#2380

Medium

auto_awesomeState transition dynamic programming

LeetCode Problem Workspace

Time Needed to Rearrange a Binary String

Calculate the exact seconds required to convert all 01 pairs into 10 in a binary string using state transitions.

Problem Statement

You are given a binary string s consisting only of 0s and 1s. Every second, all occurrences of the substring 01 flip simultaneously into 10. The process repeats until no 01 substrings remain in the string.

Return the total number of seconds required for the string to stabilize with no 01 substrings. For example, given s = "0110101", the string transforms step by step until reaching "1111000", requiring 4 seconds in total.

Examples

Example 1

Input: s = "0110101"

Output: 4

After one second, s becomes "1011010". After another second, s becomes "1101100". After the third second, s becomes "1110100". After the fourth second, s becomes "1111000". No occurrence of "01" exists any longer, and the process needed 4 seconds to complete, so we return 4.

Example 2

Input: s = "11100"

Output: 0

No occurrence of "01" exists in s, and the processes needed 0 seconds to complete, so we return 0.

Constraints

1 <= s.length <= 1000
s[i] is either '0' or '1'.

Solution Approach

Simulate Direct Transformation

Iterate over the string repeatedly, swapping all 01 pairs simultaneously in each step. Count the number of iterations until the string has no 01 pairs left. This brute-force approach directly mirrors the problem's state transitions.

Track Zero Positions

Keep a list of positions of 0s and update their positions based on the nearest 1s. Increment a counter each time a 0 moves past a 1. This method reduces unnecessary iterations by focusing on state changes rather than the whole string.

Dynamic Programming Approach

Use an array to store the time each 0 will move past the preceding 1s. Update times using the maximum of previous relevant times plus one. The final answer is the maximum time across all 0s, capturing the state transition dynamics efficiently.

Complexity Analysis

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

Time complexity depends on the approach: direct simulation can reach O(n^2) in worst cases, while tracking positions or DP can achieve O(n). Space complexity ranges from O(n) for storing positions or DP arrays.

What Interviewers Usually Probe

The candidate may attempt a naive loop-based simulation first.
Look for candidates identifying overlapping flips and simultaneous state changes.
Efficient solutions often emerge by tracking 0 positions or using DP to model time steps.

Common Pitfalls or Variants

Common pitfalls

Failing to simulate flips simultaneously, leading to incorrect step counts.
Ignoring edge cases where the string has no 01 pairs from the start.
Using inefficient string concatenations repeatedly, causing performance issues.

Follow-up variants

Determine time for similar transformations in ternary strings with multiple patterns.
Compute minimal steps if only a single 01 can flip per second instead of all simultaneously.
Count the total number of flips instead of seconds until stabilization.

FAQ

What is the main idea behind Time Needed to Rearrange a Binary String?

The core concept is flipping all 01 pairs simultaneously each second until no 01 remains, tracking total iterations.

Can I optimize beyond simple simulation?

Yes, by tracking zero positions or using dynamic programming, you can reduce redundant operations and compute the time efficiently.

How does state transition dynamic programming apply here?

Each 0's movement past 1s represents a state transition; DP records the time each zero takes, allowing quick computation of total seconds.

What are common mistakes to avoid?

Not performing simultaneous flips, mishandling initial strings with no 01, or inefficiently updating the string can lead to wrong answers or slow solutions.

What constraints should I remember?

The string length is between 1 and 1000, and each character is either 0 or 1, which affects performance considerations for different approaches.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def secondsToRemoveOccurrences(self, s: str) -> int:
        ans = 0
        while s.count('01'):
            s = s.replace('01', '10')
            ans += 1
        return ans

Solution 2

#### Python3

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class Solution:
    def secondsToRemoveOccurrences(self, s: str) -> int:
        ans = 0
        while s.count('01'):
            s = s.replace('01', '10')
            ans += 1
        return ans

Continue Practicing

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