Find Unique Binary String

LeetCode 2107 | Difficulty: Medium

Medium

Problem Description

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**.

Topics: Array, Hash Table, String, Backtracking

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Approach

Backtracking

Explore all candidates by building solutions incrementally. At each step, choose an option, explore further, then unchoose (backtrack) to try the next option. Prune branches that can't lead to valid solutions.

When to use

Generate all combinations/permutations, or find solutions that satisfy constraints.

Hash Map

Use a hash map for O(1) average lookups. Store seen values, frequencies, or indices. The key question: what should I store as key, and what as value?

When to use

Need fast lookups, counting frequencies, finding complements/pairs.

String Processing

Consider character frequency counts, two-pointer approaches, or building strings efficiently. For pattern matching, think about KMP or rolling hash. For palindromes, expand from center or use DP.

When to use

Anagram detection, palindrome checking, string transformation, pattern matching.

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Solutions

Solution 1: C# (Best: 138 ms)

Metric	Value
Runtime	138 ms
Memory	37.5 MB
Date	2022-01-21

Solution

public class Solution {
    public string FindDifferentBinaryString(string[] nums) {
     string result = "";
     for(int i=0;i<nums.Length;i++)
     {
         result += (nums[i][i]=='0') ? '1' : '0';
     }
        return result;
    }
}

📜 1 more C# submission(s)

Submission (2022-01-21) — 159 ms, 37.5 MB

public class Solution {
    public string FindDifferentBinaryString(string[] nums) {
     List<long> seen = nums.Select(x=>GetNumber(x)).ToList();
    double len =  Math.Pow(2, nums[0].Length);
    for (long i = 0; i < len; i++)
    {
        if(!seen.Contains(i)) return GetBinaryString(i,nums[0].Length);
    }
    return string.Empty;    
}

private string GetBinaryString(long n, int len)
{
    char[] result = new char[len];
    for (int i = 0; i < len; i++)
    {
        result[i] = '0';
    }
    int index = len-1;
    while(n>0)
    {
        result[index--] = (char)(n%2+'0');
        n = n/2;
    }
    return new string(result);
}
    
private long GetNumber(string num)
{
    long result = 0;
    foreach(var c in num)
    {
        result = result*2 + (c-'0');
    }
    return result;
}
}

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Complexity Analysis

Approach	Time	Space
Backtracking	$O(n! or 2^n)$	$O(n)$
Hash Map	$O(n)$	$O(n)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.
• Hash map gives O(1) lookup — think about what to use as key vs value.
• Identify pruning conditions early to avoid exploring invalid branches.
• LeetCode provides 2 hint(s) for this problem — try solving without them first.

💡 Hints

Hint 1: We can convert the given strings into base 10 integers.

Hint 2: Can we use recursion to generate all possible strings?