A string of '0's and '1's is monotone increasing if it consists of some number of '0's (possibly 0), followed by some number of '1's (also possibly 0.)
We are given a string S of '0's and '1's, and we may flip any '0' to a '1' or a '1' to a '0'.
Return the minimum number of flips to make S monotone increasing.
Example 1:
Input: "00110"
Output: 1
Explanation: We flip the last digit to get 00111.
Example 2:
Input: "010110"
Output: 2
Explanation: We flip to get 011111, or alternatively 000111.
Example 3:
Input: "00011000"
Output: 2
Explanation: We flip to get 00000000.
Note:
1 <= S.length <= 20000
S only consists of '0' and '1' characters.
class Solution:
    def minFlipsMonoIncr(self, S: str) -> int:
        
        n, prefix, total, res = len(S), 0, S.count('1'), sys.maxsize
        for i in range(n + 1):
            res = min(res, prefix + len(S) - i - total + prefix)
            if i < n: prefix += 1 if S[i] == '1' else 0
        return res

class Solution:
    def minFlipsMonoIncr(self, S: str) -> int:
        
        n, prefix, total, res = len(S), 0, S.count('1'), sys.maxsize
        for i in range(n + 1):
            res = min(res, prefix + len(S) - i - total + prefix)
            if i < n: prefix += 1 if S[i] == '1' else 0
        return res
