binary Tree            1          /   \         2     3        / \     \       4   5     6    */     Node *root1 = newNode(1);    root1->left = newNode(2);    root1->right = newNode(3);    root1->left->left = newNode(4);    root1->left->right = newNode(5);    root1->right->right = newNode(6);     /* Let us construct the second Binary Tree           4         /   \        1     7       /     /  \      3     2    6   */    Node *root2 = newNode(4);    root2->left = newNode(1);    root2->right = newNode(7);    root2->left->left = newNode(3);    root2->right->left = newNode(2);    root2->right->right = newNode(6);     Node *root3 = MergeTrees(root1, root2);    printf("The Merged Binary Tree is:\n");    inorder(root3);    return 0;} // This code is contributed by Aditya Kumar (adityakumar129)
// Java program to Merge Two Binary Trees /* A binary tree node has data, pointer to left child   and a pointer to right child */class Node{    int data;    Node left, right;         public Node(int data, Node left, Node right) {        this.data = data;        this.left = left;        this.right = right;    }          /* Helper method that allocates a new node with the     given data and NULL left and right pointers. */     static Node newNode(int data)     {         return new Node(data, null, null);     }           /* Given a binary tree, print its nodes in inorder*/     static void inorder(Node node)     {         if (node == null)             return;                /* first recur on left child */         inorder(node.left);                /* then print the data of node */         System.out.printf("%d ", node.data);                /* now recur on right child */         inorder(node.right);     }           /* Method to merge given two binary trees*/     static Node MergeTrees(Node t1, Node t2)     {         if (t1 == null)             return t2;         if (t2 == null)             return t1;         t1.data += t2.data;         t1.left = MergeTrees(t1.left, t2.left);         t1.right = MergeTrees(t1.right, t2.right);         return t1;     }           // Driver method     public static void main(String[] args)     {         /* Let us construct the first Binary Tree                 1               /   \              2     3             / \     \            4   5     6         */                Node root1 = newNode(1);         root1.left = newNode(2);         root1.right = newNode(3);         root1.left.left = newNode(4);         root1.left.right = newNode(5);         root1.right.right = newNode(6);                /* Let us construct the second Binary Tree                4              /   \             1     7            /     /  \           3     2    6   */         Node root2 = newNode(4);         root2.left = newNode(1);         root2.right = newNode(7);         root2.left.left = newNode(3);         root2.right.left = newNode(2);         root2.right.right = newNode(6);                Node root3 = MergeTrees(root1, root2);         System.out.printf("The Merged Binary Tree is:\n");         inorder(root3);     }}// This code is contributed by Gaurav Miglani
# Python3 program to Merge Two Binary Trees # Helper class that allocates a new node# with the given data and None left and# right pointers.class newNode:    def __init__(self, data):        self.data = data        self.left = self.right = None # Given a binary tree, prints nodes# in inorderdef inorder(node):    if (not node):        return     # first recur on left child    inorder(node.left)     # then print the data of node    print(node.data, end = " ")     # now recur on right child    inorder(node.right) # Function to merge given two# binary treesdef MergeTrees(t1, t2):    if (not t1):        return t2    if (not t2):        return t1    t1.data += t2.data    t1.left = MergeTrees(t1.left, t2.left)    t1.right = MergeTrees(t1.right, t2.right)    return t1 # Driver codeif __name__ == '__main__':         # Let us construct the first Binary Tree    #     1    #     / \    #     2     3    # / \     \    # 4 5     6    root1 = newNode(1)    root1.left = newNode(2)    root1.right = newNode(3)    root1.left.left = newNode(4)    root1.left.right = newNode(5)    root1.right.right = newNode(6)     # Let us construct the second Binary Tree    #     4    #     / \    # 1     7    # /     / \    # 3     2 6    root2 = newNode(4)    root2.left = newNode(1)    root2.right = newNode(7)    root2.left.left = newNode(3)    root2.right.left = newNode(2)    root2.right.right = newNode(6)     root3 = MergeTrees(root1, root2)    print("The Merged Binary Tree is:")    inorder(root3) # This code is contributed by PranchalK
// C# program to Merge Two Binary Treesusing System; /* A binary tree node has