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Find Unique Binary String

#761 Most AskedMedium

Find Unique Binary String #761 Most Asked

Medium

Bloomberg LP

9 views

Topics:

ArraysStringsRecursion

Given an array of strings nums containing n unique binary strings each of length n, return a binary string of length n that does not appear in nums. If there are multiple answers, you may return any of them.

Example 1:

Input: nums = ["01","10"]
Output: "11"
Explanation: "11" does not appear in nums. "00" would also be correct.

Example 2:

Input: nums = ["00","01"]
Output: "11"
Explanation: "11" does not appear in nums. "10" would also be correct.

Example 3:

Input: nums = ["111","011","001"]
Output: "101"
Explanation: "101" does not appear in nums. "000", "010", "100", and "110" would also be correct.

Constraints:

n == nums.length
1 <= n <= 16
nums[i].length == n
nums[i] is either '0' or '1'.
All the strings of nums are unique.

Try coding it in LeetCode

Find Unique Binary String

#761 Most AskedMedium

Find Unique Binary String #761 Most Asked

Medium

Bloomberg LP

9 views

Topics:

ArraysStringsRecursion

Example 1:

Input: nums = ["01","10"]
Output: "11"
Explanation: "11" does not appear in nums. "00" would also be correct.

Example 2:

Input: nums = ["00","01"]
Output: "11"
Explanation: "11" does not appear in nums. "10" would also be correct.

Example 3:

Input: nums = ["111","011","001"]
Output: "101"
Explanation: "101" does not appear in nums. "000", "010", "100", and "110" would also be correct.

Constraints:

n == nums.length
1 <= n <= 16
nums[i].length == n
nums[i] is either '0' or '1'.
All the strings of nums are unique.

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the maximum size of the input array `nums`?
Are the binary strings in `nums` guaranteed to be of the same length?
Is the input array `nums` guaranteed to be non-empty?
If there are multiple possible unique binary strings, can I return any one of them?
What characters are allowed within the strings besides 0 and 1?

Brute Force Solution

Approach

The goal is to find a binary string that isn't in a given list of binary strings. A brute force strategy involves generating every possible binary string of a certain length and then checking if each one is present in the given list.

Here's how the algorithm would work step-by-step:

First, determine the length that the binary string should be. This is based on the length of the strings in the given list.
Next, start creating binary strings. Begin with the simplest one consisting of all zeros.
Then, generate the next possible binary string in sequence, like counting in binary. Think of it as flipping the rightmost bit from 0 to 1, and then carrying over if needed.
For each generated string, check if it exists in the given list of binary strings.
If the generated string is not in the list, you have found your unique string. Stop and return this string.
If the generated string *is* in the list, continue to generate the next binary string and repeat the check until you find one that is not in the list, or until you've generated all possible strings of that length.

Code Implementation

def find_unique_binary_string_brute_force(binary_strings):
    string_length = len(binary_strings[0])

    number_of_possible_strings = 2**string_length
    for i in range(number_of_possible_strings):
        # Convert the integer to its binary string representation
        binary_representation = bin(i)[2:].zfill(string_length)

        # Check if the generated string is present in the input list
        if binary_representation not in binary_strings:
            return binary_representation

    # If no unique string is found, return an empty string (should not happen)
    return ""

Big(O) Analysis

Time Complexity

O(n * 2^n) – Let n be the number of binary strings in the input list, and let k be the length of each string. The algorithm iterates through all possible binary strings of length k, which is 2^k. For each generated string, it checks if it exists in the given list, which takes O(n) time in the worst case (linear search). Therefore, the overall time complexity is O(n * 2^k). Since k is determined by the length of strings in the input list and could potentially be related to n in some scenarios, in the worst case, it is reasonable to represent the complexity as O(n * 2^n), where n is the number of strings in the input and each string has a length proportional to it.

Space Complexity

O(1) – The algorithm generates binary strings and checks if they exist in the input list. The length of generated string is determined by the length of the input strings, but the algorithm doesn't store all possible strings at once. It generates one string at a time and checks its existence in the input. No additional data structures are used to store intermediate results or visited strings, therefore, the space complexity is constant regardless of the number of input strings.

