Approach

When faced with the question, "How would you implement a method to find a specific range of values within a sorted array?" it's essential to structure your response logically. Here’s a step-by-step framework for tackling this problem:

1. Understand the Problem: Clarify what is meant by finding a range of values. This typically involves identifying all elements within a specified lower and upper bound in a sorted array.

2. Choose the Right Algorithm: Since the array is sorted, leverage efficient algorithms such as Binary Search to optimize your solution.

3. Implement the Solution: Clearly outline the steps in coding your solution, including edge cases.

4. Test the Solution: Discuss how you would validate that your method works correctly with various test cases.

Key Points

To craft a strong response, consider the following essential aspects:

• Clarity: Ensure you articulate your thought process clearly.

• Efficiency: Highlight the importance of using efficient algorithms, especially binary search.

• Edge Cases: Mention how you would handle scenarios where the range is outside the bounds of the array or where there are no values in the specified range.

• Code Readability: Emphasize writing clean, maintainable code.

Interviewers are looking for candidates who can not only solve problems but also communicate their thought processes and demonstrate an understanding of algorithm efficiency.

Standard Response

Here’s a comprehensive sample answer showcasing how to implement the method to find a specific range of values within a sorted array:

To find a specific range of values within a sorted array, I would implement a solution using binary search for efficiency. Here’s how I would approach this problem:

• Define the Method: I would create a method called findRange, which takes three parameters: a sorted array of integers, a lower bound (inclusive), and an upper bound (inclusive).

• Use Binary Search:

• Find the Lower Bound Index: I would use a modified binary search to locate the first index where the value is greater than or equal to the lower bound.

• Find the Upper Bound Index: Similarly, I would perform another binary search to find the last index where the value is less than or equal to the upper bound.

• Extract the Range: Once I have both indices, I would extract the subarray that represents the range of values.

• Edge Case Handling: I would include checks to handle cases where the bounds are outside the bounds of the array or if there are no elements within the specified range.

Here’s a code example in Python to illustrate this approach:

def findRange(sorted_array, lower_bound, upper_bound):
 def findLowerBound(array, target):
 low, high = 0, len(array) - 1
 while low <= high:
 mid = (low + high) // 2
 if array[mid] < target:
 low = mid + 1
 else:
 high = mid - 1
 return low # First index >= target

 def findUpperBound(array, target):
 low, high = 0, len(array) - 1
 while low <= high:
 mid = (low + high) // 2
 if array[mid] <= target:
 low = mid + 1
 else:
 high = mid - 1
 return high # Last index <= target

 lower_index = findLowerBound(sorted_array, lower_bound)
 upper_index = findUpperBound(sorted_array, upper_bound)

 # Check if the indices are valid
 if lower_index <= upper_index and lower_index < len(sorted_array):
 return sorted_array[lower_index:upper_index + 1]
 else:
 return [] # No elements in range

# Example Usage
sorted_array = [1, 3, 5, 7, 9, 11]
print(findRange(sorted_array, 5, 10)) # Output: [5, 7, 9]

• The findLowerBound function efficiently locates the first occurrence of a value meeting the lower bound condition.

• The findUpperBound function efficiently locates the last occurrence of a value meeting the upper bound condition.

• The final result returns a subarray of values between the specified bounds.

• In this implementation:

Tips & Variations

Common Mistakes to Avoid

• Not Considering Edge Cases: Failing to check for scenarios where the range is out of bounds or when the sorted array is empty can lead to errors.

• Inefficient Search: Using a linear search instead of binary search results in a less optimal solution, especially for large datasets.

Alternative Ways to Answer

• Iterative Approach: While binary search is optimal, discussing a linear