1422. Maximum Score After Splitting a String
Description
Given a string s
of zeros and ones, return the maximum score after splitting the string into two non-empty substrings (i.e. left substring and right substring).
The score after splitting a string is the number of zeros in the left substring plus the number of ones in the right substring.
Example 1:
Input: s = "011101" Output: 5 Explanation: All possible ways of splitting s into two non-empty substrings are: left = "0" and right = "11101", score = 1 + 4 = 5 left = "01" and right = "1101", score = 1 + 3 = 4 left = "011" and right = "101", score = 1 + 2 = 3 left = "0111" and right = "01", score = 1 + 1 = 2 left = "01110" and right = "1", score = 2 + 1 = 3
Example 2:
Input: s = "00111" Output: 5 Explanation: When left = "00" and right = "111", we get the maximum score = 2 + 3 = 5
Example 3:
Input: s = "1111" Output: 3
Constraints:
2 <= s.length <= 500
- The string
s
consists of characters'0'
and'1'
only.
Solutions
Solution 1: Counting
We use two variables $l$ and $r$ to record the number of 0s in the left substring and the number of 1s in the right substring, respectively. Initially, $l = 0$, and $r$ is equal to the number of 1s in the string $s$.
We traverse the first $n - 1$ characters of the string $s$. For each position $i$, if $s[i] = 0$, then $l$ is incremented by 1; otherwise, $r$ is decremented by 1. Then we update the answer to be the maximum value of $l + r$.
The time complexity is $O(n)$, where $n$ is the length of the string $s$. The space complexity is $O(1)$.
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