LeetCode: 701. Insert into a Binary Search Tree

题目

原题地址:https://leetcode.com/problems/insert-into-a-binary-search-tree/

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

Constraints:

  • The number of nodes in the given tree will be between 0 and 10^4.
  • Each node will have a unique integer value from 0 to -10^8, inclusive.
  • -10^8 <= val <= 10^8
  • It's guaranteed that val does not exist in the original BST.

解法

利用 BST 特性进行节点插入

根据 BST 的特性可以知道,一个节点的所有左侧子节点的值都要小于或等于该节点值,所有右侧子节点的值都要大于或等于该节点的值。 可以基于这个特性把节点插入到正确的位置(同时题目限制了所有节点的值都是唯一的,也就是不存在跟待插入的值一样的节点):

  1. 如果要插入的值小于当前节点的值,说明需要把它插入到左侧的子节点中。
  2. 如果要插入的值大于当前节点的值,说明需要把它插入到右侧的子节点中。

相应的 Python 代码类似下面这样:

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution(object):
    def insertIntoBST(self, root, val):
        if root is None:
            return TreeNode(val)

        if val < root.val:
            root.left = self.insertIntoBST(root.left, val)
        if val > root.val:
            root.right = self.insertIntoBST(root.right, val)

        return root

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