data, pointerto left child and a pointer to right child */public class Node{public int data;public Node left, right; public Node(int data, Node left,                      Node right){    this.data = data;    this.left = left;    this.right = right;} /* Helper method that allocates a newnode with the given data and NULL leftand right pointers. */public static Node newNode(int data){    return new Node(data, null, null);} /* Given a binary tree, print its   nodes in inorder*/public static void preorder(Node node){    if (node == null)    {        return;    }       /* then print the data of node */    Console.Write("{0:D} ", node.data);     /* first recur on left child */    inorder(node.left);     /* now recur on right child */    inorder(node.right);} /* Method to merge given two binary trees*/public static Node MergeTrees(Node t1, Node t2){    if (t1 == null)    {        return t2;    }    if (t2 == null)    {        return t1;    }    t1.data += t2.data;    t1.left = MergeTrees(t1.left, t2.left);    t1.right = MergeTrees(t1.right, t2.right);    return t1;} // Driver Codepublic static void Main(string[] args){    /* Let us construct the first Binary Tree            1        / \        2     3        / \     \        4 5     6    */     Node root1 = newNode(1);    root1.left = newNode(2);    root1.right = newNode(3);    root1.left.left = newNode(4);    root1.left.right = newNode(5);    root1.right.right = newNode(6);     /* Let us construct the second Binary Tree            4        / \        1     7        /     / \    3     2 6 */    Node root2 = newNode(4);    root2.left = newNode(1);    root2.right = newNode(7);    root2.left.left = newNode(3);    root2.right.left = newNode(2);    root2.right.right = newNode(6);     Node root3 = MergeTrees(root1, root2);    Console.Write("The Merged Binary Tree is:\n");    preorder(root3);}} // This code is contributed by Shrikant13
<script> // Javascript program to Merge Two Binary Treesclass Node{    constructor(data)    {        this.left = null;        this.right = null;        this.data = data;    }} // Helper method that allocates a new// node with the given data and NULL// left and right pointers.function newNode(data){    return new Node(data);} // Given a binary tree, print its// nodes in inorderfunction inorder(node){    if (node == null)        return;         // First recur on left child    inorder(node.left);         // Then print the data of node    document.write(node.data + " ");         // Now recur on right child    inorder(node.right);}   // Method to merge given two binary treesfunction MergeTrees(t1, t2){    if (t1 == null)        return t2;    if (t2 == null)        return t1;             t1.data += t2.data;    t1.left = MergeTrees(t1.left, t2.left);    t1.right = MergeTrees(t1.right, t2.right);    return t1;} // Driver code/* Let us construct the first Binary Tree             1           /   \          2     3         / \     \        4   5     6     */let root1 = newNode(1);root1.left = newNode(2);root1.right = newNode(3);root1.left.left = newNode(4);root1.left.right = newNode(5);root1.right.right = newNode(6); /* Let us construct the second Binary Tree              4            /   \           1     7          /     /  \         3     2    6   */let root2 = newNode(4);root2.left = newNode(1);root2.right = newNode(7);root2.left.left = newNode(3);root2.right.left = newNode(2);root2.right.right = newNode(6); let root3 = MergeTrees(root1, root2);document.write("The Merged Binary Tree is:" + "</br>");inorder(root3); // This code is contributed by divyeshrabadiya07 </script>
Output: 
The Merged Binary Tree is:
7 3 5 5 2 10 12
Complexity Analysis: 
Time complexity : O(n) A total of n nodes need to be traversed. Here, n represents the minimum number of nodes from the two given trees.
Auxiliary Space : O(n) The depth of the recursion tree can go upto n in case of a skewed tree. In average case, depth will be O(logn).
Iterative Algorithm:
Create a stackPush the root nodes of both the trees onto the stack.While the stack is not empty, perform following steps : Pop a node pair from the top of the stackFor every node pair removed, add the values corresponding to the two nodes and update the value of the corresponding node in the first treeIf the left child of the first tree exists, push the left child(pair) of both the trees onto the stack.If the left child of the first tree doesn’t exist, append the left child of the second tree to the current node of the first treeDo same for right child pair as well.If both the current nodes are NULL, continue with popping the next nodes from the stack.Return root of updated Tree
Create a stack
Push the root nodes of both the trees onto the stack.
