Resistance calculator
(Redirected from Resistance Calculator)
- Infix: ((((10 + 2) * 6 + 8) * 6 + 4) * 8 + 4) * 8 + 6
- RPN: 10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +
- Voltage = 18.0 V
Resistance calculator is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- Introduction
- Calculate the resistance of a network of resistors.
- The resistors can be connected in series or parallel.
- Use infix or RPN to state the network.
- Calculate resistance, voltage, current and power for every resistor and operation.
- Background
- Serial Resistors: the sum of the resistors gives the equivalent resistor
- Parallel Resistors: the inverse of the sum of the inverse of the resistors
- The voltage drops over the resistors
- Current = Resistance / Voltage
- Power = Current * Voltage
- Input
- Output
- 10.000 ohms in the upper left corner is the equivalent resistance.
- The first operation is 10 + 2 = 12 which can be found in the three middle rows.
Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r
11l
RPN
T Resistor
Float resistance
voltage = 0.0
Resistor? a, b
Char symbol
F (resistance = 0.0, Resistor? a = N, b = N; symbol = Char(‘r’))
.resistance = resistance
.a = a
.b = b
.symbol = symbol
F.virtual.new res() -> Float
R .resistance
F.virtual.new setVoltage(Float voltage) -> Void
.voltage = voltage
F current()
R .voltage / .res()
F effect()
R .current() * .voltage
F report(level = ‘’) -> Void
print(‘#4.3 #4.3 #4.3 #4.3 #.#.’.format(.res(), .voltage, .current(), .effect(), level, .symbol))
I .a != N {.a.report(level‘| ’)}
I .b != N {.b.report(level‘| ’)}
T Serial(Resistor)
F (Resistor a, b)
.a = move(b)
.b = a
.symbol = Char(‘+’)
F.virtual.override res() -> Float
R .a.res() + .b.res()
F.virtual.override setVoltage(Float voltage) -> Void
V ra = .a.res()
V rb = .b.res()
.a.setVoltage(ra / (ra + rb) * voltage)
.b.setVoltage(rb / (ra + rb) * voltage)
.voltage = voltage
T Parallel(Resistor)
F (Resistor a, b)
.a = move(b)
.b = a
.symbol = Char(‘*’)
F.virtual.override res() -> Float
R 1 / (1 / .a.res() + 1 / .b.res())
F.virtual.override setVoltage(Float voltage) -> Void
.a.setVoltage(voltage)
.b.setVoltage(voltage)
.voltage = voltage
F build(s)
[Resistor] stack
L(word) s.split(‘ ’)
I word == ‘+’
Resistor p = stack.pop()
stack.append(Serial(p, stack.pop()))
E I word == ‘*’
Resistor p = stack.pop()
stack.append(Parallel(p, stack.pop()))
E
stack.append(Resistor(Float(word)))
R stack.pop()
Resistor node = build(‘10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +’)
print(‘ Ohm Volt Ampere Watt Network tree’)
node.setVoltage(18.0)
node.report()
C++
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <map>
#include <memory>
#include <numeric>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
class Resistor {
public:
Resistor(const char& symbol, const double& resistance,
const std::shared_ptr<Resistor>& a, const std::shared_ptr<Resistor>& b)
: symbol(symbol), resistance(resistance), voltage(0.0), a(a), b(b) {}
Resistor(const char& symbol, const double& resistance)
: symbol(symbol), resistance(resistance), voltage(0.0) {}
char symbol;
double resistance;
double voltage;
std::shared_ptr<Resistor> a;
std::shared_ptr<Resistor> b;
};
double get_resistance(const std::shared_ptr<Resistor>& resistor) {
switch ( resistor->symbol ) {
case '+' : return get_resistance(resistor->a) + get_resistance(resistor->b);
case '*' : return 1.0 / ( 1.0 / get_resistance(resistor->a) + 1.0 / get_resistance(resistor->b) );
default : return resistor->resistance;
}
}
void set_voltage(const std::shared_ptr<Resistor>& resistor, const double& voltage) {
switch ( resistor->symbol ) {
case '+' : {
const double ra = get_resistance(resistor->a);
const double rb = get_resistance(resistor->b);
set_voltage(resistor->a, ra / ( ra + rb ) * voltage);
set_voltage(resistor->b, rb / ( ra + rb ) * voltage);
resistor->voltage = resistor->a->voltage + resistor->b->voltage;
break;
}
case '*' : {
set_voltage(resistor->a, voltage);
set_voltage(resistor->b, voltage);
resistor->voltage = voltage;
break;
}
default : resistor->voltage = voltage;
}
}
double get_current(const std::shared_ptr<Resistor>& resistor) {
return resistor->voltage / get_resistance(resistor);
}
double get_power(const std::shared_ptr<Resistor>& resistor) {
return resistor->voltage * get_current(resistor);
}
void report(const std::shared_ptr<Resistor>& resistor, const std::string& level) {
std::cout << std::fixed << std::setprecision(3) << std::setw(8) << get_resistance(resistor)
<< std::setw(8) << resistor->voltage << std::setw(8) << get_current(resistor)
<< std::setw(8) << get_power(resistor) << level << resistor->symbol << std::endl;
if ( resistor->a ) {
report(resistor->a, level + "| ");
}
if ( resistor->b ) {
report(resistor->b, level + "| ");
}
}
