[LeetCode] 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 2and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

利用BST的性质来进行判断，如果两个子节点的最大值都小于root节点的值，那么他们的最低公共父节点一定在root节点的左侧，如果两个子节点的最小值都大于root节点值，那么他们的最低公共父节点一定在root节点的右侧。如果不符合以上2个情况，则root就是他们的最低公共父节点。

/**
 * 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 || p == nullptr || q == nullptr)
            return root;
        if (max(p->val, q->val) < root->val)
            return lowestCommonAncestor(root->left, p, q);
        else if (min(p->val, q->val) > root->val)
            return lowestCommonAncestor(root->right, p, q);
        else
            return root;
    }
};
// 29 ms