Binary Search Tree Simulator

For every node, all values in the left subtree are smaller and all values in the right subtree are larger. This ordering rule determines search, insertion, deletion, predecessor, successor, minimum, maximum, and sorted traversal behavior.

Balanced operationsO(log n)

Worst-case operationsO(n)

Inorder traversalSorted values

Duplicate policyRejected

BST operations

Integer value

Animation speed 400 ms

Example tree loaded. Choose an operation.

Nodes0

Height0

Leaves0

Comparisons0

Search / operation path

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Traversal result

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Deletion cases

leaf:
  remove it

one child:
  replace it with that child

two children:
  copy the inorder successor
  delete that successor
  from the right subtree

BST concepts

Search decisions

At each node, equality finishes the search. A smaller target moves left; a larger target moves right.

Predecessor and successor

The predecessor is the greatest smaller key. The successor is the smallest larger key. They may be found in a subtree or among ancestors.

Deletion

Deleting a node with two children uses the minimum node in its right subtree, called the inorder successor.

Degeneration

Inserting sorted values can create a chain. The BST stays valid, but height and operation time become linear.

Traversal orders

Traversal	Order	Typical use
Inorder	Left, Root, Right	Read BST values in sorted order.
Preorder	Root, Left, Right	Serialize or copy tree structure.
Postorder	Left, Right, Root	Delete or evaluate subtrees first.
Level order	Breadth by breadth	Inspect the tree one level at a time.