235. Lowest Common Ancestor of a Binary Search Tree (E)

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 p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Given binary search tree: root = [6,2,8,0,4,7,9,null,null,3,5]

Example 1:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
Output: 6
Explanation: The LCA of nodes 2 and 8 is 6.

Example 2:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
Output: 2
Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

Note:

• All of the nodes’ values will be unique.
• p and q are different and both values will exist in the BST.

题意

在二叉查找树BST中找到两个指定结点的最近共同祖先。

思路

根据定义，两个结点分列于共同祖先的左右两侧(也可以共同祖先重合)，又有BST的排列规则，可以有以下搜索方法：如果p、q的值都小于当前结点，说明共同祖先只可能在左子树；如果p、q的值都大于当前结点，说明共同祖先只可能在右子树；如果p值小于当前结点、q值大于当前结点，或p值大于当前结点、q值小于当前结点，或p、q中一点就是当前结点，说明当前结点就是要找的共同祖先。

代码实现

class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        while (root != null) {
            if (p.val < root.val && q.val < root.val) {
                root = root.left;
            } else if (p.val > root.val && q.val > root.val) {
                root = root.right;
            } else {
                break;
            }
        }
        return root;
    }
}