The problem requires splitting a binary string into three parts with an equal number of '1's. The solution needs to check if the sum of '1's is divisible by 3 and find the possible splits based on the positions of '1's. Given the constraints, an efficient approach is necessary to handle large inputs.
Problem Statement
Given a binary string s, split it into three non-empty parts s1, s2, and s3 such that s1 + s2 + s3 = s. The goal is to return the number of valid ways to perform the split such that the number of '1's in each part is equal.
If the sum of '1's in the entire string is not divisible by 3, no such split is possible. You should return the result modulo $10^9 + 7$ as the answer could be large.
Examples
Example 1
Input: s = "10101"
Output: 4
There are four ways to split s in 3 parts where each part contain the same number of letters '1'. "1|010|1" "1|01|01" "10|10|1" "10|1|01"
Example 2
Input: s = "1001"
Output: 0
Example details omitted.
Example 3
Input: s = "0000"
Output: 3
There are three ways to split s in 3 parts. "0|0|00" "0|00|0" "00|0|0"
Constraints
- 3 <= s.length <= 105
- s[i] is either '0' or '1'.
Solution Approach
Check Divisibility by 3
First, check if the total count of '1's in the string is divisible by 3. If not, return 0 immediately as it's impossible to split the string in the required way.
Locate Positions of '1's
Identify the positions of all '1's in the string. Then, determine the target count of '1's per part. The positions can help in finding where to split the string into valid parts with equal '1's.
Calculate Possible Splits
Once we have the positions, calculate how many valid splits can occur by considering the possible ways to divide the positions of '1's into three groups. The answer is determined by the number of valid combinations of these splits.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity mainly depends on identifying the positions of '1's in the string, which takes $O(n)$ time, where $n$ is the length of the string. Finding the splits also takes linear time in the worst case, making the overall complexity $O(n)$ for time. Space complexity is $O(n)$ for storing the positions of '1's in the string.
What Interviewers Usually Probe
- Candidate shows an understanding of the need to first check divisibility by 3.
- Candidate knows how to identify the positions of '1's efficiently.
- Candidate considers how to count valid splits based on the positions of '1's.
Common Pitfalls or Variants
Common pitfalls
- Ignoring the requirement that the total number of '1's must be divisible by 3.
- Failing to account for strings that contain no '1's or have fewer than three '1's.
- Incorrectly calculating the number of valid splits by not considering all the possible ways to split the string.
Follow-up variants
- What if the string contains only '0's?
- How would you approach the problem if the string could contain other characters besides '0' and '1'?
- What optimizations can be made if we are allowed to split the string into more than three parts?
How GhostInterview Helps
- GhostInterview helps by guiding you through the essential steps of checking for divisibility by 3 and identifying the key positions in the string.
- It offers suggestions on efficient techniques to count valid splits without resorting to brute force methods.
- GhostInterview ensures that you keep the solution optimal even for large strings by emphasizing time complexity considerations.
Topic Pages
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- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
How do I approach the problem of splitting a binary string into three parts?
Start by checking if the total number of '1's in the string is divisible by 3. Then, calculate the positions of '1's and figure out how to split them into three parts with equal '1's.
What should I do if the sum of '1's is not divisible by 3?
If the total number of '1's is not divisible by 3, immediately return 0 because a valid split is not possible.
Why do I need to store the positions of '1's?
Storing the positions of '1's allows you to efficiently find where to split the string into three parts with equal numbers of '1's.
What is the time complexity of the solution?
The time complexity is O(n), where n is the length of the string. This is due to the need to check the positions of all '1's and calculate possible splits.
Can this problem be solved with dynamic programming?
Dynamic programming is not necessary for this problem as it can be solved efficiently with a linear scan of the string and careful counting of valid splits.
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