Pivotal Reversal

Consider performing the following operation on $S$ - a binary string of length $N$: - Choose $X$ such that $1 < X < N$ and $S_X = 1$. - Reverse the subarray $S[X - 1, X + 1]$, i.e. effectively swapping $S_{X - 1}$ and $S_{X + 1}$. Let $T$ denote another binary string of length $N$, and $f(S, T)$ be the minimum number of operations to convert $S$ into $T$ with the above operation. If $S$ cannot b