# Find the Index of the Number Using a Binary Tree

Finding out the index of a number within a binary tree is a common task and involves references to its left and right child. The term index in the node typically refers to a position of a node within the tree that allows for efficient navigation and access to specified nodes. The binary tree doesn't have the straightforward concept of the index; rather, they have a structured way in which each nod comprises the left and right node, and then each node narrows down to a leaf node.

Some advantages of the index in the binary tree are: -

1. Indices help in the efficient search and various other searching techniques in the binary tree.
2. It also provides flexibility when it comes to insertion operation, deletion, or we have to make any changes in the node.
3. They are also helpful in handling extensive datasheets due to their logarithmic time complexities.
4. They are also compatible with a variety of different trees such as AVL tree, Red-black Tree, and several others. They can be very beneficial in the storage management process.

In this article, we will explore the concept of finding the index of a binary tree and see the program for the same in different programming languages.

### Implementation

Output: A step-by-step introduction to the code

1. The code begins by including all the necessary headers of the files for carrying out the various input and output operations.
2. Next, we define a 'getSum' function which is responsible for getting the sum and has two parameters, one is BSTree, and the other one is Ind, which is an index.
3. Inside the 'getSum' function, we initialize the value to 0 so that it will store the value of the sum.
4. The 'index' in the BITree will be increased by 1.
5. Next, we must create a while loop and traverse all the ancestors of the currently present node.
6. Inside the loop, the current element of the binary tree is added to the sum.
7. Next, we have to modify the index to the parent node, and we will do that by subtracting the most specific bit.
8. After that, we finally get the sum back as 0.
9. We then create the 'updateBSTree' function, which will update the index in the binary tree.
10. As we saw in the 'getSum' function, the index is incremented by 1 to get matched indexing for the BSTree.
11. Then we create a while loop to traverse all the indexes of the BST.
12. Inside the loop, the value of the present node is added to the BSTree.
13. The primary function of the program serves as the entry point of the program and is used to test the above functions.
14. The 'getSum' function obtains the sum of the elements in the binary tree, and BSTree is generally taken up as the argument, and the result is printed accordingly.

### Example 2)

Output: A step-by-step introduction to the code

1. The code begins by importing the necessary Java packages for the program.
2. Next, we define a 'getSum' function which is responsible for getting the sum and has two parameters, one is BSTree, and the other one is Ind, which is an index.
3. Inside the 'getSum' function, we initialize the value to 0 so that it will store the value of the sum.
4. The 'index' in the BITree will be increased by 1.
5. Next, we have to create a while loop and traverse all the ancestors of the currently present node.
6. Inside the loop, the current element of the binary tree is added to the sum.
7. Next, we have to modify the index to the parent node, and we will do that by subtracting the most specific bit.
8. After that, we finally get the sum back as 0.
9. We then create the 'updateBSTree' function, which will update the index in the binary tree.
10. As we saw in the 'getSum' function, the index is incremented by 1 to get matched indexing for the BSTree.
11. Then we create a while loop to traverse all the indexes of the BST.
12. Inside the loop, the value of the present node is added to the BSTree.
13. The primary function of the program serves as the entry point of the program and is used to test the above functions.
14. The 'getSum' function obtains the sum of the elements in the binary tree, and BSTree is generally taken up as the argument, and the result is printed accordingly.

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