How to find the n-th node of the Inorder Traversal of a Binary Tree in C++

By Karun Thannickal

In this tutorial, we will learn how to find the n-th node of the inorder traversal of a Binary Tree in C++.

First, we will quickly recap what inorder traversal of a Binary Tree is.
Then we shall look at how displaying the n-th node of the traversal is different from traversing the entire tree.
Finally, we look at the C++ code to implement this.

Inorder traversal of a Binary Tree in C++

Examples of Linear data structures include stacks and queues. Such data structures are usually traversed in one direction. A Binary Tree is a well-known example of a non-linear data structure. Every element in a Binary Tree is also referred to as a node. A node in a Binary tree contains some data. Apart from this it also points to at most 2 nodes (called children). They are known as the left child and right child respectively. The following image shows a Binary Tree and we will refer to this example throughout this tutorial.

The 2 most common approaches to traversing a tree are Breadth-First Searching (BFS) and Depth First Searching (DFS).
Inorder traversal is a DFS approach. The algorithm for Inorder traversal is as follows.

1. Traverse the left sub-tree.
2. Access the data of the current node.
3. Traverse the right sub-tree.

If we display the data in the nodes of the Binary Tree shown in the above image we get

This article has more on Binary Tree Traversals in C++.

Finding the n-th node

In the usual Inorder traversal of a Binary Tree, the entire tree is accessed. That is, we go through all the nodes of the tree. Our problem in this tutorial is to display the n-th node of a given Binary Tree.

Consider the Binary Tree shown above. If, say, n is 4, we are required to output only ’12’.

There are 2 simple ways to implement this both having the same idea.

1. Use a static counter variable within the ‘n-th node function’.
2. Use a global counter variable.

We shall look at the method with the static counter variable in this tutorial.

Algorithm

Within the function ‘nth_in_order’ that takes a node address and ‘n’ as parameters,

1. Initialize static variable ‘ct’ to 0.
2. Perform Inorder traversal with ‘ct’ incremented at every node.
3. If ‘ct’ is equal to ‘n’, display the data in the node and return to the calling function.

Code: find the n-th node of the Inorder Traversal of a Binary Tree in C++

#include <iostream>
#include <vector>

using namespace std;

struct node //We create a node structure having 
            //1 integer datatype and 2 children
{
  int data;
  node* left;
  node* right;
};

node* new_node(int d) // Function to ensure proper 
                      // creation of new nodes in main()
{
  node* n;
  do
  {
    n = (node*)malloc(sizeof(node));
  } while (n == NULL); // The do-while loop ensures 
                       // that n is created properly

  n->data = d;
  n->left = NULL;
  n->right = NULL;

  
  return n;
}


void nth_in_order(node* ptr, int n) // This function prints the n-th node 
                                    // in the inorder traversal of
                                    // the created Binary Tree
{
  static int ct = 0;

  if (ptr == NULL)
    return;

  if (ct <= n)
  {
    nth_in_order(ptr->left, n);
    
    ct++;

    if (ct == n)
    {
      cout << ptr->data << " ";
      return;
    }
    
    
    nth_in_order(ptr->right, n);
  }
  
}


int main()
{
  node* root = new_node(81); 
  root->left = new_node(42);
  root->left->left = new_node(8);
  root->left->left->left = new_node(1);
  root->left->right = new_node(12);
  root->left->right->right = new_node(2);
  root->right = new_node(3);
  root->right->left = new_node(90);
  root->right->right = new_node(4); // I have created the same 
                                    // Binary tree as given in the
                                    // examples in the tutorial

  int n;
  cin >> n;

  nth_in_order(root, n);
 		
  return 0;
}

Example Input

4

Example Output

12

Conclusion

In this tutorial, we have seen how to display the n-th node in the inorder traversal of a Binary Tree using C++.
Note: We have assumed that the user enters a valid value for ‘n’.

You can also learn about a more efficient traversal here.
Morris Inorder Tree Traversal in C++