Lowest Common Ancestor of a Binary Tree

Posted 2020-06-14

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 v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

        _______3______
       /                  ___5__          ___1__
   /      \        /         6      _2       0       8
         /           7   4

For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

 

hint：利用先序遍历分别获取root节点到目标节点的路径，然后比较两路径最长公布部分，就可以发现他们的LCA

/**
 * 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) {
        vector<TreeNode*> p_path, q_path;
        vector<TreeNode*> path;
        get_path(root, p, &path, &p_path);  // 获取root到p的节点路径
        path.clear();
        get_path(root, q, &path, &q_path);  // 获取root到q的节点路径
        int len = min(p_path.size(), q_path.size());
        int i = 0;
        while (i < len && p_path[i] == q_path[i]) { // 找到第一个不同的节点，那么前一个节点就是LCD
            ++i;
        }
        
        return p_path[i-1];
    }
    
    void get_path(TreeNode* root, TreeNode* target, vector<TreeNode*>* path, vector<TreeNode*>* target_path) {
        if (!target_path->empty() && target_path->back() == target) {   // 如果已经找到了root到target节点的路径，那就直接不用搜
            return ;
        }
        
        if (root == NULL) { // 空姐点直接不搜
            return ;
        }
        
        path->push_back(root);  // 访问根节点，加入路径
        if (path->back() == target) {   // 判断是否是到target节点
            *target_path = *path;
        }
        get_path(root->left, target, path, target_path);    // 继续深搜左子树
        get_path(root->right, target, path, target_path);   // 继续深搜右子树
        path->pop_back();   // 回溯
    }
};

 

原来还有一道BST的LCA

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

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

        _______6______
       /                  ___2__          ___8__
   /      \        /         0      _4       7       9
         /           3   5

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

 

 

 hint：LCA->val 在 p->val与q->val之间

/**
 * 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) {
        int max_val = p->val, min_val = q->val;
        if (max_val < min_val) {
            swap(max_val, min_val);
        }
        
        TreeNode* cur = root;
        while (cur != NULL) {
            if (cur->val < min_val) {   // 若当前节点比两目标节点的值都小，需右移
                cur = cur->right;
            } else if (cur->val > max_val) {    // 若当前节点比两目标节点的值都大，需左移
                cur = cur->left;
            } else {
                break;
            }
        }
        
        return cur;
    }
};