Lowest Common Ancestor of a Binary Search Tree -- LeetCode

Posted 2020-06-10

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.

 

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思路：利用二叉搜索树的性质，可以判断出p和q与当前root的位置关系。若p和q的值都小于root，则它们的公共祖先一定在root的左子树；若p和q的值都大于root，则它们的公共祖先一定在root的右子树。

否则，q和q一定是一个在左子树一个在右子树，当前的root即是最小的公共祖先。

 1 class Solution {
 2 public:
 3     TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
 4         if (p->val < root->val && q->val < root->val)
 5             return lowestCommonAncestor(root->left, p, q);
 6         if (p->val > root->val && q->val > root->val)
 7             return lowestCommonAncestor(root->right, p, q);
 8         return root;
 9     }
10 };