Question

This is an interview question. Find the second max in BST.

The max element is the rightmost leaf in the BST. The second max is either its parent or its left child. So the solution is to traverse the BST to find the rightmost leaf and check its parent and left child.

Does it make sense?

Answer 1

Recall that you can list the nodes of a BST in reverse order by doing a modified inorder traversal where you explore the right subtree first. This leads to a simple algorithm:

Node rightmost = findRightmostNode(root)
if (rightmost.left != null) {
    return findRightmostNode(rightmost.left)
else{
    return rightmost.parent
}

It would return null if the tree has only one element.