Maximum Score After Splitting a String

Maximum Score After Splitting a String - Problem

Given a string s consisting of zeros and ones only, return the maximum score after splitting the string into two non-empty substrings (left substring and right substring).

The score is calculated as:

Number of zeros in the left substring
Plus number of ones in the right substring

Both substrings must be non-empty after the split.

Input & Output

Example 1 — Basic Case

$ Input: s = "011101"

› Output: 5

💡 Note: Split after index 0: left="0" (1 zero), right="11101" (4 ones), score = 1+4 = 5. This is the maximum possible.

Example 2 — All Zeros

$ Input: s = "00"

› Output: 1

💡 Note: Only one valid split: left="0" (1 zero), right="0" (0 ones), score = 1+0 = 1.

Example 3 — Mixed String

$ Input: s = "1111"

› Output: 3

💡 Note: Best split after index 0: left="1" (0 zeros), right="111" (3 ones), score = 0+3 = 3.

Constraints

2 ≤ s.length ≤ 500
The string s consists of zeros and ones only

Visualization

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Asked in

G Google 15 a Amazon 12 M Microsoft 8

The key insight is to avoid recounting characters at each split position. Use prefix sum technique: first count total ones, then maintain running counts as we iterate. Best approach achieves O(n) time, O(1) space.

Common Approaches

✓ Brute Force - Try Every Split

⏱️ Time: O(n²) Space: O(1)

For each valid split position, count zeros in the left substring and ones in the right substring. Keep track of the maximum score found.

Prefix Sum Optimization

⏱️ Time: O(n) Space: O(1)

First pass counts total ones in the string. Second pass iterates through each split position, maintaining running count of zeros on left and calculating ones on right efficiently.

Brute Force - Try Every Split — Algorithm Steps

Iterate through each valid split position (1 to n-1)
For each split, count zeros in left part and ones in right part
Update maximum score if current split gives better result

Visualization

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Step-by-Step Walkthrough

Try Split 1

Split after position 1, count zeros left and ones right

Try Split 2

Split after position 2, count zeros left and ones right

Find Maximum

Compare all scores to find the maximum

Code -

solution.c — C

#include <stdio.h>
#include <string.h>

int solution(char* s) {
    int n = strlen(s);
    int maxScore = 0;
    
    for (int i = 1; i < n; i++) {
        int leftZeros = 0, rightOnes = 0;
        
        for (int j = 0; j < i; j++) {
            if (s[j] == '0') leftZeros++;
        }
        
        for (int j = i; j < n; j++) {
            if (s[j] == '1') rightOnes++;
        }
        
        int score = leftZeros + rightOnes;
        if (score > maxScore) {
            maxScore = score;
        }
    }
    
    return maxScore;
}

int main() {
    char s[1005];
    fgets(s, sizeof(s), stdin);
    s[strcspn(s, "\n")] = 0;
    
    int result = solution(s);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

For each of n-1 split positions, we count characters in both substrings taking O(n) time

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables to track counts and maximum score

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - Try Every Split — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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