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[Leetcode]236. Lowest Common Ancestor of a Binary Tree(C++)

题目描述

题目链接:236. Lowest Common Ancestor of a Binary Tree

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

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).”

例子

例子 1

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of nodes 5 and 1 is 3.

例子 2

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

例子 3

Input: root = [1,2], p = 1, q = 2
Output: 1

Constraints

  • The number of nodes in the tree is in the range [2, 10^5].
  • -10^9 <= Node.val <= 10^9
  • All Node.val are unique.
  • p != q
  • p and q will exist in the BST.

解题思路

这里涉及到在二叉树中对节点的搜索,思路如下:

  • 对一棵树同时搜索 p 或者 q
  • 如果根结点是空,直接返回空指针
  • 如果根结点是 p 或者 q,直接返回根结点(因为假如另一个节点在同一棵树内的话(题目保证了两个节点都会存在),最深的祖先节点一定是根结点)
  • 否则对左右两颗子树进行同样操作,得到返回结果 leftright
    • 假如 leftright 都非空,表示在左子树和右子树都搜到了其中一个节点,此时根结点为最近祖先节点,返回根结点
    • 假如 leftright 只有一个非空节点,表示除了该非空节点的子树外,其他节点都不包含另一个节点,表明另一个节点一定在该节点的子树下,返回该节点作为最近祖先节点
    • 假如 leftright 都为节点:不可能,因为题目保证两个节点都存在

代码如下:

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/**
* 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 == nullptr) return nullptr;
if (root == p || root == q) return root;
// search node in left subtree
TreeNode* left_search = lowestCommonAncestor(root->left, p, q);
TreeNode* right_search = lowestCommonAncestor(root->right, p, q);
// we find node in both subtree
if (left_search && right_search) {
return root;
} else if (left_search) {
return left_search;
} else {
return right_search;
}
}
};
  • 时间复杂度: O(n)
  • 空间复杂度: O(h) — 递归深度

GitHub 代码同步地址: 236.LowestCommonAncestorOfABinaryTree.cpp

其他题目:
GitHub: Leetcode-C++-Solution
博客: Leetcode-Solutions