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?
Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.
给n个数,0到n之间有一个数字缺失了,让找到这个缺失数字。要求线性时间复杂度和常数级的额外空间复杂度。
解法1:排序,然后二分查找。此题数组不是排序的,所以适合。但面试时,如果问道要知道。
解法2:求差值,用0~n个数的和减去给定数组数字的和,差值就是要找的数字。
解法3:位操作Bit Manipulation,将这个数组与0~n之间完整的数异或一下累加到res,相同的数字异或后都变为了0,最后剩下的结果就是缺失的数字。
Java:
class Solution { public int missingNumber(int[] nums) { if (nums == null || nums.length == 0) return 0; int result = 0; Arrays.sort(nums); for (int i = 0; i < nums.length; i++) { if (result != nums[i]) { return result; } result++; } return nums.length; } }
Java:
class Solution { public int missingNumber(int[] nums) { int xor = 0, i = 0; for (i = 0; i < nums.length; i++) { xor = xor ^ i ^ nums[i]; } return xor ^ i; } }
Python:
class Solution(object): def missingNumber(self, nums): return sum(xrange(len(nums)+1)) - sum(nums)
Python:
class Solution(object): def missingNumber(self, nums): """ :type nums: List[int] :rtype: int """ return reduce(operator.xor, nums, reduce(operator.xor, xrange(len(nums) + 1)))
C++: 用等差数列公式
class Solution { public: int missingNumber(vector<int>& nums) { int sum = 0, n = nums.size(); for (auto &a : nums) { sum += a; } return 0.5 * n * (n + 1) - sum; } };
C++:
class Solution { public: int missingNumber(vector<int>& nums) { int res = 0; for (int i = 0; i < nums.size(); ++i) { res ^= (i + 1) ^ nums[i]; } return res; } };
类似题目:
[CareerCup] 5.7 Find Missing Integer 查找丢失的数