【简单】Lintcode 85:Insert Node in a Binary Search Tree

Given a binary search tree and a new tree node, insert the node into the tree. You should keep the tree still be a valid binary search tree.

 Notice

You can assume there is no duplicate values in this tree + node.

Example

Given binary search tree as follow, after Insert node 6, the tree should be:

  2             2
 / \           / \
1   4   -->   1   4
   /             / \ 
  3             3   6

解题思路1：

    递归。利用平衡二叉树的性质即可写出。

/**
 * 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: The root of the binary search tree.
     * @param node: insert this node into the binary search tree
     * @return: The root of the new binary search tree.
     */
    TreeNode * insertNode(TreeNode * root, TreeNode * node) 
    {
        // write your code here
        //递归到底的返回
        if(root == NULL)
            return new TreeNode(node->val);
        
        if(root->val > node->val)
        {
            root->left = insertNode(root->left,node);
        }
        else //root->val < node->val
        {
            root->right = insertNode(root->right,node);
        }
        
        return root;
    }
};

解题思路2：

    非递归方法：双指针法。

/**
 * 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: The root of the binary search tree.
     * @param node: insert this node into the binary search tree
     * @return: The root of the new binary search tree.
     */
    TreeNode * insertNode(TreeNode * root, TreeNode * node) 
    {
        // write your code here
        TreeNode * cur = root;//指向需要插入节点的位置
        TreeNode * pre = cur;//指向需要插入节点位置的父节点
        
        //定位cur与pre的位置
        while(cur != NULL)
        {
            if(cur->val > node->val)
            {
                pre = cur;
                cur = cur->left;
            }
            else
            {
                pre = cur;
                cur = cur->right;
            }
        }
        
        //定位好之后新建节点
        cur = new TreeNode(node->val); 
        
        //将新建的节点连接上pre，完成插入
        if(pre == NULL)
            root = cur;
        else if(pre->val > node->val)
            pre->left = cur;
        else
            pre->right = cur;
        
        return root;
    }
};