LeetCode 235. Lowest Common Ancestor of a Binary Search Tree

https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/description/

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.

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• 图论题，Tree + 递归。
• 因为是BST，所以可以类似二分查找。如果两个node都 < root，则从左子树找；如果都 > root，则从右子树找；如果一个 <= ，一个 >= ，则正好在两侧或者就是这个root，说明root就是最小公共祖先。注意，节点可以是自己的最小公共祖先。
• Lowest Common Ancestor in a Binary Search Tree. | Algorithms
  • https://algorithms.tutorialhorizon.com/lowest-common-ancestor-in-a-binary-search-tree/

/**
 * 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) {
        if (root == nullptr)
            return root;
        
        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;        
    }
};