LeetCode: 236. Lowest Common Ancestor of a Binary Tree

题目描述

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).”

Given the following binary tree: 1root = [3,5,1,6,2,0,8,null,null,7,4]1

Example 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.

Example 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.

Note:

• All of the nodes’ values will be unique.
• p and q are different and both values will exist in the binary tree.

解题思路 —— 递归求解

根据左右子树含有待求公共祖先节点的节点数，判断其是否为公共祖先节点。

AC 代码

/**
 * 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 
{
private:
    // nodes：待求公共祖先节点的子节点
    // nodesInTree: root 子树中包含的 nodes 中的节点的数目
    TreeNode* lowestCommonAncestor(TreeNode* root, const vector<TreeNode*>& nodes, int&& nodesInTree) 
    {
        int nodesInTreeRef;
        return lowestCommonAncestor(root, nodes, nodesInTreeRef);
    }
    TreeNode* lowestCommonAncestor(TreeNode* root, const vector<TreeNode*>& nodes, int& nodesInTree) 
    {
        if(root == nullptr)
        {
            return nullptr;
        }
        
        TreeNode* commonAncestor = nullptr;
        
        // LCA 在 root 的左子树
        int nodesInLeftTree = 0;
        commonAncestor = lowestCommonAncestor(root->left, nodes, nodesInLeftTree);
        if(nodesInLeftTree == nodes.size()) 
        {
            nodesInTree = nodesInLeftTree;
            return commonAncestor;
        }
        
        // LCA 在 root 的右子树
        int nodesInRightTree = 0;
        commonAncestor = lowestCommonAncestor(root->right, nodes, nodesInRightTree);
        if(nodesInRightTree == nodes.size()) 
        {
            nodesInTree = nodesInRightTree;
            return commonAncestor;
        }
        
        // root 为 LCA 
        nodesInTree = nodesInLeftTree+nodesInRightTree;
        if(find(nodes.begin(), nodes.end(), root) != nodes.end())
        {
            ++nodesInTree;
        }
        if(nodesInTree == nodes.size()) return root;
        
        return nullptr;
    }
public:
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) 
    {
        return lowestCommonAncestor(root, {p, q}, 0);
    }
};