void report(const std::shared_ptr<Resistor>& resistor) {
report(resistor, " ");
}
bool is_digit(const char& ch) {
return ch >= '0' && ch <= '9';
}
std::string convert_to_RPN(const std::string& text) {
std::map<char, uint32_t> precedence = { { '(', 0 }, { '+', 1 }, { '*', 2 } };
std::vector<std::string> items{ };
std::stack<char> stack{ };
uint32_t end = 0;
while ( end < text.length() ) {
uint32_t start = end;
const char ch = text[end];
end += 1;
if ( ch == '(' ) {
stack.push(ch);
} else if ( ch == '+' || ch == '*' ) {
while ( ! stack.empty() && precedence[ch] <= precedence[stack.top()] ) {
items.emplace_back(std::string(1, stack.top()) + " "); stack.pop();
}
stack.push(ch);
} else if ( ch == ')' ) {
while ( stack.top() != '(' ) {
items.emplace_back(std::string(1, stack.top()) + " "); stack.pop();
}
stack.pop();
} else {
if ( is_digit(ch) ) {
while ( end < text.length() && is_digit(text[end]) ) {
end += 1;
}
items.emplace_back(text.substr(start, end - start) + " "); // Extract a multi-digit number
}
}
}
while ( ! stack.empty() ) {
items.emplace_back(std::string(1, stack.top()) + " "); stack.pop();
}
return std::accumulate(items.begin(), items.end(), std::string{ });
}
std::vector<std::string> split_string(const std::string& text, const char& delimiter) {
std::vector<std::string> words;
std::istringstream stream(text);
std::string word;
while ( std::getline(stream, word, delimiter) ) {
words.emplace_back(word);
}
return words;
}
std::shared_ptr<Resistor> build(const std::string& text) {
std::stack<std::shared_ptr<Resistor>> stack{ };
for ( const std::string& word : split_string(text, ' ') ) {
if ( word == "+" ) {
std::shared_ptr<Resistor> b = stack.top(); stack.pop();
std::shared_ptr<Resistor> a = stack.top(); stack.pop();
std::shared_ptr<Resistor> resistor = std::make_shared<Resistor>( '+', 0.0, a, b );
stack.push(resistor);
} else if ( word == "*" ) {
std::shared_ptr<Resistor> b = stack.top(); stack.pop();
std::shared_ptr<Resistor> a = stack.top(); stack.pop();
std::shared_ptr<Resistor> resistor = std::make_shared<Resistor>( '*', 0.0, a, b );
stack.push(resistor);
} else {
const double value = std::stod(word);
std::shared_ptr<Resistor> resistor = std::make_shared<Resistor>( 'r', value );
stack.push(resistor);
}
}
std::shared_ptr<Resistor> result = stack.top(); stack.pop();
return result;
}
void calculator(const std::string& title, const std::string& resistors, const double& voltage) {
std::cout << title << std::endl;
std::shared_ptr<Resistor> root = build(resistors);
std::cout << " Ohm Volt Ampere Watt Network tree" << std::endl;
set_voltage(root, voltage);
report(root);
}
int main() {
calculator("RPN syntax:", "10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +", 18.0);
std::cout << std::endl;
calculator("Infix syntax:", convert_to_RPN("((((10 + 2) * 6 + 8) * 6 + 4) * 8 + 4) * 8 + 6"), 18.0);
}
- Output:
RPN syntax: Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r Infix syntax: Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r
CoffeeScript
RPN
nd = (num) -> num.toFixed(3).padStart 8
class Resistor
constructor : (@resistance,@a=null,@b=null,@symbol='r') ->
res : -> @resistance
setVoltage : (@voltage) ->
current : -> @voltage / @res()
effect : -> @current() * @voltage
report : (level) ->
print "#{nd @res()} #{nd @voltage} #{nd @current()} #{nd @effect()} #{level}#{@symbol}"
if @a then @a.report level + "| "
if @b then @b.report level + "| "
class Serial extends Resistor
constructor : (a,b) -> super 0,a,b,'+'
res : -> @a.res() + @b.res()
setVoltage : (@voltage) ->
ra = @a.res()
rb = @b.res()
@a.setVoltage ra/(ra+rb) * @voltage
@b.setVoltage rb/(ra+rb) * @voltage
class Parallel extends Resistor
constructor : (a,b) -> super 0,a,b,'*'
res : -> 1 / (1 / @a.res() + 1 / @b.res())
setVoltage : (@voltage) ->
@a.setVoltage @voltage
@b.setVoltage @voltage
build = (s) ->
stack = []
for word in s.split ' '
if word == '+' then stack.push new Serial stack.pop(), stack.pop()
else if word == '*' then stack.push new Parallel stack.pop(), stack.pop()
else stack.push new Resistor parseFloat word
stack.pop()
node = build "10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +"
node.setVoltage 18.0
print " Ohm Volt Ampere Watt Network tree"
node.report ""
FreeBASIC
Infix
Const NULL As Any Ptr = 0
Type Resistor
symbol As String
resistance As Double
voltage As Double
a As Resistor Ptr
b As Resistor Ptr
End Type
Function res(r As Resistor Ptr) As Double
Select Case r->symbol
Case "+"
Return res(r->a) + res(r->b)
Case "*"
Return 1 / (1 / res(r->a) + 1 / res(r->b))
Case Else
Return r->resistance
End Select
End Function
Sub setVoltage(r As Resistor Ptr, voltage As Double)
Select Case r->symbol
Case "+"
Dim ra As Double = res(r->a)
Dim rb As Double = res(r->b)
setVoltage(r->a, ra / (ra + rb) * voltage)