While the stack is not empty, perform following steps : Pop a node pair from the top of the stackFor every node pair removed, add the values corresponding to the two nodes and update the value of the corresponding node in the first treeIf the left child of the first tree exists, push the left child(pair) of both the trees onto the stack.If the left child of the first tree doesn’t exist, append the left child of the second tree to the current node of the first treeDo same for right child pair as well.If both the current nodes are NULL, continue with popping the next nodes from the stack.
Pop a node pair from the top of the stackFor every node pair removed, add the values corresponding to the two nodes and update the value of the corresponding node in the first treeIf the left child of the first tree exists, push the left child(pair) of both the trees onto the stack.If the left child of the first tree doesn’t exist, append the left child of the second tree to the current node of the first treeDo same for right child pair as well.If both the current nodes are NULL, continue with popping the next nodes from the stack.
Pop a node pair from the top of the stack
For every node pair removed, add the values corresponding to the two nodes and update the value of the corresponding node in the first tree
If the left child of the first tree exists, push the left child(pair) of both the trees onto the stack.
If the left child of the first tree doesn’t exist, append the left child of the second tree to the current node of the first tree
Do same for right child pair as well.
If both the current nodes are NULL, continue with popping the next nodes from the stack.
Return root of updated Tree
C++
Java
Python3
C#
Javascript
// C++ program to Merge Two Binary Trees#include <bits/stdc++.h>using namespace std; /* A binary tree node has data, pointer to left childand a pointer to right child */struct Node{    int data;    struct Node *left, *right;}; // Structure to store node pair onto stackstruct snode{    Node *l, *r;}; /* Helper function that allocates a new node with thegiven data and NULL left and right pointers. */Node *newNode(int data){    Node *new_node = new Node;    new_node->data = data;    new_node->left = new_node->right = NULL;    return new_node;} /* Given a binary tree, print its nodes in inorder*/void inorder(Node * node){    if (! node)        return;     /* first recur on left child */    inorder(node->left);     /* then print the data of node */    printf("%d ", node->data);     /* now recur on right child */    inorder(node->right);} /* Function to merge given two binary trees*/ Node* MergeTrees(Node* t1, Node* t2){    if (! t1)        return t2;    if (! t2)        return t1;    stack<snode> s;    snode temp;    temp.l = t1;    temp.r = t2;    s.push(temp);    snode n;    while (! s.empty())    {        n = s.top();        s.pop();        if (n.l == NULL|| n.r == NULL)            continue;        n.l->data += n.r->data;        if (n.l->left == NULL)            n.l->left = n.r->left;        else        {            snode t;            t.l = n.l->left;            t.r = n.r->left;            s.push(t);        }        if (n.l->right == NULL)            n.l->right = n.r->right;        else        {            snode t;            t.l = n.l->right;            t.r = n.r->right;            s.push(t);        }    }    return t1;} // Driver codeint main(){    /* Let us construct the first Binary Tree            1          /   \         2     3        / \     \       4   5     6    */      Node *root1 = newNode(1);    root1->left = newNode(2);    root1->right = newNode(3);    root1->left->left = newNode(4);    root1->left->right = newNode(5);    root1->right->right = newNode(6);      /* Let us construct the second Binary Tree           4         /   \        1     7       /     /  \      3     2    6   */    Node *root2 = newNode(4);    root2->left = newNode(1);    root2->right = newNode(7);    root2->left->left = newNode(3);    root2->right->left = newNode(2);    root2->right->right = newNode(6);      Node *root3 = MergeTrees(root1, root2);    printf("The Merged Binary Tree is:\n");    inorder(root3);    return 0;}
