LintCode 1311: Lowest Common Ancestor of a Binary Search Tree (BST两节点最小公共祖先，经典题)

1311. 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 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 binary search tree: root = {6,2,8,0,4,7,9,#,#,3,5}

Example
Example 1:

Input:
{6,2,8,0,4,7,9,#,#,3,5}
2
8
Output: 6
Explanation: The LCA of nodes 2 and 8 is 6.
Example 2:

Input:
{6,2,8,0,4,7,9,#,#,3,5}
2
4
Output: 2
Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.
Notice
All of the nodes’ values will be unique.
p and q are different and both values will exist in the BST.

解法1：DFS

/**
 * Definition of TreeNode:
 * class TreeNode {
 * public:
 *     int val;
 *     TreeNode *left, *right;
 *     TreeNode(int val) {
 *         this->val = val;
 *         this->left = this->right = NULL;
 *     }
 * }
 */

class Solution {
public:
    /**
     * @param root: root of the tree
     * @param p: the node p
     * @param q: the node q
     * @return: find the LCA of p and q
     */
    TreeNode * lowestCommonAncestor(TreeNode * root, TreeNode * p, TreeNode * q) {
        if (!root) 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;
    }
};

解法2：迭代

/**
 * Definition of TreeNode:
 * class TreeNode {
 * public:
 *     int val;
 *     TreeNode *left, *right;
 *     TreeNode(int val) {
 *         this->val = val;
 *         this->left = this->right = NULL;
 *     }
 * }
 */

class Solution {
public:
    /**
     * @param root: root of the tree
     * @param p: the node p
     * @param q: the node q
     * @return: find the LCA of p and q
     */
    TreeNode * lowestCommonAncestor(TreeNode * root, TreeNode * p, TreeNode * q) {
        if (!root) return NULL;
        while(root) {
            if (root->val > p->val && root->val > q->val) root = root->left;
            else if (root->val < p->val && root->val < q->val) root = root->right;
            else return root;
        }
    }
};