setVoltage(r->b, rb / (ra + rb) * voltage)
Case "*"
setVoltage(r->a, voltage)
setVoltage(r->b, voltage)
End Select
r->voltage = voltage
End Sub
Function current(r As Resistor Ptr) As Double
Return r->voltage / res(r)
End Function
Function effect(r As Resistor Ptr) As Double
Return current(r) * r->voltage
End Function
Sub report(r As Resistor Ptr, level As String)
Print Using "###.### ###.### ###.### ###.### & &"; res(r); r->voltage; current(r); effect(r); level; r->symbol
If r->a <> NULL Then report(r->a, level + " |")
If r->b <> NULL Then report(r->b, level + " |")
End Sub
Function sum(r1 As Resistor Ptr, r2 As Resistor Ptr) As Resistor Ptr
Dim r As Resistor Ptr = Callocate(1, Sizeof(Resistor))
r->symbol = "+"
r->a = r1
r->b = r2
Return r
End Function
Function mul(r1 As Resistor Ptr, r2 As Resistor Ptr) As Resistor Ptr
Dim r As Resistor Ptr = Callocate(1, Sizeof(Resistor))
r->symbol = "*"
r->a = r1
r->b = r2
Return r
End Function
Dim As Resistor Ptr r(9)
Dim As Double resistances(9) = {6, 8, 4, 8, 4, 6, 8, 10, 6, 2}
For i As Integer = 0 To 9
r(i) = Callocate(1, Sizeof(Resistor))
r(i)->symbol = "r"
r(i)->resistance = resistances(i)
Next
Dim As Resistor Ptr node
node = sum(r(7), r(9))
node = mul(node, r(8))
node = sum(node, r(6))
node = mul(node, r(5))
node = sum(node, r(4))
node = mul(node, r(3))
node = sum(node, r(2))
node = mul(node, r(1))
node = sum(node, r(0))
setVoltage(node, 18)
Print " Ohm Volt Ampere Watt Network tree"
report(node, "")
Sleep
- Output:
Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r
RPN
Const NULL As Any Ptr = 0
Type Resistor
symbol As String
resistance As Double
voltage As Double
a As Resistor Ptr
b As Resistor Ptr
End Type
Sub push(s() As Resistor Ptr, r As Resistor Ptr)
Redim Preserve s(Ubound(s) + 1)
s(Ubound(s)) = r
End Sub
Sub pop(s() As Resistor Ptr, Byref r As Resistor Ptr)
r = s(Ubound(s))
Redim Preserve s(Ubound(s) - 1)
End Sub
Function res(r As Resistor Ptr) As Double
Select Case r->symbol
Case "+"
Return res(r->a) + res(r->b)
Case "*"
Return 1 / (1 / res(r->a) + 1 / res(r->b))
Case Else
Return r->resistance
End Select
End Function
Sub setVoltage(r As Resistor Ptr, voltage As Double)
Select Case r->symbol
Case "+"
Dim ra As Double = res(r->a)
Dim rb As Double = res(r->b)
setVoltage(r->a, ra / (ra + rb) * voltage)
setVoltage(r->b, rb / (ra + rb) * voltage)
Case "*"
setVoltage(r->a, voltage)
setVoltage(r->b, voltage)
End Select
r->voltage = voltage
End Sub
Function current(r As Resistor Ptr) As Double
Return r->voltage / res(r)
End Function
Function effect(r As Resistor Ptr) As Double
Return current(r) * r->voltage
End Function
Sub report(r As Resistor Ptr, level As String)
Print Using "###.### ###.### ###.### ###.### & &"; res(r); r->voltage; current(r); effect(r); level; r->symbol
If r->a <> NULL Then report(r->a, level + " |")
If r->b <> NULL Then report(r->b, level + " |")
End Sub
Sub splitString(s As String, delim As String, result() As String)
Dim As Integer start = 1, endd
While start <= Len(s)
endd = Instr(start, s, delim)
If endd = 0 Then endd = Len(s) + 1
Redim Preserve result(Ubound(result) + 1)
result(Ubound(result)) = Mid(s, start, endd - start)
start = endd + Len(delim)
Wend
End Sub
Sub build(rpn As String, Byref node As Resistor Ptr)
Dim As Resistor Ptr s()
Dim As String tokens()
splitString(rpn, " ", tokens())
Dim As Integer i
For i = 0 To Ubound(tokens)
Dim As Resistor Ptr r = Callocate(1, Sizeof(Resistor))
Select Case tokens(i)
Case "+", "*"
pop(s(), r->b)
pop(s(), r->a)
r->symbol = tokens(i)
Case Else
r->resistance = Val(tokens(i))
r->symbol = "r"
End Select
push(s(), r)
Next
pop(s(), node)
End Sub
Dim As Resistor Ptr node
build("10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +", node)
setVoltage(node, 18)
Print " Ohm Volt Ampere Watt Network tree"
report(node, "")
Sleep
- Output:
Same as Infix version
Go
Infix
package main
import "fmt"
type Resistor struct {
symbol rune
resistance, voltage float64
a, b *Resistor
}
func (r *Resistor) res() float64 {
switch r.symbol {
case '+':
return r.a.res() + r.b.res()
case '*':
return 1 / (1/r.a.res() + 1/r.b.res())
default:
return r.resistance
}
}
func (r *Resistor) setVoltage(voltage float64) {
switch r.symbol {
case '+':
ra := r.a.res()
rb := r.b.res()
r.a.setVoltage(ra / (ra + rb) * voltage)
r.b.setVoltage(rb / (ra + rb) * voltage)
case '*':
r.a.setVoltage(voltage)
r.b.setVoltage(voltage)
}
r.voltage = voltage
}
func (r *Resistor) current() float64 {
return r.voltage / r.res()
}
func (r *Resistor) effect() float64 {
return r.current() * r.voltage
}
func (r *Resistor) report(level string) {
fmt.Printf("%8.3f %8.3f %8.3f %8.3f %s%c\n", r.res(), r.voltage, r.current(), r.effect(), level, r.symbol)
if r.a != nil {
r.a.report(level + "| ")
}
if r.b != nil {
r.b.report(level + "| ")
}
}
