The “Single Element in a Sorted Array” problem is a great example of using binary search in a clever way. In this blog, we\u2019ll explain the problem, walk you through both brute force and optimal solutions, and make everything easy to understand with code comments, dry runs, and clear explanations.<\/p>\n\n\n\n
You are given a sorted array consisting of only integers where every element appears exactly twice, except for one element which appears exactly once.<\/p>\n\n\n\n
Return the single element that appears only once<\/em>.<\/p>\n\n\n\n Your solution must run in Here’s the [Problem Link<\/span><\/mark><\/a><\/strong>] to begin with.<\/p>\n\n\n\n Example 1:<\/strong><\/p>\n\n\n\n Example 2:<\/strong><\/p>\n\n\n\n Constraints:<\/strong><\/p>\n\n\n\n Let\u2019s solve the problem in the most straightforward way:<\/p>\n\n\n\n This approach is easy to understand but not efficient for large arrays.<\/p>\n\n\n\nO(log n)<\/code> time and O(1)<\/code> space.<\/p>\n\n\n\nInput:<\/strong> nums = [1,1,2,3,3,4,4,8,8]
Output:<\/strong> 2<\/pre>\n\n\n\nInput:<\/strong> nums = [3,3,7,7,10,11,11]
Output:<\/strong> 10<\/pre>\n\n\n\n\n
1 <= nums.length <= 105<\/sup><\/code><\/li>\n\n\n\n0 <= nums[i] <= 105<\/sup><\/code><\/li>\n<\/ul>\n\n\n
\n\n\n\nBrute Force Solution (Linear Scan)<\/h2>\n\n\n\n
Intuition and Approach<\/h3>\n\n\n\n
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Go through the array from start to end.<\/li>\n\n\n\n\n
Since the array is sorted and all elements except one appear twice, the unique element will not be equal to its neighbors.<\/li>\n<\/ol>\n\n\n\nCode Implementation<\/h3>\n\n\n\n