Break apart modified binary search adaptations and solutions for diverse search problems.

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Modified Binary Search


# Statement
You are given a sorted array of integers, `nums`, where all integers appear twice except for one. Your task is to find and return the single integer that appears only once.

The solution should have a time complexity of $O(\log n)$ or better and a space complexity of $O(1)$.

**Constraints:**

- $1 \leq$ `nums.length` $\leq 10^3$

- $0 \leq$ `nums[i]` $\leq 10^3$

Let's solve the Single Element in a Sorted Array problem using the Modified Binary Search pattern.

Solution: Single Element in a Sorted Array

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Solution: Single Element in a Sorted Array

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