func (r *Resistor) add(other *Resistor) *Resistor {
return &Resistor{'+', 0, 0, r, other}
}
func (r *Resistor) mul(other *Resistor) *Resistor {
return &Resistor{'*', 0, 0, r, other}
}
func main() {
var r [10]*Resistor
resistances := []float64{6, 8, 4, 8, 4, 6, 8, 10, 6, 2}
for i := 0; i < 10; i++ {
r[i] = &Resistor{'r', resistances[i], 0, nil, nil}
}
node := r[7].add(r[9]).mul(r[8]).add(r[6]).mul(r[5]).add(r[4]).mul(r[3]).add(r[2]).mul(r[1]).add(r[0])
node.setVoltage(18)
fmt.Println(" Ohm Volt Ampere Watt Network tree")
node.report("")
}
RPN
package main
import (
"fmt"
"strconv"
"strings"
)
type Stack []*Resistor
func (s *Stack) push(r *Resistor) {
*s = append(*s, r)
}
func (s *Stack) pop() *Resistor {
le := len(*s)
if le == 0 {
panic("Attempt to pop from an empty stack")
}
le--
r := (*s)[le]
*s = (*s)[:le]
return r
}
type Resistor struct {
symbol rune
resistance, voltage float64
a, b *Resistor
}
func (r *Resistor) res() float64 {
switch r.symbol {
case '+':
return r.a.res() + r.b.res()
case '*':
return 1 / (1/r.a.res() + 1/r.b.res())
default:
return r.resistance
}
}
func (r *Resistor) setVoltage(voltage float64) {
switch r.symbol {
case '+':
ra := r.a.res()
rb := r.b.res()
r.a.setVoltage(ra / (ra + rb) * voltage)
r.b.setVoltage(rb / (ra + rb) * voltage)
case '*':
r.a.setVoltage(voltage)
r.b.setVoltage(voltage)
}
r.voltage = voltage
}
func (r *Resistor) current() float64 {
return r.voltage / r.res()
}
func (r *Resistor) effect() float64 {
return r.current() * r.voltage
}
func (r *Resistor) report(level string) {
fmt.Printf("%8.3f %8.3f %8.3f %8.3f %s%c\n", r.res(), r.voltage, r.current(), r.effect(), level, r.symbol)
if r.a != nil {
r.a.report(level + "| ")
}
if r.b != nil {
r.b.report(level + "| ")
}
}
func build(rpn string) *Resistor {
st := new(Stack)
for _, token := range strings.Fields(rpn) {
switch token {
case "+":
b, a := st.pop(), st.pop()
st.push(&Resistor{'+', 0, 0, a, b})
case "*":
b, a := st.pop(), st.pop()
st.push(&Resistor{'*', 0, 0, a, b})
default:
r, _ := strconv.ParseFloat(token, 64)
st.push(&Resistor{'r', r, 0, nil, nil})
}
}
return st.pop()
}
func main() {
node := build("10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +")
node.setVoltage(18)
fmt.Println(" Ohm Volt Ampere Watt Network tree")
node.report("")
}
Java
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Stack;
public final class ResistanceCalculator {
public static void main(String[] args) {
rpnSyntax("RPN syntax:", "10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +", 18.0);
System.out.println();
infixSyntax("Infix syntax:", "((((10 + 2) * 6 + 8) * 6 + 4) * 8 + 4) * 8 + 6", 18.0);
}
private static void rpnSyntax(String title, String rpn, double voltage) {
System.out.println(title);
Resistor root = build(rpn);
System.out.println(" Ohm Volt Ampere Watt Network tree");
root.setVoltage(voltage);
root.report();
}
private static void infixSyntax(String title, String infix, double voltage) {
rpnSyntax(title, convertToRPN(infix), voltage);
}
private static Resistor build(String text) {
Stack<Resistor> stack = new Stack<Resistor>();
for ( String word : text.split(" ") ) {
if ( word.equals("+") ) {
stack.push( new SerialResistor(stack.pop(), stack.pop()) );
} else if ( word.equals("*") ) {
stack.push( new ParallelResistor(stack.pop(), stack.pop()) );
} else {
stack.push( new Resistor(Double.valueOf(word)) );
}
}
return stack.pop();
}
private static String convertToRPN(String text) {
final Map<Character, Integer> precedence = Map.ofEntries(
Map.entry('(', 0), Map.entry('+', 1), Map.entry('*', 2) );
List<String> items = new ArrayList<String>();
Stack<Character> stack = new Stack<Character>();
int end = 0;
while ( end < text.length() ) {
int start = end;
final char ch = text.charAt(end);
end += 1;
switch ( ch ) {
case '(' -> stack.push(ch);
case '+', '*' -> {
while ( ! stack.isEmpty() && precedence.get(ch) <= precedence.get(stack.peek()) ) {
items.add(String.valueOf(stack.pop()));
}
stack.push(ch);
}
case ')' -> {
while ( stack.peek() != '(' ) {
items.add(String.valueOf(stack.pop()));
}
stack.pop();
}
default -> {
if ( Character.isDigit(ch) ) {
while ( end < text.length() && Character.isDigit(text.charAt(end)) ) {
end += 1;
}
items.add(text.substring(start, end)); // Extract a multi-digit number
}
}
}
}
while ( ! stack.isEmpty() ) {
items.add(String.valueOf(stack.pop()));
}
return String.join(" ", items);
}
}
class Resistor {
public Resistor(char aSymbol, double aResistance, Resistor aA, Resistor aB) {
symbol = aSymbol;
resistance = aResistance;
a = aA;
b = aB;
}
public Resistor(double aResistance) {
this('r', aResistance, null, null);
}
protected double getResistance() { return resistance; }
protected double getVoltage() { return voltage; }
protected void setVoltage(double aVoltage) { voltage = aVoltage; }
