Lowest Common Ancestor of a Binary Search Tree

Description

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.

Code

關鍵在於：只要不是以下兩個 case

1. curr->val > p->val && curr->val > q->val
2. `curr→val < p→val && curr→val < q→val

就會是：

1. `curr→val == p→val && curr→val > q→val
2. `curr→val > p→val && curr→val == q→val
3. `curr→val < p→val && curr→val == q→val
4. `curr→val == p→val && curr→val < q→val

代表 curr 的值和 p, q 其中一個一樣，curr 即是 p, q 的 Lowest Common Ancestor。

或者是：

1. curr->val > p->val && curr->val < q->val
2. `curr→val < p→val && curr→val > q→val

這也代表 curr 即是 p, q 的 Lowest Common Ancestor。

Recursive

和 Lowest Common Ancestor of a Binary Tree 不一樣的地方在於我們可以利用 binary search tree 的特性。

/**
 * 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;
    }
 
};

Iterative

/**
 * 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) {
        TreeNode* curr = root;
        while(true) {
            if(curr->val > p->val && curr->val > q->val) 
                curr = curr->left;
            else if(curr->val < p->val && curr->val < q->val) 
                curr = curr->right;
            else 
                break;
        }
 
        return curr;
    }
 
};

Source

• Lowest Common Ancestor of a Binary Search Tree - LeetCode