Find Unique Binary String

class Solution {
public:
    string uniqueBinaryString(vector<string>& bits) {
        string result;
        for (int j = 0; j < bits.size(); j++) {
            char bit = bits[j][j];
            result += (bit == '0') ? '1' : '0';
        }
        
        return result;
    }
};

The provided C++ solution addresses the problem of finding a unique binary string from a vector of binary strings. The approach involves creating a new binary string where each bit is determined by flipping the corresponding diagonal bit of the input string at index j. Specifically, if the bit is '0', it is changed to '1', and if it is '1', it is changed to '0'. This guarantees that the resulting binary string will be unique compared to each string in the list, as it differs by at least one bit in the diagonal positions.

The algorithm iterates through each string in the vector, examining and flipping the bit at the index corresponding to the string's position in the list, effectively using a diagonal traversal of the bits matrix. The result is a string that cannot be found in the original list of binary strings, ensuring its uniqueness.

class Solution {
    public String generateUniqueBinary(String[] input) {
        StringBuilder result = new StringBuilder();
        for (int index = 0; index < input.length; index++) {
            Character currentChar = input[index].charAt(index);
            result.append(currentChar == '0' ? '1' : '0');
        }
        
        return result.toString();
    }
}

The solution presented generates a unique binary string given an array of binary strings. The Java method generateUniqueBinary in the Solution class is imperative for solving this. Let's break down the working of this code:

• Initialization: A StringBuilder named result is initiated to help in building the resultant binary string.
• Iteration through the Input Array: The code loops through each string in the provided array of binary strings.
• Bit Flipping Logic: For each string, it takes the character located at the position corresponding to the current index of the loop. It flips the bit (from '0' to '1' or from '1' to '0') and appends this flipped bit to the result.
• Result Compilation: After iterating through all the strings, the accumulated characters in the result StringBuilder form the unique binary string.

This method ensures that the generated binary string will not match any of the binary strings in the given array, leveraging Cantor's diagonal argument by flipping the diagonal bits. The final string is returned as the output of the method.

class Solution:
    def findUniqueBinaryStr(self, numbers: List[str]) -> str:
        result_str = []
        for index in range(len(numbers)):
            present_char = numbers[index][index]
            result_str.append("1" if present_char == "0" else "0")
        
        return "".join(result_str)

The Python solution provided constructs a unique binary string from a list of binary strings by ensuring that each character in the resulting string differs from the corresponding character at the same index in each string of the list. Here's an overview of how the solution is implemented:

• Initiate an empty list called result_str.
• Iterate through each binary string in the input list using its index.
• For each position in the binary string, check the character at the current index.
• Append a '1' to result_str if the character is '0', or a '0' if the character is '1'. This guarantees that the new string will differ from each input string at least at one respective position.
• After iterating through all binary strings, join the list result_str into a single string.

The resultant string is unique among the input list of binary strings, as it directly counters each character at every index in each string in the list.