114 lines
2.6 KiB
Markdown
114 lines
2.6 KiB
Markdown
# Leetcode Lowest-Common-Ancestor-Of-a-Binary-Search-Tree
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#### 2022-07-08 11:53
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> ##### Algorithms:
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>
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> #algorithm #binary_search #DFS
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>
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> ##### Data structures:
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>
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> #DS #binary_tree #binary_search_tree
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>
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> ##### Difficulty:
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>
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> #coding_problem #difficulty-easy
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>
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> ##### Additional tags:
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>
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> #leetcode
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>
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> ##### Revisions:
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>
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> N/A
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##### Related topics:
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##### Links:
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- [Link to problem](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/)
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---
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### Problem
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Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.
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According to the [definition of LCA on Wikipedia](https://en.wikipedia.org/wiki/Lowest_common_ancestor): “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**).”
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#### Examples
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**Example 1:**
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**Input:** root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
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**Output:** 6
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**Explanation:** The LCA of nodes 2 and 8 is 6.
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**Example 2:**
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**Input:** root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
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**Output:** 2
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**Explanation:** The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.
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**Example 3:**
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**Input:** root = [2,1], p = 2, q = 1
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**Output:** 2
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#### Constraints
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- The number of nodes in the tree is in the range `[2, 105]`.
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- `-109 <= Node.val <= 109`
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- All `Node.val` are **unique**.
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- `p != q`
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- `p` and `q` will exist in the BST.
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### Thoughts
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> [!summary]
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> This is a #binary_search
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Because of the features of BST, the maximum val of a left sub-tree is smaller than node, so the valid LCA must meet this:
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```
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root->val >= small && root->val <= big
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```
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otherwise, search the left or right subtree.
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### Solution
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```cpp
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/**
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* Definition for a binary tree node.
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* struct TreeNode {
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* int val;
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* TreeNode *left;
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* TreeNode *right;
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* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
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* };
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*/
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class Solution {
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public:
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TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
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// DFS-like recursion
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// Base cases
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int big = max(q->val, p->val);
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int small = min(q->val, p->val);
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if (root->val >= small && root->val <= big) {
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return root;
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} else if (root->val > big) {
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return lowestCommonAncestor(root->left, p, q);
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} else {
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return lowestCommonAncestor(root->right, p, q);
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}
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}
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};
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```
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