Minimum Number of Flips to Make the Binary String Alternating

Minimum Number of Flips to Make the Binary String Alternating

1. What is this problem about?

In the Minimum Number of Flips to Make the Binary String Alternating interview question, you are given a binary string. You can perform two types of operations:

1. Type 1: Remove the first character and append it to the end.
2. Type 2: Flip a character (0 to 1 or 1 to 0). The goal is to find the minimum number of Type 2 operations (flips) needed to make the string alternating (e.g., "010101..." or "101010...") after any number of Type 1 operations.

2. Why is this asked in interviews?

This problem is popular at companies like IBM and Google because it tests "Sliding Window" efficiency. While you could try every possible rotation (Type 1), doing so naively would take O(n^2) time. The interviewer is looking for the O(n) solution, which demonstrates that the candidate understands how to update a result incrementally as the "window" of the string moves.

3. Algorithmic pattern used

This utilizes the Sliding Window, String, Dynamic Programming interview pattern. Instead of actually rotating the string, you double it (S + S). Then, you compare this doubled string against two target alternating patterns ("0101..." and "1010..."). By using a sliding window of size n over the doubled string, you can maintain a count of "mismatches" with the target patterns. As the window slides, you just subtract the mismatch from the outgoing character and add the mismatch from the incoming character.

4. Example explanation

Input: "111000", n=6 Doubled: "111000111000" Target 1: "010101010101" Target 2: "101010101010" Window 1 (first 6): "111000" vs "010101". Mismatches: 1st, 3rd, 4th, 6th. Count = 4. Slide the window one step: "110001" vs "101010". Update the count in O(1). The minimum count across all possible windows of size 6 is your answer.

5. Common mistakes candidates make

The most common mistake is trying all rotations and re-calculating the flips from scratch, leading to a Time Limit Exceeded (TLE) error. Another mistake is not realizing that doubling the string is equivalent to all possible circular rotations. Some candidates also forget to handle both possible alternating patterns (starting with 0 vs. starting with 1).

6. Interview preparation tip

Whenever you see a problem involving "circular shifts" or "rotations," think about doubling the string. This is a very common trick that turns a circular problem into a linear one, allowing you to use powerful techniques like Sliding Window.