protected double getCurrent() { return voltage / resistance; }
protected double getPower() { return getCurrent() * voltage; }
protected void report() { report(""); }
protected void report(String level) {
System.out.println(String.format("%8.3f%8.3f%8.3f%8.3f%s %c",
getResistance(), getVoltage(), getCurrent(), getPower(), level, symbol));
if ( a != null ) { a.report(level + " | "); }
if ( b != null ) { b.report(level + " | "); }
}
private char symbol;
private double resistance;
private double voltage;
private Resistor a;
private Resistor b;
}
final class SerialResistor extends Resistor {
public SerialResistor(Resistor aA, Resistor aB) {
super('+', 0.0, aB, aA);
a = aA;
b = aB;
}
protected double getResistance() { return a.getResistance() + b.getResistance(); }
protected double getVoltage() { return voltage; }
protected void setVoltage(double aVoltage) {
final double resistanceA = a.getResistance();
final double resistanceB = b.getResistance();
a.setVoltage(aVoltage * resistanceA / ( resistanceA + resistanceB ));
b.setVoltage(aVoltage * resistanceB / ( resistanceA + resistanceB ));
voltage = aVoltage;
}
protected double getCurrent() { return voltage / getResistance(); }
protected double getPower() { return getCurrent() * voltage; }
private double voltage;
private Resistor a;
private Resistor b;
}
final class ParallelResistor extends Resistor {
public ParallelResistor(Resistor aA, Resistor aB) {
super('*', 0.0, aB, aA);
a = aA;
b = aB;
}
protected double getResistance() { return 1.0 / ( 1.0 / a.getResistance() + 1.0 / b.getResistance() ); }
protected double getVoltage() { return voltage; }
protected void setVoltage(double aVoltage) {
a.setVoltage(aVoltage);
b.setVoltage(aVoltage);
voltage = aVoltage;
}
protected double getCurrent() { return voltage / getResistance(); }
protected double getPower() { return getCurrent() * voltage; }
private double voltage;
private Resistor a;
private Resistor b;
}
- Output:
RPN syntax: Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r Infix syntax: Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r
Julia
Infix
using Formatting
import Base.+, Base.*
mutable struct Resistor
operator::Char
voltage::Float64
resistance::Float64
a::Union{Resistor, Nothing}
b::Union{Resistor, Nothing}
end
function res(r::Resistor)
if r != nothing
if r.operator == '+'
return res(r.a) + res(r.b)
elseif r.operator == '*'
return 1 / ((1 / res(r.a)) + (1 / res(r.b)))
end
return r.resistance
end
end
function setvoltage(r, voltage)
if r != nothing
if r.operator == '+'
ra = res(r.a)
rb = res(r.b)
setvoltage(r.a, voltage * ra / (ra + rb))
setvoltage(r.b, voltage * rb / (ra + rb))
elseif r.operator == '*'
setvoltage(r.a, voltage)
setvoltage(r.b, voltage)
end
r.voltage = voltage
end
end
current(r) = r.voltage / res(r)
effect(r) = r.voltage * current(r)
function report(r, level=1)
nfmt(x::Real) = rpad(format(x, precision=3), 12)
afmt(arr::Vector) = join(map(nfmt, arr), "| ")
println(afmt([res(r), r.voltage, current(r), effect(r)]), "| "^level, r.operator)
if r.a != nothing
report(r.a, level + 1)
end
if r.b != nothing
report(r.b, level + 1)
end
end
Base.:+(a::Resistor, b::Resistor) = Resistor('+', 0.0, 0.0, a, b)
Base.:*(a::Resistor, b::Resistor) = Resistor('*', 0.0, 0.0, a, b)
(R1, R2, R3, R4, R5, R6, R7, R8, R9, R10) =
map(r -> Resistor('r', 0.0, r, nothing, nothing), [6, 8, 4, 8, 4, 6, 8, 10, 6, 2])
node = ((((R8 + R10) * R9 + R7) * R6 + R5) * R4 + R3) * R2 + R1
setvoltage(node, 18)
println(" Ohm Volt Ampere Watt Network tree")
report(node)
- Output:
Ohm Volt Ampere Watt Network tree 10.000 | 18.000 | 1.800 | 32.400 | + 4.000 | 7.200 | 1.800 | 12.960 | | * 8.000 | 7.200 | 0.900 | 6.480 | | | + 4.000 | 3.600 | 0.900 | 3.240 | | | | * 8.000 | 3.600 | 0.450 | 1.620 | | | | | + 4.000 | 1.800 | 0.450 | 0.810 | | | | | | * 12.000 | 1.800 | 0.150 | 0.270 | | | | | | | + 4.000 | 0.600 | 0.150 | 0.090 | | | | | | | | * 12.000 | 0.600 | 0.050 | 0.030 | | | | | | | | | + 10.000 | 0.500 | 0.050 | 0.025 | | | | | | | | | | r 2.000 | 0.100 | 0.050 | 0.005 | | | | | | | | | | r 6.000 | 0.600 | 0.100 | 0.060 | | | | | | | | | r 8.000 | 1.200 | 0.150 | 0.180 | | | | | | | | r 6.000 | 1.800 | 0.300 | 0.540 | | | | | | | r 4.000 | 1.800 | 0.450 | 0.810 | | | | | | r 8.000 | 3.600 | 0.450 | 1.620 | | | | | r 4.000 | 3.600 | 0.900 | 3.240 | | | | r 8.000 | 7.200 | 0.900 | 6.480 | | | r 6.000 | 10.800 | 1.800 | 19.440 | | r
RPN
function rpn(arr::Vector)
stack = Any[]
for op in arr
if isa(op, Function)
arg2 = pop!(stack)
arg1 = pop!(stack)
push!(stack, op(arg1, arg2))
else
push!(stack, op)
end
end
length(stack) != 1 && error("invalid RPN expression array: $arr")
return stack[1]
end
node = rpn([R8, R10, +, R9, *, R7, +, R6, *, R5, +, R4, *, R3, +, R2, *, R1, +])
setvoltage(node, 18)
report(node)
- Output:
Same as infix version.