// Java program to Merge Two Binary Treesimport java.util.*; class GFG{ /* A binary tree node has data, pointer to left childand a pointer to right child */static class Node{    int data;    Node left, right;}; // Structure to store node pair onto stackstatic class snode{    Node l, r;}; /* Helper function that allocates a new node with thegiven data and null left and right pointers. */static Node newNode(int data){    Node new_node = new Node();    new_node.data = data;    new_node.left = new_node.right = null;    return new_node;} /* Given a binary tree, print its nodes in inorder*/static void inorder(Node  node){    if (node == null)        return;     /* first recur on left child */    inorder(node.left);     /* then print the data of node */    System.out.printf("%d ", node.data);     /* now recur on right child */    inorder(node.right);} /* Function to merge given two binary trees*/ static Node MergeTrees(Node t1, Node t2){    if ( t1 == null)        return t2;    if ( t2 == null)        return t1;    Stack<snode> s = new Stack<>();    snode temp = new snode();    temp.l = t1;    temp.r = t2;    s.add(temp);    snode n;    while (! s.isEmpty())    {        n = s.peek();        s.pop();        if (n.l == null|| n.r == null)            continue;        n.l.data += n.r.data;        if (n.l.left == null)            n.l.left = n.r.left;        else        {            snode t = new snode();            t.l = n.l.left;            t.r = n.r.left;            s.add(t);        }        if (n.l.right == null)            n.l.right = n.r.right;        else        {            snode t = new snode();            t.l = n.l.right;            t.r = n.r.right;            s.add(t);        }    }    return t1;} // Driver codepublic static void main(String[] args){    /* Let us construct the first Binary Tree            1          /   \         2     3        / \     \       4   5     6    */      Node root1 = newNode(1);    root1.left = newNode(2);    root1.right = newNode(3);    root1.left.left = newNode(4);    root1.left.right = newNode(5);    root1.right.right = newNode(6);      /* Let us construct the second Binary Tree           4         /   \        1     7       /     /  \      3     2    6   */    Node root2 = newNode(4);    root2.left = newNode(1);    root2.right = newNode(7);    root2.left.left = newNode(3);    root2.right.left = newNode(2);    root2.right.right = newNode(6);      Node root3 = MergeTrees(root1, root2);    System.out.printf("The Merged Binary Tree is:\n");    inorder(root3);}} // This code is contributed by gauravrajput1
# Python3 program to Merge Two Binary Trees  ''' A binary tree node has data, pointer to left childand a pointer to right child '''class Node:         def __init__(self, data):                 self.data = data        self.left = None        self.right = None         # Structure to store node pair onto stackclass snode:         def __init__(self, l, r):                 self.l = l        self.r = r  ''' Helper function that allocates a new node with thegiven data and None left and right pointers. '''def newNode(data):     new_node = Node(data)    return new_node     ''' Given a binary tree, print its nodes in inorder'''def inorder(node):     if (not node):        return;      ''' first recur on left child '''    inorder(node.left);      ''' then print the data of node '''    print(node.data, end=' ');      ''' now recur on right child '''    inorder(node.right);  ''' Function to merge given two binary trees'''  def MergeTrees(t1, t2):     if (not t1):        return t2;    if (not t2):        return t1;    s = []         temp = snode(t1, t2)         s.append(temp);    n = None         while (len(s) != 0):             n = s[-1]        s.pop();                 if (n.l == None or n.r == None):            continue;                     n.l.data += n.r.data;        if (n.l.left == None):            n.l.left = n.r.left;        else:            t=snode(n.l.left, n.r.left)            s.append(t);                 if (n.l.right == None):            n.l.right = n.r.right;        else:             t=snode(n.l.right, n.r.right)            s.append(t);             return t1;  # Driver codeif __name__=='__main__':         ''' Let us construct the first Binary Tree            1          /   \         2     3        / \     \       4   5     6    '''       root1 = newNode(1);    root1.left = newNode(2);    root1.right = newNode(3);    root1.left.left = newNode(4);    root1.left.right = newNode(5);    root1.right.right = newNode(6);       ''' Let us construct the second Binary Tree           4         /   \        1     7       /     /  \      3     2    6   '''         root2 = newNode(4);    root2.left = newNode(1);    root2.right = newNode(7);    root2.left.left = newNode(3);    root2.right.left = newNode(2);    root2.right.right = newNode(6);       root3 = MergeTrees(root1, root2);    print("The Merged Binary Tree is:");    inorder(root3);     # This code is contributed by rutvik76
// C# program to Merge Two Binary Treesusing System;using System.Collections.Generic; class GFG{ // A binary tree node has data, pointer// to left child and a pointer to right// childpublic class Node{    public int data;    public Node left, right;}; // Structure to store node pair onto stackpublic class snode{    public Node l, r;}; // Helper function that allocates a new// node with the given data and null// left and right pointers.static Node newNode(int data){    Node new_node = new Node();    new_node.data = data;    new_node.left = new_node.right = null;    return new_node;} // Given a binary tree, print