Lowest Common Ancestor of a Binary Search Tree

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 nodes2and8is6. Another example is LCA of nodes2and4is2, since a node can be a descendant of itself according to the LCA definition.

Solution:

We must understand the all tree conditions that could happen for a LCA from the basic problem LCA of a binary tree. After we understand that, we knew that in a BST, we can judge if current root is our LCA by comparing their values. In addition, we can also figure out which direction (left/right) we should go in the tree to find our LCA.

public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
    if (root == null) {
        return null;
    }
    if (root.val < p.val && root.val > q.val) {
        return root;
    }
    if (root.val > p.val && root.val < q.val) {
        return root;
    }
    if (root == p || root == q) {
        return root;
    }
    return root.val > p.val && root.val > q.val ? lowestCommonAncestor(root.left, p, q) : lowestCommonAncestor(root.right, p, q);
}