Nim
import strutils, strformat
type
Node = ref object
kind: char # + = serial * = parallel r = resistor
resistance: float
voltage: float
a: Node
b: Node
proc res(node: Node): float =
if node.kind == '+': return node.a.res + node.b.res
if node.kind == '*': return 1 / (1 / node.a.res + 1 / node.b.res)
node.resistance
proc current(node: Node): float = node.voltage / node.res
proc effect (node: Node): float = node.current * node.voltage
proc report(node: Node, level: string = "") =
echo fmt"{node.res:8.3f} {node.voltage:8.3f} {node.current:8.3f} {node.effect:8.3f} {level}{node.kind}"
if node.kind in "+*":
node.a.report level & "| "
node.b.report level & "| "
proc setVoltage(node: Node, voltage: float) =
node.voltage = voltage
if node.kind == '+':
let ra = node.a.res
let rb = node.b.res
node.a.setVoltage ra / (ra+rb) * voltage
node.b.setVoltage rb / (ra+rb) * voltage
if node.kind == '*':
node.a.setVoltage voltage
node.b.setVoltage voltage
proc build(tokens: seq[string]): Node =
var stack: seq[Node]
for token in tokens:
stack.add if token == "+": Node(kind: '+', a: stack.pop, b: stack.pop)
elif token == "*": Node(kind: '*', a: stack.pop, b: stack.pop)
else: Node(kind: 'r', resistance: parseFloat(token))
stack.pop
proc calculate(voltage: float, tokens: seq[string]): Node =
echo ""
echo " Ohm Volt Ampere Watt Network tree"
let node = build tokens
node.setVoltage voltage
node.report
node
RPN
proc rpn(voltage:float, s:string): Node = calculate(voltage, s.split ' ')
var node = rpn(18, "10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +")
assert 10 == node.res
assert 18 == node.voltage
assert 1.8 == node.current()
assert 32.4 == node.effect()
assert '+' == node.kind
Infix
proc parse(s: string): seq[string] =
var tmp = ""
for ch in s:
case ch
of ' ':
if tmp != "": result.add tmp
tmp = ""
continue
of '+', '*', '(', ')':
if tmp != "": result.add tmp
tmp = ""
result.add $ch
else:
tmp &= ch
if tmp != "": result.add tmp
proc shuntRPN(s: string): seq[string] =
let ops = "+*"
var tokens = parse s
var stack: seq[string]
var op: string
for token in tokens:
case token
of "(":
stack.add token
of ")":
while stack.len > 0:
op = stack.pop()
if op == "(": break
result.add op
else:
if token in ops:
while stack.len > 0:
op = stack[^1]
if op notin ops: break
if ops.find(token) >= ops.find(op): break
discard stack.pop()
result.add op
stack.add token
else: result.add token
while stack.len > 0: result.add stack.pop()
proc infix(voltage:float, s:string): Node = calculate(voltage, shuntRPN s)
node = infix(18, "((((10+2)*6+8)*6+4)*8+4)*8+6")
assert 10 == node.res
assert 18 == node.voltage
assert 1.8 == node.current()
assert 32.4 == node.effect()
assert '+' == node.kind
Perl
Infix
use v5.36;
package Resistor;
require Exporter;
our @ISA = qw(Exporter);
our @EXPORT = qw(set_voltage report);
use overload '+' => \&serial, '*' => \∥
sub new ($class, $args) {
my $self = {
symbol => $args->{symbol},
voltage => $args->{voltage},
resistance => $args->{resistance},
a => $args->{a},
b => $args->{b},
};
return bless $self, $class;
}
sub res ($self) {
if ($self->{symbol} eq '+') { return res($self->{a}) + res($self->{b}) }
elsif ($self->{symbol} eq '*') { return 1 / (1/res($self->{a}) + 1/res($self->{b})) }
else { return $self->{resistance} }
}
sub set_voltage ($self,$voltage) {
if ($self->{symbol} eq '+') {
my $ra = res($self->{a});
my $rb = res($self->{b});
set_voltage($self->{a}, $ra / ($ra+$rb) * $voltage );
set_voltage($self->{b}, $rb / ($ra+$rb) * $voltage );
} elsif ($self->{symbol} eq '*') {
set_voltage($self->{a}, $voltage );
set_voltage($self->{b}, $voltage );
}
$self->{voltage} = $voltage;
}
sub current ($self) { return $self->{voltage} / res($self) }
sub effect ($self) { return $self->{voltage} * current($self) }
sub serial ($a,$b,$) { Resistor->new( {symbol => '+', a => $a, b => $b} ) }
sub parallel ($a,$b,$) { Resistor->new( {symbol => '*', a => $a, b => $b} ) }
sub report ($self,$level = 0) {
state @results;
push @results, ' Ohm Volt Ampere Watt Network tree' and $level = 1 unless $level;
my $pad = ('| ') x $level;
my $f = sprintf '%9.3f' x 4, res($self), $self->{voltage}, current($self), effect($self);
say "$f $pad" . $self->{symbol};
report($self->{a}, $level+1) if defined $self->{a};
report($self->{b}, $level+1) if defined $self->{b};
join "\n", @results;
}
}
package main;
Resistor->import;
my ($R1, $R2, $R3, $R4, $R5, $R6, $R7, $R8, $R9, $R10) =
map { Resistor->new( {symbol => 'r', resistance => $_} ) } <6 8 4 8 4 6 8 10 6 2>;
my $node = (((($R8 + $R10) * $R9 + $R7) * $R6 + $R5)
* $R4 + $R3) * $R2 + $R1;
set_voltage($node,18);
say report($node);
- Output:
Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 | + 4.000 7.200 1.800 12.960 | | * 8.000 7.200 0.900 6.480 | | | + 4.000 3.600 0.900 3.240 | | | | * 8.000 3.600 0.450 1.620 | | | | | + 4.000 1.800 0.450 0.810 | | | | | | * 12.000 1.800 0.150 0.270 | | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | | r 4.000 1.800 0.450 0.810 | | | | | | r 8.000 3.600 0.450 1.620 | | | | | r 4.000 3.600 0.900 3.240 | | | | r 8.000 7.200 0.900 6.480 | | | r 6.000 10.800 1.800 19.440 | | r
Phix
with javascript_semantics constant RPN = true // or false for infix (same output) -- node contents: enum KIND, -- '+', '*', or 'r' RESISTANCE, VOLTAGE, A, B -- nested nodes or NULL function resistance(sequence node) switch node[KIND] do case '+': return resistance(node[A]) + resistance(node[B]) case '*': return 1 / (1/resistance(node[A]) + 1/resistance(node[B])) case 'r': return node[RESISTANCE] default: ?9/0 -- unknown node kind end switch end function function setVoltage(sequence node, atom voltage) integer kind = node[KIND] atom r = node[RESISTANCE] -- v = node[VOLTAGE] -- not needed! object na = node[A], nb = node[B] switch kind do case '+': atom ra := resistance(na), rb := resistance(nb) na = setVoltage(na, ra / (ra + rb) * voltage) nb = setVoltage(nb, rb / (ra + rb) * voltage) case '*': na = setVoltage(na,voltage) nb = setVoltage(nb,voltage) end switch node = {kind,r,voltage,na,nb} return node end function function current(sequence node) return node[VOLTAGE] / resistance(node) end function function effect(sequence node) return current(node) * node[VOLTAGE] end function procedure report(sequence node, string level="") printf(1,"%8.3f %8.3f %8.3f %8.3f %s%c\n", {resistance(node), node[VOLTAGE], current(node), effect(node), level, node[KIND]}) if node[A]!=NULL then report(node[A],level & "| ") end if if node[B]!=NULL then report(node[B],level & "| ") end if end procedure function push_op(sequence stack, string tok) switch tok do case "+","*": sequence b = stack[$], a = stack[$-1] stack = stack[1..$-1] stack[$] = {tok[1], 0, 0, a, b} default: integer {{r}} = scanf(tok,"%d") stack = append(stack,{'r', r, 0, NULL, NULL}) end switch return stack end function -- RPN function rpn(string s) sequence stack = {}, tokens = split(s) for i=1 to length(tokens) do stack = push_op(stack,tokens[i]) end for return stack[$] end function -- Infix, slightly trickier: constant ops = {"+","*"} function infix(string s) string lastnum = "" sequence tokens = {} for i=1 to length(s) do integer ch = s[i] if ch>='0' and ch<='9' then lastnum &= ch else if length(lastnum) then tokens = append(tokens,lastnum) lastnum = "" end if tokens = append(tokens,ch&"") end if end for if length(lastnum) then tokens = append(tokens,lastnum) end if sequence stack = {}, result = {} for i=1 to length(tokens) do string token = tokens[i], op switch token do case "(": stack = append(stack,token) case ")": while true do op = stack[$] stack = stack[1..$-1] if op == "(" then exit end if result = push_op(result,op) end while else: integer tp = find(token,ops) if tp then while length(stack) do op = stack[$] integer sp = find(op,ops) if not sp or tp>=sp then exit end if stack = stack[1..$-1] result = push_op(result,op) end while stack = append(stack,token) else result = push_op(result,token) end if end switch end for for i=length(stack) to 1 by -1 do result = push_op(result,stack[i]) end for return result[1] end function sequence node = iff(RPN?rpn("10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +") :infix("((((10+2)*6+8)*6+4)*8+4)*8+6")) node = setVoltage(node,18) printf(1," Ohm Volt Ampere Watt Network tree\n") report(node,"")
- Output:
Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r
Python
RPN
class Resistor :
def __init__(self, resistance, a=None, b=None, symbol='r'):
self.resistance = resistance
self.a = a
self.b = b
self.symbol = symbol
def res(self) : return self.resistance
def setVoltage(self, voltage): self.voltage = voltage
def current(self) : return self.voltage / self.res()
def effect(self) : return self.current() * self.voltage
def report(self,level=""):
print(f"{self.res():8.3f} {self.voltage:8.3f} {self.current():8.3f} {self.effect():8.3f} {level}{self.symbol}")
if self.a: self.a.report(level + "| ")
if self.b: self.b.report(level + "| ")
class Serial(Resistor) :
def __init__(self, a, b) : super().__init__(0, b, a, '+')
def res(self) : return self.a.res() + self.b.res()
def setVoltage(self, voltage) :
ra = self.a.res()
rb = self.b.res()
self.a.setVoltage(ra/(ra+rb) * voltage)
self.b.setVoltage(rb/(ra+rb) * voltage)
self.voltage = voltage
class Parallel(Resistor) :
def __init__(self,a,b) : super().__init__(0, b, a, '*')
def res(self) : return 1 / (1 / self.a.res() + 1 / self.b.res())
def setVoltage(self, voltage) :
self.a.setVoltage(voltage)
self.b.setVoltage(voltage)
self.voltage = voltage
def build(s) :
