How do I insert a node into a binary search tree?

How do I insert a node into a binary search tree?

To insert a node, start at the root. If the new value is less than the current node, go left; if greater, go right.

What if the tree is empty?

If the tree is empty, the new node becomes the root of the tree.

Can you show me a code example for this?

Sure! Here's a simple Python example:

class Node:
    def __init__(self, key):
        self.left = None
        self.right = None
        self.val = key

    def insert(self, root, key):
        if root is None:
            return Node(key)
        else:
            if root.val < key:
                root.right = self.insert(root.right, key)
            else:
                root.left = self.insert(root.left, key)
        return root

What are the time complexities for insertion?

The average time complexity for insertion in a binary search tree is O(log n), but in the worst case (unbalanced tree), it can be O(n).