#761

Hard

LeetCode Problem Workspace

Special Binary String

Solve the Special Binary String problem using string manipulation and recursion, optimizing lexicographical order.

Problem Statement

Given a special binary string, you are tasked with performing moves to maximize the lexicographical order. A move consists of swapping two consecutive, non-empty special substrings. These substrings are considered consecutive if the last character of the first substring is immediately followed by the first character of the second substring. The goal is to make these swaps to achieve the lexicographically largest string possible.

A special binary string is one where a substring is either '10' or '1100'. Your task is to find an efficient way to make the necessary swaps using recursion to achieve the largest possible lexicographical string. This involves considering consecutive substrings and performing the swaps recursively until you reach the desired result.

Examples

Example 1

Input: s = "11011000"

Output: "11100100"

The strings "10" [occuring at s[1]] and "1100" [at s[3]] are swapped. This is the lexicographically largest string possible after some number of swaps.

Example 2

Input: s = "10"

Output: "10"

Example details omitted.

Constraints

1 <= s.length <= 50
s[i] is either '0' or '1'.
s is a special binary string.

Solution Approach

Recursive Substring Identification

The key to solving this problem is identifying the special substrings and recursively breaking down the string. Use recursion to break down the string into smaller substrings and evaluate which ones can be swapped. At each step, ensure that the swap results in a lexicographically larger string.

Lexicographical Optimization

Once you identify valid substrings for swapping, prioritize lexicographically larger strings. By recursively swapping special substrings, you can ensure that each transformation brings you closer to the largest possible string. This process requires careful consideration of substring order at each recursive step.

Efficient Recursion and String Manipulation

Optimize the recursion to reduce unnecessary operations. Handle base cases where no further swaps are needed and ensure that string manipulation is efficient. By focusing on recursion depth and efficient substring swapping, you can achieve a solution that works within the problem's constraints.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depends on the final recursive approach, as it involves breaking down the string into smaller substrings and swapping them. The recursion depth and the number of substrings involved will impact the overall time and space complexity. Optimizing the recursion and limiting unnecessary operations will help improve performance within the given constraints.

What Interviewers Usually Probe

The candidate should demonstrate an understanding of recursive string manipulation techniques.
Look for the candidate's ability to handle special substring identification and swapping in a recursive manner.
Assess how efficiently the candidate optimizes recursion depth and string manipulation operations.

Common Pitfalls or Variants

Common pitfalls

Failing to identify the correct substrings for swapping can lead to incorrect results.
Overcomplicating the recursion logic or failing to handle base cases can lead to unnecessary complexity.
Not optimizing the recursion can result in excessive computation time for larger inputs.

Follow-up variants

Consider handling input strings with varying lengths and more complex special substrings.
Explore different ways to optimize recursion for larger input sizes while maintaining correct functionality.
Experiment with alternative ways to represent the special substrings to simplify the recursive approach.

FAQ

What is the key to solving the Special Binary String problem?

The key to solving the Special Binary String problem is using recursion to identify and swap consecutive special substrings in order to maximize the lexicographical order.

How can recursion help in solving the Special Binary String problem?

Recursion allows for breaking down the string into smaller special substrings, evaluating potential swaps, and optimizing the string to achieve the largest possible lexicographical order.

What should I focus on when swapping substrings in this problem?

Focus on identifying consecutive special substrings and ensuring each swap results in a lexicographically larger string. Prioritize lexicographical optimization.

What are common pitfalls in solving the Special Binary String problem?

Common pitfalls include failing to identify correct special substrings, overcomplicating the recursion, and not optimizing recursion depth for performance.

How does GhostInterview help with the Special Binary String problem?

GhostInterview offers structured guidance for recursive string manipulation, provides hints on optimizing recursion depth, and highlights common mistakes to help you solve the problem efficiently.

terminal

Solution

Solution 1: Recursion + Sorting

We can treat the special binary sequence as "valid parentheses", where $1$ represents an opening parenthesis and $0$ represents a closing parenthesis. For example, "11011000" can be viewed as "(()(()))".

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class Solution:
    def makeLargestSpecial(self, s: str) -> str:
        if s == '':
            return ''
        ans = []
        cnt = 0
        i = j = 0
        while i < len(s):
            cnt += 1 if s[i] == '1' else -1
            if cnt == 0:
                ans.append('1' + self.makeLargestSpecial(s[j + 1 : i]) + '0')
                j = i + 1
            i += 1
        ans.sort(reverse=True)
        return ''.join(ans)

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