Optimal Solution

Approach

The goal is to create a binary string that is different from all strings in the given set. We can achieve this by looking at the characters in the strings at specific positions and flipping them to guarantee a unique result.

Here's how the algorithm would work step-by-step:

Consider only the first position of the first string.
If the character at that position is 0, change it to 1. If it is 1, change it to 0. This is now the first character of our unique string.
Move to the second string, and consider its second position. Do the same flipping: if it's 0, change it to 1, and if it's 1, change it to 0. This becomes the second character of our unique string.
Continue this process, using the third position of the third string, the fourth position of the fourth string, and so on until we have a character for each position in our unique string.
Because we are flipping the character at the corresponding index for each string, we are guaranteed that the generated string will be different from all strings in the input set.

Code Implementation

def find_different_binary_string(numbers: list[str]) -> str:
    unique_string = ""
    for index, number in enumerate(numbers):
        # Flip the bit at the corresponding index to ensure uniqueness.
        if number[index] == '0':
            unique_string += '1'

        else:
            unique_string += '0'

    return unique_string

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the input array nums of size n. For each string in nums, it accesses a single character at a specific index. This character access and the corresponding flip operation take constant time. Since this process is repeated n times, the overall time complexity is O(n).

Space Complexity

O(N) – The algorithm constructs a new binary string of length N, where N is the number of strings in the input set (and the length of each string). This new string requires storing N characters. No other significant data structures are used beyond this, making the space complexity directly proportional to the input size N.

Edge Cases

Case	How to Handle
Null or empty input array	Return an empty string or handle the null/empty array with an appropriate exception.
Input array contains duplicate binary strings	The solution needs to avoid generating the same string that already exists in the input.
Maximum input size nearing memory limits	The solution must efficiently use memory and avoid allocating excessive amounts of memory.
All possible binary strings of length n are present in the input	The solution should handle the case where no simple flip will yield a unique string, and consider other strategies like increasing the string length if the number of strings is a power of 2.
Input strings are not of the same length	The problem statement should be clarified, or the code needs to handle varying lengths by padding or other means.
Input contains non-binary characters (not '0' or '1')	The code should either validate the input strings to consist only of '0' and '1' characters, or handle invalid characters gracefully with error handling.
Integer overflow when converting binary string to integer	The solution should use a different approach such as constructing the result string iteratively or directly manipulating the string rather than converting it to an integer.
n is very large, leading to potential stack overflow during recursion (if using recursion)	Iterative solutions should be preferred over recursive ones for larger 'n' to avoid stack overflow errors.

Null or empty input array

How to Handle:

Return an empty string or handle the null/empty array with an appropriate exception.

Input array contains duplicate binary strings

How to Handle:

The solution needs to avoid generating the same string that already exists in the input.

Maximum input size nearing memory limits

How to Handle:

The solution must efficiently use memory and avoid allocating excessive amounts of memory.

All possible binary strings of length n are present in the input

How to Handle:

The solution should handle the case where no simple flip will yield a unique string, and consider other strategies like increasing the string length if the number of strings is a power of 2.

Input strings are not of the same length

How to Handle:

The problem statement should be clarified, or the code needs to handle varying lengths by padding or other means.

Input contains non-binary characters (not '0' or '1')

How to Handle:

The code should either validate the input strings to consist only of '0' and '1' characters, or handle invalid characters gracefully with error handling.

Integer overflow when converting binary string to integer

How to Handle:

The solution should use a different approach such as constructing the result string iteratively or directly manipulating the string rather than converting it to an integer.

n is very large, leading to potential stack overflow during recursion (if using recursion)

How to Handle:

Iterative solutions should be preferred over recursive ones for larger 'n' to avoid stack overflow errors.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the maximum size of the input array `nums`?
Are the binary strings in `nums` guaranteed to be of the same length?
Is the input array `nums` guaranteed to be non-empty?
If there are multiple possible unique binary strings, can I return any one of them?
What characters are allowed within the strings besides 0 and 1?

