algoadvance

Given a string s of zeros and ones, we want to split the string into two non-empty substrings left and right such that the score is maximized. The score of a split is defined as the number of ‘0’s in the left substring plus the number of ‘1’s in the right substring.

Return the maximum score we can achieve from any possible split of the string s.

Clarifying Questions

  1. Length of the String: Is there a constraint on the length of the string s?
    • The problem does not specify, but typically, interview problems are designed to handle around (10^5) characters. We’ll assume reasonable input sizes unless stated otherwise.
  2. Valid Splits: Should both substrings be non-empty after the split?
    • Yes, according to the problem statement, both left and right must be non-empty.
  3. Examples:
    • If s = "011101", then splitting it at different positions like “0 11101”, “01 1101”, etc., and computing the score will help validate the implementation.

Strategy

  1. Initialize Counters:
    • max_score to track the maximum score found.
    • left_zeros to count ‘0’s in the left substring.
    • right_ones to count ‘1’s in the right substring.
  2. Traverse the String:
    • First counts the total number of ‘1’s in the string to initialize our right_ones counter.
    • Iterate through the string while maintaining the counts of ‘0’s in the left part and ‘1’s in the right part.
    • For each position, calculate the score and update max_score.
  3. Consider Valid Splits:
    • Iterate up to len(s) - 1 to ensure non-empty substrings.

Time Complexity

Code

Here’s the implementation in Python:

def maxScore(s: str) -> int:
    # Initial count of '1's in the entire string
    right_ones = s.count('1')
    left_zeros = 0
    max_score = 0
    
    # Traverse the string, but stop at second last character to ensure non-empty right substring
    for i in range(len(s) - 1):
        if s[i] == '0':
            left_zeros += 1
        else:
            right_ones -= 1
        
        # Calculate score for the current partition
        current_score = left_zeros + right_ones
        max_score = max(max_score, current_score)
    
    return max_score

# Example usage
print(maxScore("011101"))  # Output: 5
print(maxScore("00111"))   # Output: 5
print(maxScore("1111"))    # Output: 3

This code correctly follows our outlined strategy and calculates the maximum score possible after splitting the string at any given position.

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