# 701. Insert into a Binary Search Tree 二叉搜索树中的插入操作

@TOC

## # 题目描述

Given the root node of a binary search tree (BST) and a value to be inserted into the tree, insert the value into the BST. Return the root node of the BST after the insertion. It is guaranteed that the new value does not exist in the original BST.

Note that there may exist multiple valid ways for the insertion, as long as the tree remains a BST after insertion. You can return any of them.

For example,

``````Given the tree:
4
/ \
2   7
/ \
1   3
And the value to insert: 5
``````

You can return this binary search tree:

``````     4
/   \
2     7
/ \   /
1   3 5
``````

This tree is also valid:

``````     5
/   \
2     7
/ \
1   3
\
4
``````

## # 解题方法

``````# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
def insertIntoBST(self, root, val):
"""
:type root: TreeNode
:type val: int
:rtype: TreeNode
"""
if not root:
node = TreeNode(val)
return node
if val < root.val:
if not root.left:
node = TreeNode(val)
root.left = node
else:
self.insertIntoBST(root.left, val)
else:
if not root.right:
node = TreeNode(val)
root.right = node
else:
self.insertIntoBST(root.right, val)
return root
``````

``````# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
def insertIntoBST(self, root, val):
"""
:type root: TreeNode
:type val: int
:rtype: TreeNode
"""
if not root:
return TreeNode(val)
if val > root.val:
root.right = self.insertIntoBST(root.right, val)
if val < root.val:
root.left = self.insertIntoBST(root.left, val)
return root
``````

C++版本如下：

``````/**
* 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* insertIntoBST(TreeNode* root, int val) {
if (!root) return new TreeNode(val);
if (val < root->val) root->left = insertIntoBST(root->left, val);
if (val > root->val) root->right = insertIntoBST(root->right, val);
return root;
}
};
``````

## # 日期

2018 年 9 月 4 日 ———— 迎接明媚的阳光！