Delete a node from binary search tree in java

If you want to practice data structure and algorithm programs, you can go through 100+ data structure and algorithm interview questions.

In this post, we will see how to delete a node from binary search tree.

There are two parts to it.
  • Search the node
  • After searching that node, delete the node.
There are three cases which we may need to consider while deleting a node from binary search tree.
  • If node has no child
  • If node has one child
  • If node has two children.

If node has no child

It is pretty straight forward case. We need to search the node and make it null.

Delete node of Binary Search tree with no child

If node has one children

If node have one children then we need to connect parent of removed node directly to child of the removed node.

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Delete node of Binary Search tree with one child

If node has two children

It is complicated case. If it has two nodes, we need to connect parent of node to the leftmost node(minimum) of right sub tree or rightmost node(maximum) of left subtree.
Lets understand this case with example:
Delete node of Binary Search tree with two child

As you can see, we are replacing node 40 with node 50. Node 50 is minimum element in right subtree of 40 and deleting node 50 after moving as there will duplicate nodes.

Why minimum element of right sub tree?

Here we are using binary search tree property that tree can be represented in multiple ways.

For example:

Binary Search tree representation

We are using same property while deleting nodes with two children.

Java program to delete node in Binary search tree

When you run above program, you will get following output:


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Comments

  1. Thank you very much for nice explanation.

    There is a small correction to deletion code.
    // Deleting minimum node from right now
    deleteNode(root.right, minNodeForRight.data);

    The above statement should be assigned to root.right, else the duplicate node won’t be removed.

    Thanks,
    Kasi

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