LeetCode——Single Element in a Sorted Array

Question

Given a sorted array consisting of only integers where every element appears twice except for one element which appears once. Find this single element that appears only once.

Example 1:

Input: [1,1,2,3,3,4,4,8,8]

Output: 2

Example 2:

Input: [3,3,7,7,10,11,11]

Output: 10

Note: Your solution should run in O(log n) time and O(1) space.

Solution

这个题可以直接对所有元素取一遍异或可以得到答案，但是不满足时间复杂度的要求，log n的要求，明显只能计算一半；因为有一个单出来的，那么这个值所在的那一半肯定有奇数个数字。

Code

class Solution {
public:
    int singleNonDuplicate(vector<int>& nums) {
        if (nums.size() == 1)
            return nums[0];
        int middle = nums.size() / 2;
        int left = middle - 1;
        int right = middle + 1;
        if (nums[middle] != nums[left] && nums[middle] != nums[right])
            return nums[middle];
        if (nums[middle] == nums[left] ) {
            if ((middle + 1) & 1 != 0) {
                int res = 0;
                for (int i = 0; i <= middle; i++)
                    res = res ^ nums[i];
                return res;
            } else {
                int res = 0;
                for (int i = middle + 1; i < nums.size(); i++)
                    res = res ^ nums[i];
                return res;
            }

        }
        if (nums[middle] == nums[right]) {
            if ((middle + 1) & 1 != 0) {
                int res = 0;
                for (int i = middle; i < nums.size(); i++)
                    res = res ^ nums[i];
                return res;
            } else {
                int res = 0;
                for (int i = 0; i < middle; i++)
                    res = res ^ nums[i];
                return res;
            }

        }
    }
};