540. Single Element in a Sorted Array

Problem Statement

You are given a sorted array consisting of only integers where every element appears exactly twice, except for one element which appears exactly once.

Return the single element that appears only once.

Your solution must run in O(log n) time and O(1) space.

Example 1:

Input: nums = [1,1,2,3,3,4,4,8,8]
Output: 2

Example 2:

Input: nums = [3,3,7,7,10,11,11]
Output: 10

Constraints:

1 <= nums.length <= 105
0 <= nums[i] <= 105

Intuition

Approach:

Note that,

When a single element appears ordering of indexes is changes

1 1 2 2 3 4 4
0 1 2 3 4 5 6

Note at odd index, second repeat comes at odd
But then after the single element appears, second repeat comes at even

take advantage of  that

Video Links

Approach 1:

C++

class Solution {
public:
    int singleNonDuplicate(vector<int>& nums) {
        if(nums.size() == 1)
            return nums[0];

        int low=0, high=nums.size()-1;
        while(low<high){
            int mid = low+(high-low)/2;
            if(mid % 2 != 0){
                if(nums[mid] == nums[mid-1])
                    low = mid+1;
                else if(nums[mid] == nums[mid+1])
                    high= mid-1;
                else
                    return nums[mid];
            }
            else{
                if(nums[mid] == nums[mid+1])
                    low = mid+2;
                else if(nums[mid] == nums[mid-1])
                    high = mid-2;
                else
                    return nums[mid];
            }
        }

        return nums[low];
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++