Leetcode is a well-known platform for honing coding and problem-solving skills, often used for interview preparation. One such problem that has grabbed attention is the “Maximum Score After Splitting a String” problem. This problem is generally classified under the array and string manipulation categories, requiring a combination of insights to solve efficiently.

This in-depth article will cover:

- Problem Statement & Examples
- Brute-force Approach
- Optimized Approach
- Python Code Implementations
- Test Cases and Runtime Analysis
- Conclusion

## 1. Problem Statement & Examples

### Problem Statement

Given a string `s`

of zeros and ones, you need to return the maximum score after splitting the string into two **non-empty** parts such that the number of zeros on the left part and the number of ones on the right part is maximized.

Example 1:

```
Input: s = "0111001"
Output: 4
Explanation:
Splitting at index 3 results in two parts: "011" and "1001".
Number of zeros in the left part = 0
Number of ones in the right part = 4
Total score = 0 + 4 = 4
```

Example 2:

```
Input: s = "00111"
Output: 3
Explanation:
Splitting at index 2 results in two parts: "00" and "111".
Number of zeros in the left part = 2
Number of ones in the right part = 1
Total score = 2 + 1 = 3
```

## 2. Brute-force Approach

A straightforward way to solve this problem is to:

- Iterate over the string, keeping a count of zeros and ones.
- Try every possible splitting point, calculating the score for each.
- Return the maximum score.

However, this approach has a time complexity of O(n^2), which is inefficient for large strings.

## 3. Optimized Approach

You can optimize the solution using a single pass through the string:

- Calculate the total counts of zeros (
`total_zeros`

) and ones (`total_ones`

) first. - Initialize variables
`left_zeros`

and`left_ones`

to keep track of the zeros and ones on the left part as you iterate. - Loop through the string to find the score at each split point.

This approach has a time complexity of O(n), which is much better.

## 4. Python Code Implementations

### Brute-force Solution

```
def maxScore(s: str) -> int:
max_score = 0
for i in range(1, len(s)):
left, right = s[:i], s[i:]
score = left.count('0') + right.count('1')
max_score = max(max_score, score)
return max_score
```

### Optimized Solution

```
def maxScore(s: str) -> int:
total_zeros, total_ones = s.count('0'), s.count('1')
max_score, left_zeros, left_ones = 0, 0, 0
for i in range(len(s) - 1):
if s[i] == '0':
left_zeros += 1
else:
left_ones += 1
score = left_zeros + (total_ones - left_ones)
max_score = max(max_score, score)
return max_score
```

## 5. Test Cases and Runtime Analysis

Both solutions pass the LeetCode test cases, but the optimized solution is much faster.

- Brute-force: O(n^2)
- Optimized: O(n)

## 6. Conclusion

The “Maximum Score After Splitting a String” problem is a compelling task that tests your string manipulation and problem-solving skills. Although a brute-force approach is straightforward to implement, it’s not efficient for large datasets. The optimized O(n) solution is better suited for tackling this problem effectively.