# leetcode\_235

## 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.

## Solutions

1. **recursion**

```cpp
/**
 * 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 mid = root->val;
        if (p->val < mid && q->val < mid)
            return lowestCommonAncestor(root->left, p, q);
        else if (p->val > mid && q->val > mid)
            return lowestCommonAncestor(root->right, p, q);
        else
            return root;
    }
};
```

1. **iteration**

```cpp
class Solution {
public:
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        while (root) {
            int mid = root->val;
            if (p->val > mid && q->val > mid)
                root = root->right;
            else if (p->val < mid && q->val < mid)
                root = root->left;
            else
                break;
        }

        return root;
    }
};
```