Flip String to Monotone Increasing - Solution & Explanation

This approach utilizes prefix sums to calculate the minimum number of flips required to make a binary string monotone increasing. The idea is to traverse the string while maintaining a prefix count of '1's and suffix count of '0's. For each position i, calculate how many flips would be necessary to make all characters before i '0' + make all characters from i '1'.

This solution iterates through the string and calculates prefix sums for '1's. Then it computes the potential flips required at each breakpoint to make the string monotone increasing and returns the minimum.

This approach leverages dynamic programming to find the minimum flips. Two states are maintained for any position: one representing the minimal flips to have a monotone ending with '0' and the other with '1'. Update these states as we traverse the string.

The dynamic programming approach maintains two counters that track the minimal flips for maintaining monotonic sequences. As the string is parsed, appropriate states are updated.