Lowest Common Ancestor of a Binary Search Tree

最新推荐文章于 2022-10-04 11:47:29 发布

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最新推荐文章于 2022-10-04 11:47:29 发布

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本文介绍了一种在二叉搜索树(BST)中寻找两个指定节点的最低公共祖先(LCA)的方法。通过递归遍历，根据节点值大小决定搜索方向，最终返回公共祖先节点。

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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.

/**
 * 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 == NULL)
        {
            return NULL;
        }    

        if(root -> val > p -> val && root -> val > q -> val)
        {
            return lowestCommonAncestor(root -> left, p, q);
        }
        if(root -> val < p -> val && root -> val < q -> val)
        {
            return lowestCommonAncestor(root -> right, p, q);
        }

        return root;
    }
};