## Algorithm

Problem Name: 926. Flip String to Monotone Increasing

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:

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

Example 2:

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

Example 3:

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

Constraints:

• `1 <= s.length <= 105`
• `s[i]` is either `'0'` or `'1'`.

## Code Examples

### #1 Code Example with C Programming

```Code - C Programming```

``````
int minFlipsMonoIncr(char* S) {
/*
1   0   0   1   1   1   1   1   1   1   1   0   0   1   1       n = 15
0   1   1   1   2   3   4   5   6   7   8   9   9   9   10  11  <- num of 1 ahead
4   4   3   2   2   2   2   2   2   2   2   2   1   0   0   0       <- num of 0 after
4   5   4   3   4   5   ...
*/
int i, n, ones[20001], zeros[20001];
int flip2zero, flip2one, flip, min;

n = 0;
ones[0] = 0;
while (S[n]) {
ones[n + 1] = ones[n] + (S[n] == '1' ? 1 : 0);

}

i = n;
zeros[i --] = 0;
while (i >= 0) {
zeros[i] = zeros[i + 1] + (S[i] == '0' ? 1 : 0);
i --;
}

min = n;
for (i = 0; i  < = n; i ++) {
flip = ones[i] + zeros[i];  // at i, ones ahead need to flip to zero
//  and zeros after need to flip to one
if (min > flip) min = flip;
}

return min;
}
``````
Copy The Code &

Input

cmd
s = "00110"

Output

cmd
1

### #2 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const minFlipsMonoIncr = function(s) {
const n = s.length
let res = 0, oneCnt = 0
for(const e of s) {
if(e === '1') oneCnt++
else {
const stayZero = oneCnt
const flipToOne = res + 1
res = Math.min(stayZero, flipToOne)
}
}

return res
};
``````
Copy The Code &

Input

cmd
s = "00110"

Output

cmd
1

### #3 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def minFlipsMonoIncr(self, s):
res = cur = s.count("0")
for c in s: res, cur = c == "1" and (res, cur + 1) or (min(res, cur - 1), cur - 1)
return res
``````
Copy The Code &

Input

cmd
s = "010110"

Output

cmd
2