its// nodes in inorderstatic void inorder(Node  node){    if (node == null)        return;     // First recur on left child    inorder(node.left);     // Then print the data of node    Console.Write(node.data + " ");     // Now recur on right child    inorder(node.right);} // Function to merge given two binary treesstatic Node MergeTrees(Node t1, Node t2){    if ( t1 == null)        return t2;    if ( t2 == null)        return t1;             Stack<snode> s = new Stack<snode>();    snode temp = new snode();    temp.l = t1;    temp.r = t2;    s.Push(temp);    snode n;         while (s.Count != 0)    {        n = s.Peek();        s.Pop();                 if (n.l == null|| n.r == null)            continue;                     n.l.data += n.r.data;                 if (n.l.left == null)            n.l.left = n.r.left;        else        {            snode t = new snode();            t.l = n.l.left;            t.r = n.r.left;            s.Push(t);        }                 if (n.l.right == null)            n.l.right = n.r.right;        else        {            snode t = new snode();            t.l = n.l.right;            t.r = n.r.right;            s.Push(t);        }    }    return t1;} // Driver codepublic static void Main(String[] args){    /* Let us construct the first Binary Tree            1          /   \         2     3        / \     \       4   5     6    */    Node root1 = newNode(1);    root1.left = newNode(2);    root1.right = newNode(3);    root1.left.left = newNode(4);    root1.left.right = newNode(5);    root1.right.right = newNode(6);      /* Let us construct the second Binary Tree           4         /   \        1     7       /     /  \      3     2    6   */    Node root2 = newNode(4);    root2.left = newNode(1);    root2.right = newNode(7);    root2.left.left = newNode(3);    root2.right.left = newNode(2);    root2.right.right = newNode(6);      Node root3 = MergeTrees(root1, root2);         Console.Write("The Merged Binary Tree is:\n");         inorder(root3);}} // This code is contributed by aashish1995
<script>  // JavaScript program to Merge Two Binary Trees  /* A binary tree node has data, pointer to left childand a pointer to right child */class Node{    constructor()    {        this.data=0;        this.left=this.right=null;    }}    // Structure to store node pair onto stackclass snode{    constructor()    {        this.l=null;        this.r=null;    }}  /* Helper function that allocates a new node with thegiven data and null left and right pointers. */function newNode(data){    let new_node = new Node();    new_node.data = data;    new_node.left = new_node.right = null;    return new_node;}  /* Given a binary tree, print its nodes in inorder*/function inorder(node){    if (node == null)        return;       /* first recur on left child */    inorder(node.left);       /* then print the data of node */    document.write(node.data+" ");       /* now recur on right child */    inorder(node.right);}  /* Function to merge given two binary trees*/function MergeTrees(t1,t2){    if ( t1 == null)        return t2;    if ( t2 == null)        return t1;    let s = [];    let temp = new snode();    temp.l = t1;    temp.r = t2;    s.push(temp);    let n;    while ( s.length!=0)    {        n = s.pop();                  if (n.l == null|| n.r == null)            continue;        n.l.data += n.r.data;        if (n.l.left == null)            n.l.left = n.r.left;        else        {            let t = new snode();            t.l = n.l.left;            t.r = n.r.left;            s.push(t);        }        if (n.l.right == null)            n.l.right = n.r.right;        else        {            let t = new snode();            t.l = n.l.right;            t.r = n.r.right;            s.push(t);        }    }    return t1;}  // Driver code/* Let us construct the first Binary Tree            1          /   \         2     3        / \     \       4   5     6    */  let root1 = newNode(1);root1.left = newNode(2);root1.right = newNode(3);root1.left.left = newNode(4);root1.left.right = newNode(5);root1.right.right = newNode(6);  /* Let us construct second Binary Tree           4         /   \        1     7       /     /  \      3     2    6   */let root2 = newNode(4);root2.left = newNode(1);root2.right = newNode(7);root2.left.left = newNode(3);root2.right.left = newNode(2);root2.right.right = newNode(6);  let root3 = MergeTrees(root1, root2);document.write("The Merged Binary Tree is:<br>");inorder(root3);    // This code is contributed by unknown2108  </script>
Output: 
The Merged Binary Tree is:
7 3 5 5 2 10 12
Complexity Analysis:  
Time complexity : O(n) A total of n nodes need to be traversed. Here, n represents the minimum number of nodes from the two given trees.
Auxiliary Space : O(n) The depth of the stack can go upto n in case of a skewed tree.
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