Sum of Mirror Image Nodes in a Complete Binary Tree in C++

In this problem, we are given a complete binary tree. Our task is to create a program to find the sum of the mirror image nodes of a complete binary tree in an inorder way.

Here, we have to find the inorder traversal of the left sun-tree, and then for each node, we will add the mirror image with it. This means if we are traversing the left leaf node, we will add the value of the right leaf node with it. As it is the mirror image node.

Some important definitions

Complete binary tree is a binary tree where all levels have the highest number of nodes except the last level.

Inorder traversal is a tree traversal technique in which the left subtree is visited first, the root is visited and the right sub-tree is visited.

Let’s take an example to understand the problem,

Input 

Output − 9 9 17 2

Explanation − Inorder traversal of the left subtree is 5-7-8-1.

Adding all nodes will mirror images.

5 + 4 = 9
7 + 2 = 9
8 + 9 = 17
1 + 1 = 2

To solve this problem, we will traverse the binary tree using inorder traversal. We will use two nodes, one to traverse the left subtree and the other to visit the mirror of the node. For example, we have a root node for the left subtree and for it we will have the mirrorroot that will traverse the mirror image of it.

Example

Program to illustrate the working of the solution,

 Live Demo

#include <iostream>
using namespace std;
typedef struct node {
   int data;
   struct node* left;
   struct node* right;
   node(int d){
      data = d;
      left = NULL;
      right = NULL;
   }
} Node;
void printMirrorSum(Node* root, Node* rootMirror){
   if (root->left == NULL && rootMirror->right == NULL)
      return;
   printMirrorSum(root->left, rootMirror->right);
   cout<<(root->left->data + rootMirror->right->data)<<endl;
   printMirrorSum(root->right, rootMirror->left);
}
int main(){
   Node* root = new Node(1);
   root->left = new Node(7);
   root->right = new Node(2);
   root->left->left = new Node(5);
   root->left->right = new Node(8);
   root->right->left = new Node(9);
   root->right->right = new Node(4);
   cout<<"Sum of node and mirror image nodes are :\n";
   printMirrorSum(root, root);
   if (root)
      cout<<(root->data + root->data);
   return 0;
}

Output

Sum of node and mirror image nodes are :
9
9
17
2