💡 Problem Formulation: The task is to write a Python program that finds the maximum score obtained by splitting a binary string into two non-empty parts, where the score is defined as the sum of the count of zeros in the first part and the count of ones in the second part. For example, given input ‘010101’, the maximum score would be obtained by splitting it into ‘010’ and ‘101’, yielding a score of 3 (2 zeros + 1 one).
Method 1: Using a Simple Loop
This method involves iterating through the binary string, counting zeros on the left side and ones on the right side, and updating the maximum score each time a split is made. This is a simple and straightforward implementation suitable for beginners.
Here’s an example:
def find_max_score(binary_string):
max_score, zero_count, one_count = 0, 0, binary_string.count('1')
for i in range(len(binary_string) - 1):
if binary_string[i] == '0':
zero_count += 1
else:
one_count -= 1
max_score = max(max_score, zero_count + one_count)
return max_score
print(find_max_score('010101'))Output:
3
The function find_max_score() computes the score by maintaining a zero count for the left part and a one count for the right part. It iterates over the binary string, updating the counts and recording the maximum score achieved just before each character. It ensures that the string is always split into non-empty parts.
Method 2: Prefix Sums Approach
The prefix sums approach computes an array where each element is the sum of zeros up to that point. The score can then be found by iterating over this array while keeping track of the ones to the right.
Here’s an example:
def find_max_score_prefix(binary_string):
prefix_zeros = [0] * len(binary_string)
one_count = binary_string.count('1')
for i in range(len(binary_string)):
prefix_zeros[i] = prefix_zeros[i - 1] + (binary_string[i] == '0')
max_score = max(prefix_zeros[i] + one_count - (prefix_zeros[-1] - prefix_zeros[i])
for i in range(len(binary_string) - 1))
return max_score
print(find_max_score_prefix('010101'))Output:
3
This code snippet creates an array prefix_zeros that stores the cumulative sum of zeros in the binary string. The maximum score is determined by iterating over this array and calculating the score at each possible split point, factoring in the total number of ones and the number of zeros so far.
Method 3: Using itertools
This method utilizes Python’s itertools.accumulate() function to create the prefix sums array, simplifying the code and potentially improving readability.
Here’s an example:
from itertools import accumulate
def find_max_score_itertools(binary_string):
zeros = list(accumulate(1 for char in binary_string if char == '0'))
max_score = 0
one_count = binary_string.count('1')
for i, zero in enumerate(zeros[:-1], 1):
max_score = max(max_score, zero + one_count)
one_count -= binary_string[i] == '1'
return max_score
print(find_max_score_itertools('010101'))Output:
3
The function find_max_score_itertools() computes the score in a clear and concise way by creating a zeros array using accumulate(). It calculates the maximum score considering each possible split and dynamically decreases the one count as it progresses through the string.
Method 4: Optimized Comparison
This method optimizes the score computation by directly comparing the zeros and ones count without additional data structures. It is a more space-efficient solution.
Here’s an example:
def find_max_score_optimized(binary_string):
max_score, zeros, ones = 0, 0, 0
for char in binary_string:
if char == '0':
zeros += 1
else:
ones += 1
if zeros > ones:
max_score = max(max_score, zeros + (binary_string.count('1', zeros + ones) - ones))
return max_score
print(find_max_score_optimized('010101'))Output:
3
Within the function find_max_score_optimized(), the code continuously updates the zero and one counts while iterating over the string. Whenever the count of zeros is greater than that of ones, it computes the current score by updating the one count for the remainder of the string to find the potential maximum.
Bonus One-Liner Method 5: Pythonic Approach
This one-liner leverages Python’s list comprehensions and slicing to find the maximum score in a compact, albeit less efficient, manner.
Here’s an example:
max_score_one_liner = lambda s: max(s[:i].count('0') + s[i:].count('1') for i in range(1, len(s)))
print(max_score_one_liner('010101'))Output:
3
The one-liner max_score_one_liner uses a lambda function to iterate over possible split points while counting zeros in the first part and ones in the second part to find the maximum score. This approach is elegant but could be inefficient for long strings due to repetitive counting.
Summary/Discussion
- Method 1: Simple Loop. Easy to understand. May not be the most efficient for very long strings.
- Method 2: Prefix Sums Approach. More efficient than Method 1. Requires additional space for the prefix sums array.
- Method 3: Using itertools. Clean and concise. Relies on the Python standard library, potentially less intuitive for those unfamiliar with itertools.
- Method 4: Optimized Comparison. Space-efficient. The logic is slightly more complex, making it harder to read.
- Method 5: Pythonic One-Liner. Elegant and compact. Poor performance for large strings due to repeated counting operations.