This method exploits the properties of a BST. The idea is to traverse the tree starting from the root. If both p and q are greater than the current node, then the LCA lies in the right subtree. If both are smaller, then it lies in the left subtree. Otherwise, the current node is the LCA.
Time Complexity: O(h), where h is the height of the tree.
Space Complexity: O(h) due to the recursion stack.
1#include <iostream>
2using namespace std;
3
4struct TreeNode {
5 int val;
6 TreeNode* left;
7 TreeNode* right;
8 TreeNode(int x) : val(x), left(NULL), right(NULL) {}
9};
10
11class Solution {
12public:
13 TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
14 if (!root) return nullptr;
15 if (p->val > root->val && q->val > root->val)
16 return lowestCommonAncestor(root->right, p, q);
17 else if (p->val < root->val && q->val < root->val)
18 return lowestCommonAncestor(root->left, p, q);
19 else
20 return root;
21 }
22};This C++ solution uses a class and traverses the BST recursively by comparing node values and descending accordingly. The LCA is found when p and q are on either side of the root, which is the base case.
Instead of recursion, this method uses a while loop to traverse the tree. Starting from the root, check if both nodes are greater or smaller than the current node to decide whether to proceed to the right or left subtree respectively. If neither, we've found the LCA.
Time Complexity: O(h), where h is the height of the tree.
Space Complexity: O(1) since it does not use extra space beyond variables.
1#include <stdio.h>
2
3struct TreeNode {
4 int val;
5 struct TreeNode *left;
6 struct TreeNode *right;
7};
8
9struct TreeNode* lowestCommonAncestor(struct TreeNode* root, struct TreeNode* p, struct TreeNode* q) {
10 struct TreeNode* current = root;
11 while (current != NULL) {
12 if (p->val > current->val && q->val > current->val) {
13 current = current->right;
14 } else if (p->val < current->val && q->val < current->val) {
15 current = current->left;
16 } else {
17 return current;
18 }
19 }
20 return NULL;
21}This C implementation uses an iterative approach via a loop to find the LCA. It makes use of BST properties to decide movement between left and right nodes.