Maximum Binary String After Change

Problem Description

You are given a binary string binary consisting of only 0's or 1's. You can apply each of the following operations any number of times:

• Operation 1: If the number contains the substring "00", you can replace it with "10".
• Operation 2: If the number contains the substring "10", you can replace it with "01".

Return the maximum binary string you can obtain after any number of operations. Binary string x is greater than binary string y if x's decimal representation is greater than y's decimal representation.

Key Insights

• The operations allow for the transformation of sequences of 0s and 1s, particularly "00" to "10" and "10" to "01".
• The goal is to maximize the number of 1s at the beginning of the binary string, as leading 1s contribute more to the binary value.
• The presence of trailing 0s can be transformed to 1s by cascading the transformations, leading to a binary string that maximizes the binary value.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can follow these steps:

1. Count the number of leading 1s and the total number of 0s in the string.
2. The maximum binary string can be constructed by placing all counted 1s at the beginning followed by all 0s turned into 1s, and then ending with a single 0 if there were any 0s present.
3. This approach ensures that we maximize the binary value since leading 1s are more significant.

Code Solutions