Alternating Groups II

Alternating Groups II

What is this problem about?

The "Alternating Groups II interview question" scales up the complexity of the circular group problem. Instead of looking for groups of size 3, you are given a length k and must find all sequences of k consecutive tiles where every adjacent pair in the sequence has different colors. Again, the array is circular, meaning these groups of length k can span across the boundary of the array.

Why is this asked in interviews?

Microsoft and Google use the "Alternating Groups II coding problem" to evaluate a candidate's ability to optimize a sliding window. A naive $O(N \cdot K)$ approach would be too slow for large inputs. Candidates must demonstrate an $O(N)$ solution by tracking the "length of the current alternating sequence" as they traverse the array.

Algorithmic pattern used

This problem is a classic Sliding Window (Optimized) challenge.

1. Linearization: To handle the circularity, you can append the first k-1 elements of the array to the end.
2. Sequential Check: Iterate through the extended array and maintain a counter current_alternating_length.
3. Counter Logic:
   • If color[i] != color[i-1], increment the counter.
   • If color[i] == color[i-1], reset the counter to 1.
4. Result Tracking: Whenever the counter reaches or exceeds k, it means the last k elements form an alternating group. Increment your total result.

Example explanation

Colors: [0, 1, 0, 1, 0], $k = 3$. Extended (first 2 appended): [0, 1, 0, 1, 0, 0, 1]

1. (0,1): Diff. Length = 2.
2. (1,0): Diff. Length = 3. ($>= k$, Result = 1)
3. (0,1): Diff. Length = 4. ($>= k$, Result = 2)
4. (1,0): Diff. Length = 5. ($>= k$, Result = 3)
5. (0,0): Same. Length = 1. (Reset) ... and so on.

Common mistakes candidates make

• Re-checking from scratch: Using a nested loop to check all $k$ elements for every starting position, leading to poor performance.
• Circular Math Errors: Miscalculating the number of elements to append or the total number of windows to check in the circular array.
• Off-by-one: Failing to count the very first element as part of the sequence.

Interview preparation tip

When you need to find sub-segments of a specific length with a certain property, always ask: "Can I update the result in $O(1)$ based on the previous window?" This is the essence of the "Sliding Window interview pattern."