Lowest Common Ancestor of a Binary Search Tree

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本文介绍了一种在二叉搜索树中寻找两个指定节点的最低公共祖先的有效算法。通过利用二叉搜索树的特点，即每个节点的值都大于其左子树中的任意节点的值且小于其右子树中的任意节点的值，我们能够快速定位到这两个节点的最近共同祖先。

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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.

解法：二插搜索树特点，根节点值大于左子节点值小于右子节点值。设树中任两节点为p和q,分三种情况考虑：
①root.val > p.val && root.val > q.val,说明p和q的LCA在root的左子树中；
②root.val < p.val && root.val < q.val,说明p和q的LCA在root的右子树中；
③其他情况，说明p和q的LCA就是root;

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if(root.val > p.val && root.val > q.val) {
            return lowestCommonAncestor(root.left,p,q);
        }
        else if(root.val < p.val && root.val < q.val) {
            return lowestCommonAncestor(root.right,p,q);
        }
        else {
            return root;
        }
    }
}