Brute Force Solution

Approach

Here's how the algorithm would work step-by-step:

First, determine the length that the binary string should be. This is based on the length of the strings in the given list.
Next, start creating binary strings. Begin with the simplest one consisting of all zeros.
Then, generate the next possible binary string in sequence, like counting in binary. Think of it as flipping the rightmost bit from 0 to 1, and then carrying over if needed.
For each generated string, check if it exists in the given list of binary strings.
If the generated string is not in the list, you have found your unique string. Stop and return this string.
If the generated string *is* in the list, continue to generate the next binary string and repeat the check until you find one that is not in the list, or until you've generated all possible strings of that length.

Code Implementation

def find_unique_binary_string_brute_force(binary_strings):
    string_length = len(binary_strings[0])

    number_of_possible_strings = 2**string_length
    for i in range(number_of_possible_strings):
        # Convert the integer to its binary string representation
        binary_representation = bin(i)[2:].zfill(string_length)

        # Check if the generated string is present in the input list
        if binary_representation not in binary_strings:
            return binary_representation

    # If no unique string is found, return an empty string (should not happen)
    return ""

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

Consider only the first position of the first string.
If the character at that position is 0, change it to 1. If it is 1, change it to 0. This is now the first character of our unique string.
Move to the second string, and consider its second position. Do the same flipping: if it's 0, change it to 1, and if it's 1, change it to 0. This becomes the second character of our unique string.
Continue this process, using the third position of the third string, the fourth position of the fourth string, and so on until we have a character for each position in our unique string.
Because we are flipping the character at the corresponding index for each string, we are guaranteed that the generated string will be different from all strings in the input set.

Code Implementation

def find_different_binary_string(numbers: list[str]) -> str:
    unique_string = ""
    for index, number in enumerate(numbers):
        # Flip the bit at the corresponding index to ensure uniqueness.
        if number[index] == '0':
            unique_string += '1'

        else:
            unique_string += '0'

    return unique_string

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty input array	Return an empty string or handle the null/empty array with an appropriate exception.
Input array contains duplicate binary strings	The solution needs to avoid generating the same string that already exists in the input.
Maximum input size nearing memory limits	The solution must efficiently use memory and avoid allocating excessive amounts of memory.
All possible binary strings of length n are present in the input	The solution should handle the case where no simple flip will yield a unique string, and consider other strategies like increasing the string length if the number of strings is a power of 2.
Input strings are not of the same length	The problem statement should be clarified, or the code needs to handle varying lengths by padding or other means.
Input contains non-binary characters (not '0' or '1')	The code should either validate the input strings to consist only of '0' and '1' characters, or handle invalid characters gracefully with error handling.
Integer overflow when converting binary string to integer	The solution should use a different approach such as constructing the result string iteratively or directly manipulating the string rather than converting it to an integer.
n is very large, leading to potential stack overflow during recursion (if using recursion)	Iterative solutions should be preferred over recursive ones for larger 'n' to avoid stack overflow errors.

Null or empty input array

How to Handle:

Return an empty string or handle the null/empty array with an appropriate exception.

Input array contains duplicate binary strings

How to Handle:

The solution needs to avoid generating the same string that already exists in the input.

Maximum input size nearing memory limits

How to Handle:

The solution must efficiently use memory and avoid allocating excessive amounts of memory.

All possible binary strings of length n are present in the input

How to Handle:

The solution should handle the case where no simple flip will yield a unique string, and consider other strategies like increasing the string length if the number of strings is a power of 2.

Input strings are not of the same length

How to Handle:

The problem statement should be clarified, or the code needs to handle varying lengths by padding or other means.

Input contains non-binary characters (not '0' or '1')

How to Handle:

The code should either validate the input strings to consist only of '0' and '1' characters, or handle invalid characters gracefully with error handling.

Integer overflow when converting binary string to integer

How to Handle:

The solution should use a different approach such as constructing the result string iteratively or directly manipulating the string rather than converting it to an integer.

n is very large, leading to potential stack overflow during recursion (if using recursion)

How to Handle:

Iterative solutions should be preferred over recursive ones for larger 'n' to avoid stack overflow errors.

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