【leetcode】Lowest Common Ancestor of a Binary Search Tree

Lowest Common Ancestor of a Binary Search Tree

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.

思路： 由于是二叉搜索树，因此左子树的值一定小于右子树。根据这个性质就可写出下面的算法。对比值，然后用递归的方法做。

/**
 * 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 || p==NULL || q==NULL)
            return NULL;

        if(root->val==p->val || root->val==q->val)
            return root;

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

引申： 如果不是二叉搜索树，只是一个简单的树的话，可能需要记录下p, q的位置，然后再找他们的LCA。
（http://blog.youkuaiyun.com/xudli/article/details/46838747）