LeetCode 235: Lowest Common Ancestor of a Binary Search Tree

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 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.

解题思路

在二叉查找树中，寻找两个节点的最低公共祖先：

1. 如果a、b都比根节点小，则在左子树中递归查找公共节点。
2. 如果a、b都比根节点大，则在右子树中查找公共祖先节点。
3. 如果a、b一个比根节点大，一个比根节点小，或者有一个等于根节点，则根节点即为最低公共祖先。

代码如下：

/** * Definition for a binary tree node. * struct TreeNode { *     int val; *     TreeNode *left; *     TreeNode *right; *     TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */class Solution {public:    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {        int min_v = min(p->val, q->val);        int max_v = max(p->val, q->val);        if (min_v > root->val) {            return lowestCommonAncestor(root->right, p, q);        }        if (max_v < root->val) {            return lowestCommonAncestor(root->left, p, q);        }        return root;    }};