Q11_lowest_common_ancestor_of_binary_search_tree.cpp

// 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

#include<bits/stdc++.h>
using namespace std;

struct TreeNode {
    int val;
    TreeNode *left;
    TreeNode *right;
    TreeNode() : val(0), left(nullptr), right(nullptr) {}
    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
    TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
};

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;
    }
};

// Time Complexity  : O(h) 
// Space Complexity : O(h)
// where h is the height of the tree