Minimum Changes To Make Alternating Binary String

Minimum Changes To Make Alternating Binary String

What is this problem about?

In the Minimum Changes To Make Alternating Binary String problem, you are given a string consisting only of '0's and '1's. A string is "alternating" if no two adjacent characters are the same (e.g., "0101" or "1010"). You need to find the minimum number of characters you must change to make the string alternating.

Why is this asked in interviews?

This is a classic Minimum Changes interview question at Tesla. It tests your ability to recognize that there are only two possible target strings: one starting with '0' and one starting with '1'. It evaluates if you can solve the problem in a single pass without over-complicating it with dynamic programming.

Algorithmic pattern used

The Two Target Comparison interview pattern is the way to go.

1. There are only two possible alternating strings of length N:
   • Pattern A: 010101...
   • Pattern B: 101010...
2. Count how many characters in the original string differ from Pattern A. Let this be countA.
3. The number of differences for Pattern B is simply N - countA.
4. The answer is min(countA, N - countA).

Example explanation

Input: "0100". Length = 4.

1. Pattern A (0101): Differs at index 3 ('0' vs '1'). countA = 1.
2. Pattern B (1010): Differs at index 0 ('0' vs '1'), index 1 ('1' vs '0'), and index 2 ('0' vs '1'). countB = 3. (Also 4 - 1 = 3). Minimum changes = 1.

Common mistakes candidates make

• Trying to "flip" as you go: Some candidates try to change characters greedily without realizing that the very first choice (start with 0 or 1) determines the whole string's cost.
• Using Dynamic Programming: While DP works, it's unnecessary here. Recognizing the two-pattern limit reduces the problem significantly.
• Calculating both counts separately: You only need to count differences for one pattern; the other is always the complement.

Interview preparation tip

Whenever you have a problem with very limited valid states (like only two possible alternating patterns), don't look for a general search algorithm. Just check all valid states and pick the best one. This Greedy/String interview pattern is very efficient.