lowest_common_ancestor.py

"""
Given a binary search tree (BST),
find the lowest common ancestor (LCA) of two given nodes in the BST.

According to the definition of LCA on Wikipedia:
    “The lowest common ancestor is defined between two
    nodes v and w as the lowest node in T that has both v and w
    as descendants (where we allow a node to be a descendant of itself).”

        _______6______
       /              \
    ___2__          ___8__
   /      \        /      \
   0      _4       7       9
         /  \
         3   5

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6.
Another example is LCA of nodes 2 and 4 is 2,
since a node can be a descendant of itself according to the LCA definition.
"""


def lowest_common_ancestor(root, p, q):
    """
    :type root: Node
    :type p: Node
    :type q: Node
    :rtype: Node
    """
    while root:
        if p.val > root.val < q.val:
            root = root.right
        elif p.val < root.val > q.val:
            root = root.left
        else:
            return root