# Find the In-Order Successor of a Node in a Binary Tree

Binary search trees have proven to be vigorous data structures for storing and retrieving elements in the tree. The trees are generally responsible for offering and donating an organized way of nodes and the way in which they will be arranged. This makes them very fit and reliable when it comes to performing various other tasks, such as searching in an ordered set of lists and several other operations. Among the various other operations that a binary search tree can efficiently perform, one such task is determining the in-order successor of the binary tree.

Some advantages of finding the inorder successor of binary search tree are:-

1. It makes the search operation and various other operations significantly easier, and also we can easily find out the time complexity in this.
2. Implementing the iterators becomes very efficient as when we know the inorder successor; it becomes effortless to move forward to keep track of the functionalities, such as keeping track of the iterators.
3. It is also beneficial when it comes to deletion and replacement because when we are deleting a node in the binary tree and we have to perform the in-order successor, we can easily use that to replace the gap after the deletion.

### Implementation

Output:

A step-by-step explanation of the code

1. The code begins by including all the necessary header files to carry out the program's various input and output operations.
2. A structure 'node' is defined that will represent the nodes in a binary tree. A node has three parameters that are data and a pointer to the left and right child.
3. The code will specifically return two function types: one is struct node minValue(struct node* node), and another one is struct node* inOrderSuccessor(struct node* root, struct node* n).
4. The minValue function will help us take the node pointer as input and traverse the whole tree until it reaches the leftmost node in the left subtree, which will have the minimum value.
5. Now, we will consider the in-order successor function in which we take the root node and node n for which we perform the in-order traversal.
6. Next, we define a 'newNode' function to help us allocate memory to the new node and store value in the tree.
7. The 'insert' function will help us to insert a node.
8. The primary function is the entry point of any program, and it creates a binary tree in it.
9. Finally, the program ends with a call to the 'getChar()' function that will wait for input as a character and returns 0 to indicate the successful execution of the program.

### Example 2)

Output:

A step-by-step explanation of the code

1. The code begins by importing the necessary Java packages.
2. A class is defined as named 'Binary Tree', which holds the main logic of the program for inserting nodes in the tree and finding out the minimum value.
3. A structure 'node' is defined that will represent the nodes in a binary tree. It comprises a data value and a pointer to the left and right child.
4. The code will specifically return two function types: one is struct node minValue(struct node* node), and another one is struct node* inOrderSuccessor(struct node* root, struct node* n).
5. The minValue function will help us take the node pointer as input and traverse the whole tree until it reaches the leftmost node in the left subtree, which will have the minimum value.
6. Now, we will consider the inorder successor function in which we take the root node and node n for which we perform the inorder traversal.
7. Next, we define a 'newNode' function to help us allocate memory to the new node and store value in the tree.
8. The 'insert' function will help us to insert a node.
9. The primary function is the entry point of any program, and it creates a binary tree in it.
10. Finally, the program ends with a call to the 'getChar()' function that will wait for input as a character and returns 0 to indicate the successful execution of the program.

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