LeetCode 268. Missing Number--Python解法--数学题

LeetCode 268. Missing Number–Python解法–数学题

LeetCode题解专栏：LeetCode题解
LeetCode 所有题目总结：LeetCode 所有题目总结
大部分题目C++，Python，Java的解法都有。

题目地址：Missing Number - LeetCode

Given an array containing n distinct numbers taken from 0, 1, 2, …, n, find the one that is missing from the array.

Example 1:

Input: [3,0,1]
Output: 2

Example 2:

Input: [9,6,4,2,3,5,7,0,1]
Output: 8

Note:
Your algorithm should run in linear runtime complexity. Could you implement it using only constant extra space complexity?

之所以会想到做这道题，是因为之前在看书《算法新解》的前言部分就讲了这道题目。

最容易想到的是使用排序算法，但肯定不是最优的。

另外一种略好的做法是使用set，但额外空间占用比较多。

我想到的Python解法如下：

class Solution:def missingNumber(self, nums: List[int]) -> int:number=len(nums)l=[0]*numberfor i in nums:if i<number:l[i]=1for i in range(0,number):if l[i]==0:return ireturn number

时间复杂度为O(n)，空间复杂度为O(1)。

更优的解法是直接算，

Python解法如下：

class Solution:def missingNumber(self, nums):expected_sum = len(nums)*(len(nums)+1)//2actual_sum = sum(nums)return expected_sum - actual_sum

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