> For the complete documentation index, see [llms.txt](https://blog.yushunchen.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://blog.yushunchen.com/algo/binary-tree/3.-binary-search-tree/remove-node-in-binary-search-tree.md).

# Remove Node in Binary Search Tree

{% embed url="<https://www.lintcode.com/problem/87/>" %}

## Solution 1 (Java)

```java
/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */


public class Solution {
    /*
     * @param root: The root of the binary search tree.
     * @param value: Remove the node with given value.
     * @return: The root of the binary search tree after removal.
     */
    public TreeNode removeNode(TreeNode root, int value) {
        if (root == null)
            return root;
        if (value < root.val) {
            root.left = removeNode(root.left, value);
        } else if (value > root.val) {
            root.right = removeNode(root.right, value);
        } else {
            if (root.left == null && root.right == null)
                return null;
            if (root.left == null)
                return root.right;
            if (root.right == null)
                return root.left;
            
            int predecessor = findPred(root.left);
            root.val = predecessor;
            root.left = removeNode(root.left, predecessor);
        }
        return root;
    }

    private int findPred(TreeNode root) {
        if (root.right == null) 
            return root.val;
        return findPred(root.right);
    }
}
```

### Notes

First, we use the property of the binary search tree to find the value-matching node. If we find that node, then we have 4 cases:

1. The node is a leaf node. We can directly delete it.
2. The node has one right child, we delete it by returning its right child.
3. The node has one left child, we delete it by returning its left child.
4. The node has two children. We find its predecessor node, which is the node that has the maximum value that is less than the node's value. We replace the node with its predecessor and remove the old position of its predecessor. Here, we can also use successor, which is the node that has the minimum value that is larger then the nodes' value.


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://blog.yushunchen.com/algo/binary-tree/3.-binary-search-tree/remove-node-in-binary-search-tree.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.