19. Lowest Common Ancestor of a Binary Search Tree.cpp

/*
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 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.
*/

class Solution
{
public:
  TreeNode *lowestCommonAncestor(TreeNode *root, TreeNode *p, TreeNode *q)
  {
    if (!root)
      return NULL;
    if (root == p || root == q)
      return root;
    if (root->val < p->val && root->val > q->val)
      return root;
    if (root->val > p->val && root->val < q->val)
      return root;
    if (root->val < p->val && root->val < q->val)
      return lowestCommonAncestor(root->right, p, q);
    return lowestCommonAncestor(root->left, p, q);
  }
};