#3499

Medium

LeetCode Problem Workspace

Maximize Active Section with Trade I

Maximize the number of active sections in a binary string by performing at most one trade operation.

Problem Statement

Given a binary string s of length n, you can perform at most one trade operation to maximize the number of active sections in the string. A trade involves flipping a segment of consecutive '0's into '1's or vice versa. Your goal is to return the maximum number of active sections in s after performing the optimal trade.

The string s consists only of '0's and '1's, and the task is to maximize the number of active sections formed by groups of consecutive identical characters. After performing a trade, the string may be split into additional active sections depending on the pattern formed by the trade.

Examples

Example 1

Input: s = "01"

Output: 1

Because there is no block of '1' s surrounded by '0' s, no valid trade is possible. The maximum number of active sections is 1.

Example 2

Input: s = "0100"

Output: 4

Example 3

Input: s = "1000100"

Output: 7

Constraints

1 <= n == s.length <= 105
s[i] is either '0' or '1'

Solution Approach

Identify Zero-One Segments

Start by splitting the binary string into segments of consecutive '1's and '0's. This helps in visualizing where trades can potentially increase the number of active sections. A trade is most effective when flipping a group of '0's surrounded by '1's.

Evaluate Trade Opportunities

Next, consider the optimal places for a trade. Check which '0' segments can be turned into '1' to maximize the number of splits. This involves checking whether flipping a segment of '0's between '1's can result in additional active sections.

Simulate the Trade

Simulate the effect of each potential trade. For each segment of '0's, determine how many new active sections can be created. Track the maximum number of sections across all possible trades to determine the optimal result.

Complexity Analysis

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

The time complexity is O(n), where n is the length of the string, since splitting the string and evaluating possible trades both require linear scans. The space complexity is O(n) due to storing segments of the string.

What Interviewers Usually Probe

The candidate identifies key segments of '0's and '1's and their potential for creating additional sections.
They analyze the impact of different trade scenarios on the string's structure.
They demonstrate an efficient approach to evaluating and maximizing the number of active sections.

Common Pitfalls or Variants

Common pitfalls

Not correctly identifying segments of '0's and '1's for potential trades.
Assuming that any '0' block can be flipped, when only '0' blocks surrounded by '1's are relevant.
Overcomplicating the problem by attempting to perform unnecessary trades that don’t increase the number of sections.

Follow-up variants

Consider cases where the string consists entirely of '0's or '1's.
Handle strings with mixed lengths of '0's and '1's, ensuring the trade maximizes sections.
Analyze larger inputs where performance optimizations become more critical.

FAQ

What is the core pattern behind this problem?

The core pattern revolves around identifying and manipulating zero-one segments in a binary string to maximize the number of active sections.

How can I approach maximizing the active sections?

Split the string into segments and evaluate where a trade can increase the number of sections. Focus on flipping '0' blocks surrounded by '1's.

Why is it important to focus on zero-one segments?

Zero-one segments allow you to understand the structure of the string and identify where trades will create the most impact on the number of active sections.

Can the string consist only of '1's or '0's?

Yes, if the string is entirely '1's or '0's, the maximum number of active sections will remain constant, and no trade will be possible.

How does GhostInterview help with problem-solving here?

GhostInterview provides hints and step-by-step guidance to break down the problem into smaller segments, making it easier to spot potential optimizations and avoid common pitfalls.

terminal

Solution

Solution 1: Greedy + Two Pointers

The problem is essentially equivalent to finding the number of `'1'` characters in the string $\textit{s}$, plus the maximum number of `'0'` characters in two adjacent consecutive `'0'` segments.

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class Solution:
    def maxActiveSectionsAfterTrade(self, s: str) -> int:
        n = len(s)
        ans = i = 0
        pre, mx = -inf, 0
        while i < n:
            j = i + 1
            while j < n and s[j] == s[i]:
                j += 1
            cur = j - i
            if s[i] == "1":
                ans += cur
            else:
                mx = max(mx, pre + cur)
                pre = cur
            i = j
        ans += mx
        return ans

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