Approach

When faced with the interview question, "How do you write code to find the minimum element in a rotated sorted array?", it's essential to structure your answer clearly and logically. Here’s a framework to follow:

1. Understand the Problem: Recognize what a rotated sorted array is and the implications for finding the minimum.

2. Clarify Assumptions: Specify any assumptions you are making about the array, such as whether it contains duplicates.

3. Choose an Algorithm: Decide on the algorithm you will use, typically binary search due to the sorted nature of the array.

4. Explain Your Thought Process: Walk through the logic behind your chosen approach.

5. Code Implementation: Provide a clear and concise code example.

6. Discuss Complexity: Mention the time and space complexity of your solution.

7. Wrap Up: Summarize your approach and the importance of the solution.

Key Points

• Understanding Rotated Sorted Arrays: A rotated sorted array is created by taking a sorted array and rotating it at some pivot. For example, the sorted array [0, 1, 2, 4, 5, 6, 7] can be rotated to [4, 5, 6, 7, 0, 1, 2].

• Algorithm Choice: Binary search is the most efficient way to find the minimum element in O(log n) time complexity. A linear search would take O(n), which is less efficient.

• What Interviewers Look For: They want to see your problem-solving skills, understanding of algorithms, ability to write clean code, and your capability to explain your reasoning.

Standard Response

Here’s a well-structured answer that incorporates the above points:

To find the minimum element in a rotated sorted array, I would use a binary search approach to achieve optimal time complexity. Here’s how I would structure my response:

• Understand the Problem: A rotated sorted array has elements in a sorted order but rotated at some pivot. The goal is to find the smallest element in this array.

• Assumptions: I will assume that the array is non-empty and may contain unique or duplicate elements.

• Algorithm: I will implement a binary search algorithm.

• Thought Process:

• I will initialize two pointers, left and right, at the beginning and end of the array, respectively.

• I will calculate the mid-point of the current segment of the array.

• If the mid-point element is greater than the right element, this indicates that the minimum is in the right half of the array. Therefore, I will move the left pointer to mid + 1.

• If the mid-point element is less than or equal to the right element, it means the minimum could be in the left half or it could be the mid-point itself. Thus, I will move the right pointer to mid.

• Code Implementation:

• Complexity Analysis:

• Time Complexity: O(log n) due to the binary search approach.

• Space Complexity: O(1) as we are using a constant amount of extra space.

• Wrap Up: By using a binary search algorithm, we efficiently locate the minimum element in a rotated sorted array. This approach is optimal for large datasets, ensuring performance and scalability.

Tips & Variations

Common Mistakes to Avoid

• Not Handling Edge Cases: Ensure to account for empty arrays or arrays with only one element.

• Over-complicating the Logic: Keep the solution straightforward and avoid unnecessary complexity.

Alternative Ways to Answer

• Iterative vs. Recursive Approach: Discuss the possibility of implementing a recursive