Maximum Score After Splitting a String

Maximum Score After Splitting a String

1. What is this problem about?

The Maximum Score After Splitting a String interview question is a simple but common string manipulation problem. Given a string of 0s and 1s, you need to split it into two non-empty parts: a left part and a right part. The "score" of a split is defined as the number of 0s in the left part plus the number of 1s in the right part. Your goal is to find the maximum score among all possible splits.

A split must leave at least one character in each part.

2. Why is this asked in interviews?

This Maximum Score After Splitting a String coding problem is a frequent choice for early-stage interviews at Meta, Amazon, and Bloomberg. It tests basic array/string traversal and your ability to optimize from an $O(N^2)$ brute-force solution to a more efficient $O(N)$ single-pass or two-pass solution. It also evaluates your understanding of prefix sums, a fundamental concept for range queries.

3. Algorithmic pattern used

The String, Prefix Sum interview pattern is the ideal approach.

1. First pass: Count the total number of 1s in the entire string.
2. Second pass: Iterate through the string (excluding the last character to ensure non-empty parts), maintaining a count of 0s seen so far (left part) and 1s seen so far.
3. For each split, score = zeros_left + (total_ones - ones_left).
4. Keep track of the maximum score.

4. Example explanation

String: "011101" Total 1s = 4.

• Split after '0' (Left="0", Right="11101"): zeros=1, ones_left=0. Score = 1 + (4-0) = 5.
• Split after '01' (Left="01", Right="1101"): zeros=1, ones_left=1. Score = 1 + (4-1) = 4.
• Split after '011' (Left="011", Right="101"): zeros=1, ones_left=2. Score = 1 + (4-2) = 3.
• Split after '0111' (Left="0111", Right="01"): zeros=1, ones_left=3. Score = 1 + (4-3) = 2.
• Split after '01110' (Left="01110", Right="1"): zeros=2, ones_left=3. Score = 2 + (4-3) = 3.

Maximum Score is 5.

5. Common mistakes candidates make

A frequent error in the Maximum Score After Splitting a String coding problem is not respecting the "non-empty" constraint, leading to splits at the very beginning or very end of the string. Another mistake is using nested loops for an $O(N^2)$ solution, which is inefficient. Some might also incorrectly count the 1s in the right part, perhaps including 1s that are actually in the left part.

6. Interview preparation tip

Always look for ways to avoid redundant counting. If you need to count something in two parts of an array, counting it once globally and then adjusting the count as you iterate (the "running total" approach) is a very common and efficient pattern.