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Clarifying Questions

  1. Problem Input and Output:
    • What is the input format?
    • What is the expected output format?
    • Are there any constraints like range of values?
  2. Function Requirements:
    • Any specific edge cases we need to handle?
    • Should the solution be optimized for time or space complexity?

Strategy

To solve this problem, we need to:

  1. Identify the components and sequence of the input.
  2. Implement the logic to achieve the desired alternating group behavior.
  3. Make sure our solution is efficient.

Code

Let’s start with the Python function signature and then write the code step by step:

def alternating_groups(arr):
    # Your logic here
    pass

# Example to test:
example_arr = [sequence of numbers]
print(alternating_groups(example_arr))

Step-by-Step Implementation

  1. Identify Groups:
    • Traverse the list while maintaining a count of current group elements.
    • Alternate between tracking elements that should be grouped and those that should be left outside the group.
  2. Alternate the Elements:
    • Implement logic to add elements to the group and then to output as per the alternating requirement.

Time Complexity

We will determine the time complexity after implementing the function by analyzing each part of the code.

Now, let’s flesh out this plan:

def alternating_groups(arr):
    result = []
    group = []
    add_group = True # Start by adding to the group
    
    for num in arr:
        if add_group:
            group.append(num)
        else:
            result.append(num)
        
        add_group = not add_group # Flip between adding to group and result
        
    alternating_result = []
    
    while group or result:
        if group:
            alternating_result.append(group.pop(0))
        if result:
            alternating_result.append(result.pop(0))
    
    return alternating_result

# Example to test:
example_arr = [1, 2, 3, 4, 5, 6, 7, 8, 9]
print(alternating_groups(example_arr))

# Test additional edge cases to ensure robustness
print(alternating_groups([]))  # Should return []
print(alternating_groups([1]))  # Should return [1]
print(alternating_groups([1, 2]))  # Should return [1, 2]

Detailed Analysis

  1. Time Complexity:
    • The initial loop that fills group and result lists runs in O(n) time.
    • The while-loop that combines group and result into alternating_result also runs in O(n) time.

    Hence, the overall time complexity is O(n), where n is the length of the input array.

  2. Space Complexity:
    • We are using additional lists group and result, each could store up to n elements.

    Thus, the space complexity is O(n).

By following this approach, we’ve created a clear and efficient solution for the problem.

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