P8035 [COCI 2015/2016 #7] Otpor

As is well known, resistors can be connected in two ways: series and parallel. All resistors in a circuit can be regarded as the equivalent resistance $R_{ekv}$ of the circuit. A series connection can be written as: $$\text{(R1-R2-R3-...-RK)}$$ and it satisfies: $$R_{ekv}=\sum_{i=1}^K R_i$$ A parallel connection can be written as: $$\text{(R1|R2|R3|...|RK)}$$ and it satisfies: $$R_{ekv}=\frac{1}{\sum_{i=1}^K \frac{1}{R_i}}$$ Now you are given $N$ types of resistors with resistance values $R_i$, and enough wires. Given the connection pattern of these resistors, find the equivalent resistance of the whole circuit.

The first line contains an integer $N$. The second line contains $N$ real numbers $R_i$. The third line contains a string $S$ that represents the circuit. The string contains only $\texttt R$, $\texttt 1 \sim \texttt 9$, $\texttt ($, $\texttt )$, $\texttt -$, and $\texttt |$. The data guarantees that there will be no mismatched parentheses or illegal situations, and the number of parentheses is minimized. Inside any pair of parentheses, $\texttt -$ and $\texttt |$ will not appear at the same time. The circuit contains only the given $N$ types of resistors, and each type may appear any number of times (including $0$ times).

Output the equivalent resistance of the whole circuit. Your answer is considered correct if its absolute or relative error does not exceed $10^{-5}$.

**Constraints** - For $20\%$ of the testdata, $N=3$ and the circuit contains exactly these three types of resistors. - For $40\%$ of the testdata, $S$ contains only one pair of parentheses. - For $100\%$ of the testdata, $1 \le N \le 9$, $0 \lt R_i \lt 100$, $1 \le |S| \le 10^5$. **Hints and Notes** **Translated from [COCI 2015-2016](https://hsin.hr/coci/archive/2015_2016/) [#7](https://hsin.hr/coci/archive/2015_2016/contest7_tasks.pdf) _Task 4 Otpor_.** **The score for this problem follows the original COCI settings, with a full score of $120$.** Translated by ChatGPT 5