236. Lowest Common Ancestor of a Binary Tree

ゝ一世哀愁。 2023-07-03 03:19 15阅读 0赞

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:  root = \[3,5,1,6,2,0,8,null,null,7,4\]

![format_png][]

**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.

题意：寻找二叉树上，两个结点的公共祖先。

方法一：递归

方法二：计算结点p,q到根节点的路径，比较这两个路径，返回公共祖先结点。

/**
     * 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* t1 = root;
            TreeNode* t2 = root;
            vector<TreeNode*> path1,path2;
            createPath(t1, p, path1);
            createPath(t2, q, path2);
            
            int len = (path1.size() < path2.size()? path1.size():path2.size());
            int i = 0;
            for (; i < len; i++)
            {
                if(path1[i] != path2[i])
                    break;
            }
            return  path1[i-1];
            
        }
        bool createPath(TreeNode* root, TreeNode* key, vector<TreeNode*>& path)
        {
            if (root == nullptr)
                return false;
            path.push_back(root);
            if (root == key)
                return true;     
            if (createPath(root->left, key, path) || createPath(root->right, key, path))
            {
                return true;
            }
            path.pop_back();
            return false;
        }
    };

[definition of LCA on Wikipedia]: https://en.wikipedia.org/wiki/Lowest_common_ancestor
[format_png]: https://imgconvert.csdnimg.cn/aHR0cHM6Ly9hc3NldHMubGVldGNvZGUuY29tL3VwbG9hZHMvMjAxOC8xMi8xNC9iaW5hcnl0cmVlLnBuZw?x-oss-process=image/format,png