Deletion

Deletion is the process of removing a node from a binary tree. When deleting a node, it is important to maintain the properties and structure of the binary tree.

To delete a node from a binary tree, we follow these steps:

1. If the tree is empty, return null.
2. If the node to be deleted is a leaf node (has no children), simply remove the node.
3. If the node to be deleted has only one child, replace the node with its child.
4. If the node to be deleted has two children, find the inorder successor (the node with the smallest key value in the right subtree) and replace the node to be deleted with the inorder successor. Then, recursively delete the inorder successor from the right subtree.

Here is an example implementation of deleting a node from a binary tree in Java:

1{code}

In this example, the deleteNode method takes the root of the binary tree and the key value of the node to be deleted as parameters. It recursively searches for the node to be deleted and performs the deletion based on the three cases mentioned above.

To test the deletion functionality, the example code creates a binary tree and deletes the node with the key value 50. After deleting the node, it performs an inorder traversal and displays the key values of the nodes to verify that the node has been successfully deleted.

Deleting nodes from a binary tree can be a complex operation, particularly when dealing with nodes that have two children. It requires careful consideration of various cases and the rearrangement of the tree structure. Understanding the deletion process is fundamental in effectively managing and manipulating binary trees.

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}

class Main {

  public static void main(String[] args) {

    // replace with your Java logic here

    // Sample code for deleting a node from a binary tree

    // Assume we have a BinaryTreeNode class with properties: key, left, right

    BinaryTreeNode root = createBinaryTree();

    int keyToDelete = 50;

    root = deleteNode(root, keyToDelete);

    System.out.println("After deleting node with key " + keyToDelete + ":");

    inorder(root);

  }

​

  public static BinaryTreeNode deleteNode(BinaryTreeNode root, int key) {

    if (root == null)

      return root;

​

    if (key < root.key)

      root.left = deleteNode(root.left, key);

    else if (key > root.key)

      root.right = deleteNode(root.right, key);

    else {

      if (root.left == null)

        return root.right;

      else if (root.right == null)

        return root.left;

​

      root.key = minValue(root.right);

​

      root.right = deleteNode(root.right, root.key);