Practice Parsing and Physics with the exercise "Equivalent Resistance, Circuit Building"

1093

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

Goal

Calculate the equivalent resistance of a circuit containing only resistors.

A resistor is a component used in electrical circuits. A resistor is quantified by its Resistance, which is measured in Ohms. We are interested in knowing the total resistance of a circuit of only resistors. There are two key definitions needed to determine the resistance of multiple resistors.

1. Series

The resistance of resistors in a line is equivalent to the sum of the resistance of those resistors.

    ---[R_1]---[R_2]---

Resistors in series will be noted with parentheses ( R_1 R_2 R_3 ... and so on ).

The resistance of a series arrangement is: R_eq = R_1 + R_2 + R_3 + ... and so on, where R_eq is the equivalent resistance of the series arrangement.

2. Parallel

The resistance of resistors in branching paths of the circuit is equal to 1 over the sum of 1 over the resistance of each branching path.

       +---[R_1]---+
       |           |
    ---+           +---
       |           |
       +---[R_2]---+

Resistors in parallel will be noted with brackets [ R_1 R_2 R_3 ... and so on ].

The resistance of resistors in parallel is R_eq = 1/(1/R_1 + 1/R_2 + 1/R_3 + 1/... and so on).

A branch can be treated as a single resistor by determining its equivalent resistance.

Example:

N = 3

A 24
B 8
C 48
[ ( A B ) [ C A ] ]

This will look something like this:

       +---[C]---+
       |         |
    +--+         +--+
    |  |         |  |
    |  +---[A]---+  |
    |               |
    +---[A]---[B]---+
    |               |
    +---[Battery]---+

[ ( A B ) [ C A ] ] => [ 24+8 1/(1/48+1/24) ] => [ 32 16 ] => 1/(1/32+1/16) => 32/3 => 10.666... => 10.7

Input

Line 1: An integer N for the number of unique resistors present in the circuit
Next N lines: A space separated name and the integer resistance R of a resistor
Last line: A space separated combination of parentheses, brackets, and names of resistors

Output

The equivalent resistance expressed as a float rounded to the nearest 0.1 Ohms.

Constraints

0 < N < 10
0 < R < 100

Example

Input

2
A 20
B 10
( A B )

Output

30.0

Solve it

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