# Flip String To Monotone Increasing Problem

## Description

LeetCode Problem 926.

A binary string is monotone increasing if it consists of some number of 0’s (possibly none), followed by some number of 1’s (also possibly none).

You are given a binary string s. You can flip s[i] changing it from 0 to 1 or from 1 to 0.

Return the minimum number of flips to make s monotone increasing.

Example 1:

``````1
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Input: s = "00110"
Output: 1
Explanation: We flip the last digit to get 00111.
``````

Example 2:

``````1
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Input: s = "010110"
Output: 2
Explanation: We flip to get 011111, or alternatively 000111.
``````

Example 3:

``````1
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Input: s = "00011000"
Output: 2
Explanation: We flip to get 00000000.
``````

Constraints:

• 1 <= s.length <= 10^5
• s[i] is either ‘0’ or ‘1’.

## Sample C++ Code

``````1
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class Solution {
public:
int minFlipsMonoIncr(const std::string& S, int counter_one  = 0, int counter_flip = 0) {
for (auto ch : S) {
// if c is 1, then it will not inpact the minFlips
// if c is 0, then 2 options we can do to make it mono incr
// 1. keep it as 0, and flip all the preceeding 1 to 0,
// need to know the count of ones so far
// 2. flip it to 1, will not need to do anything
if (ch == '1') {
++counter_one;
} else {
++counter_flip;
}
counter_flip = std::min(counter_one, counter_flip);
}
return counter_flip;
}
};
``````