What is the time complexity of Special Binary String?

The optimal solution for Special Binary String runs in Unknown time and uses Unknown space.

What algorithm or data structure is used to solve Special Binary String?

Special Binary String uses the following concepts: String, Divide and Conquer, Sorting. The recommended patterns to study are: Divide and Conquer, Recursion.

What are the interview tips for Special Binary String?

Understand the properties of special binary strings Practice breaking down the problem into smaller parts Think about how to maximize the result while maintaining constraints

What are common mistakes when solving Special Binary String?

Failing to recognize special substrings Not handling the recursive decomposition correctly

Special Binary String — LeetCode #761 (Hard)

Tags: String, Divide and Conquer, Sorting

Related patterns: Divide and Conquer, Recursion

Brute Force approach

Time complexity: O(n²). Space complexity: O(1).

The brute-force approach involves generating all possible configurations of the special binary string by swapping special substrings. This method is straightforward but inefficient due to the exponential number of possible swaps.

The time complexity is O(n²) because we potentially check every substring pair in the string, leading to a quadratic number of checks. The space complexity is O(1) since we only use a few variables to store counts.

Step 1: Identify all special substrings in the given string.
Step 2: Generate all possible strings by swapping each pair of consecutive special substrings.
Step 3: From the generated strings, select the lexicographically largest one.

For s = '11011000': 1. Identify special substrings: ['1100', '10', '00'] 2. Generate swaps: '1100' + '10' = '110010', '10' + '1100' = '101100' 3. Compare results: max = '110010', '101100' => max = '110010' 4. Final output: '110010'

Optimal Solution approach

Time complexity: Unknown. Space complexity: Unknown.

The optimal approach uses a recursive strategy to decompose the string into special substrings, sorts them, and then combines them back in a way that ensures the result is lexicographically largest. This method is efficient and directly leverages the properties of special binary strings.

Step 1: Recursively decompose the string into special substrings.
Step 2: Sort the special substrings in reverse order to ensure lexicographical maximization.
Step 3: Concatenate the sorted substrings to form the final result.

Common Mistakes

Failing to recognize special substrings
Not handling the recursive decomposition correctly

Interview Tips

Understand the properties of special binary strings
Practice breaking down the problem into smaller parts
Think about how to maximize the result while maintaining constraints

#761

Special Binary String

Hard

String↗Divide and Conquer↗Sorting↗Divide and Conquer↗Recursion↗

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	Unknown
Space	O(1)	Unknown

💡

Intuition

Time UnknownSpace Unknown

⚙️

Algorithm

3 steps

1Step 1: Recursively decompose the string into special substrings.
2Step 2: Sort the special substrings in reverse order to ensure lexicographical maximization.
3Step 3: Concatenate the sorted substrings to form the final result.

solution.py12 lines

1def makeLargestSpecial(s):
2    count = i = 0
3    special = []
4    for j in range(len(s)):
5        count += 1 if s[j] == '1' else -1
6        if count == 0:
7            special.append('1' + makeLargestSpecial(s[i + 1:j]) + '0')
8            i = j + 1
9    return ''.join(sorted(special, reverse=True))
10
11# Example usage
12print(makeLargestSpecial('11011000'))

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.