235.lowest-common-ancestor-of-a-binary-search-tree.cpp

//  Tag: Tree, Depth-First Search, Binary Search Tree, Binary Tree
//  Time: O(N)
//  Space: O(H)
//  Ref: -
//  Note: -

//  Given a binary search tree (BST), find the lowest common ancestor (LCA) node 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).”
//   
//  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.
//  
//  Example 3:
//  
//  Input: root = [2,1], p = 2, q = 1
//  Output: 2
//  
//   
//  Constraints:
//  
//  The number of nodes in the tree is in the range [2, 105].
//  -109 <= Node.val <= 109
//  All Node.val are unique.
//  p != q
//  p and q will exist in the BST.
//  
//  

/**
 * 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->val > p->val && root->val > q->val) {
            return lowestCommonAncestor(root->left, p, q);
        }

        if (root->val < p->val && root->val < q->val) {
            return lowestCommonAncestor(root->right, p, q);
        }

        return root;
    }
};