The operation does not change the number of 0s, so if $S$ and $T$ have different number of 0s, the objective is unachievable.

Otherwise, assume that the 0s in $S$ are its $a_1$-th, $a_2$-th, $\cdots$, $a_K$-th characters, and the 0s in $T$ are its $b_1$-th, $b_2$-th, $\cdots$, $b_K$-th characters. We will show that the answer is equal to the number of indices $i$ $(1 \leq i \leq K)$ such that $a_i \neq b_i$.

First, we need at least this number of operations because one operation changes only one of $a_1, a_2, \cdots, a_K$.

(Illustration of the operation)

Additionally, we can achieve the objective in this number of operations with, for example, the following strategy:

If there exists $i$ such that $a_i > b_i$: Let $p$ be the minimum $i$ such that $a_i > b_i$. Use the operation to change $a_p$ to $b_p$.

Otherwise: Let $q$ be the maximum $i$ such that $a_i < b_i$. Use the operation to change $a_q$ to $b_q$.

(Illustration of the strategy)

(The sentences to the left says “The minimum $i$ such that $a_i > b_i$ is $4$”, “The maximum $i$ such that $a_i < b_i$ is $3$”, and the one to the right says “We have one less $i$ such that $a_i \neq b_i$!”)

(Sample Implementations)

• C++: https://atcoder.jp/contests/arc119/submissions/22651261
• Python: https://atcoder.jp/contests/arc119/submissions/22651445
• Java: https://atcoder.jp/contests/arc119/submissions/22651594
• C: https://atcoder.jp/contests/arc119/submissions/22651652