My first instinct was to scan for those patterns and greedily flip, but that falls apart pretty fast because fixing one occurrence can create another.
First, recognize that a 'good' string must avoid alternating subsequences of length 3, which implies the string must be of the form 0*1*0* or 1*0*1* (i.e., at most two transitions). Then, compute the minimum flips to transform the given string into each of these two patterns by counting mismatches, and return the smaller count.
Pro tip: Clarify that 'subsequence' means not necessarily contiguous, and mention that the optimal good string has at most two blocks of identical characters. This shows you understand the structural constraint and can avoid brute-force.
Explain that avoiding '010' and '101' as subsequences means the string cannot have three alternating characters in order. Thus, the string must be of the form 0*1*0* or 1*0*1*.
List the two possible patterns: all 0s then all 1s then all 0s (0*1*0*), and all 1s then all 0s then all 1s (1*0*1*). Note that these include strings with fewer than three blocks.
For each pattern, count the minimum number of character flips needed to transform the given string into that pattern. This can be done by trying all possible split points between the blocks.
Use prefix sums to efficiently compute the number of flips for each split point in O(n) time, avoiding O(n^2) brute force.
Compare the minimum flips for both patterns and return the smaller value as the answer.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.