Here is the detailed explanation of Implementing Binary Trees

A **binary tree **is a non-linear hierarchical data structure consisting of a collection of nodes that stores data forming a hierarchy. It does not store data sequentially as data structures like Arrays, Linked lists, Queues and Stacks do. Instead, it stores data at multiple levels where each level can store at most 2 children nodes.

Implementing a binary tree in Java involves creating classes to represent nodes and the binary tree itself, along with methods for common operations such as insertion, deletion, and searching.

**Below are the basic steps to implement a binary tree in Java:**

**Define the Node class: **

**Create a class to represent the nodes of the binary tree. Each node should have references to its left and right children, as well as the data it stores.**

```
class TreeNode {
int data;
TreeNode left;
TreeNode right;
public TreeNode(int data) {
this.data = data;
this.left = null;
this.right = null;
}
}
```

**Define the BinaryTree class:**

** Create a class to represent the binary tree itself. This class should have a reference to the root node and methods to perform tree operations like insertion, deletion, and searching.**

```
class BinaryTree {
private TreeNode root;
public BinaryTree() {
this.root = null;
}
// Methods for tree operations (insert, delete, search) will go here
}
```

**Implement insertion:**

** Write a method to insert a new node into the binary tree. This method should traverse the tree to find the appropriate position for the new node based on the binary search tree property (left child < parent < right child).**

```
public void insert(int data) {
root = insertRecursive(root, data);
}
private TreeNode insertRecursive(TreeNode root, int data) {
if (root == null) {
return new TreeNode(data);
}
if (data < root.data) {
root.left = insertRecursive(root.left, data);
} else if (data > root.data) {
root.right = insertRecursive(root.right, data);
}
return root;
}
```

**Implement searching: **

**Write a method to search for a value in the binary tree. This method should traverse the tree recursively, comparing the target value with the data in each node.**

```
public boolean search(int data) {
return searchRecursive(root, data);
}
private boolean searchRecursive(TreeNode root, int data) {
if (root == null) {
return false;
}
if (data == root.data) {
return true;
} else if (data < root.data) {
return searchRecursive(root.left, data);
} else {
return searchRecursive(root.right, data);
}
}
```

**Implement deletion:**

** Write a method to delete a node from the binary tree. This method should handle different cases depending on whether the node to be deleted is a leaf node, has one child, or has two children.**

```
public void delete(int data) {
root = deleteRecursive(root, data);
}
private TreeNode deleteRecursive(TreeNode root, int data) {
if (root == null) {
return null;
}
if (data < root.data) {
root.left = deleteRecursive(root.left, data);
} else if (data > root.data) {
root.right = deleteRecursive(root.right, data);
} else {
// Node to delete found
if (root.left == null) {
return root.right;
} else if (root.right == null) {
return root.left;
}
// Node has two children
root.data = minValue(root.right);
root.right = deleteRecursive(root.right, root.data);
}
return root;
}
private int minValue(TreeNode root) {
int minVal = root.data;
while (root.left != null) {
minVal = root.left.data;
root = root.left;
}
return minVal;
}
```