stack = []
for word in s.split(' '):
if word == "+": stack.append(Serial(stack.pop(), stack.pop()))
elif word == "*": stack.append(Parallel(stack.pop(), stack.pop()))
else: stack.append(Resistor(float(word)))
return stack.pop()
node = build("10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +")
print(" Ohm Volt Ampere Watt Network tree")
node.setVoltage(18.0)
node.report()
Infix
class Resistor :
def __init__(self, resistance, a=None, b=None, symbol='r') :
self.resistance = resistance
self.a = a
self.b = b
self.symbol = symbol
def res(self) : return self.resistance
def setVoltage(self, voltage) : self.voltage = voltage
def current(self) : return self.voltage / self.res()
def effect(self) : return self.current() * self.voltage
def report(self,level="") :
print(f"{self.res():8.3f} {self.voltage:8.3f} {self.current():8.3f} {self.effect():8.3f} {level}{self.symbol}")
if self.a: self.a.report(level + "| ")
if self.b: self.b.report(level + "| ")
def __add__(self,other) : return Serial(self,other)
def __mul__(self,other) : return Parallel(self,other)
class Serial(Resistor) :
def __init__(self, a, b) : super().__init__(0, a, b, '+')
def res(self) : return self.a.res() + self.b.res()
def setVoltage(self, voltage) :
ra = self.a.res()
rb = self.b.res()
self.a.setVoltage(ra/(ra+rb) * voltage)
self.b.setVoltage(rb/(ra+rb) * voltage)
self.voltage = voltage
class Parallel(Resistor) :
def __init__(self,a,b) : super().__init__(0, a, b, '*')
def res(self) : return 1 / (1 / self.a.res() + 1 / self.b.res())
def setVoltage(self, voltage):
self.a.setVoltage(voltage)
self.b.setVoltage(voltage)
self.voltage = voltage
[R1,R2,R3,R4,R5,R6,R7,R8,R9,R10] = [Resistor(res) for res in [6,8,4,8,4,6,8,10,6,2]]
node = ((((R8+R10) * R9 + R7) * R6 + R5) * R4 + R3) * R2 + R1
node.setVoltage(18)
print(" Ohm Volt Ampere Watt Network tree")
node.report()
Raku
(formerly Perl 6)
Infix
class Resistor {
has Str $.symbol;
has Numeric ( $.voltage, $.resistance );
has Resistor ( $.a, $.b );
method res ( ) {
given $.symbol {
when '+' { return $.a.res + $.b.res }
when '*' { return 1 / (1 / $.a.res + 1 / $.b.res) }
default { return $.resistance }
}
}
method set-voltage ( Numeric $voltage ) {
given $.symbol {
when '+' {
my $ra = $.a.res;
my $rb = $.b.res;
$.a.set-voltage( $ra / ($ra+$rb) * $voltage );
$.b.set-voltage( $rb / ($ra+$rb) * $voltage );
}
when '*' {
$.a.set-voltage( $voltage );
$.b.set-voltage( $voltage );
}
}
$!voltage = $voltage;
}
method current ( ) { return $.voltage / self.res }
method effect ( ) { return $.voltage * self.current }
method report ( Int $level = 1 ) {
my $pad = '| ' x $level;
my $f = ( self.res, $.voltage, self.current, self.effect ).fmt('%8.3f');
say "$f $pad$.symbol";
$.a.report( $level+1 ) if $.a;
$.b.report( $level+1 ) if $.b;
}
}
multi sub infix:<+> (Resistor $a, Resistor $b) { $a.new( symbol => '+', :$a, :$b ) }
multi sub infix:<*> (Resistor $a, Resistor $b) { $a.new( symbol => '*', :$a, :$b ) }
my Resistor ($R1, $R2, $R3, $R4, $R5, $R6, $R7, $R8, $R9, $R10) =
map { Resistor.new: symbol => 'r', resistance => $_ },
6, 8, 4, 8, 4, 6, 8, 10, 6, 2;
my $node = (((($R8 + $R10) * $R9 + $R7) * $R6 + $R5)
* $R4 + $R3) * $R2 + $R1;
$node.set-voltage(18);
say ' Ohm Volt Ampere Watt Network tree';
$node.report;
- Output:
Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 | + 4.000 7.200 1.800 12.960 | | * 8.000 7.200 0.900 6.480 | | | + 4.000 3.600 0.900 3.240 | | | | * 8.000 3.600 0.450 1.620 | | | | | + 4.000 1.800 0.450 0.810 | | | | | | * 12.000 1.800 0.150 0.270 | | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | | r 4.000 1.800 0.450 0.810 | | | | | | r 8.000 3.600 0.450 1.620 | | | | | r 4.000 3.600 0.900 3.240 | | | | r 8.000 7.200 0.900 6.480 | | | r 6.000 10.800 1.800 19.440 | | r
Wren
Infix
import "./fmt" for Fmt
class Resistor {
construct new(symbol, resistance, voltage, a, b) {
_symbol = symbol
_resistance = resistance
_voltage = voltage
_a = a
_b = b
}
symbol { _symbol }
resistance { _resistance }
voltage { _voltage}
res {
if (_symbol == "+") return _a.res + _b.res
if (_symbol == "*") return 1 / (1/_a.res + 1/_b.res)
return _resistance
}
current { _voltage / res }
effect { current * _voltage }
voltage=(v) {
if (_symbol == "+") {
var ra = _a.res
var rb = _b.res
_a.voltage = ra / (ra + rb) * v
_b.voltage = rb / (ra + rb) * v
} else if (_symbol == "*") {
_a.voltage = v
_b.voltage = v
}
_voltage = v
}
report(level) {
Fmt.lprint("$8.3f $8.3f $8.3f $8.3f $s$s", [res, _voltage, current, effect, level, symbol])
if (_a != null) _a.report(level + "| ")
if (_b != null) _b.report(level + "| ")
}
+(other) { Resistor.new("+", 0, 0, this, other) }
*(other) { Resistor.new("*", 0, 0, this, other) }
}
var r = List.filled(10, null)
var resistances = [6, 8, 4, 8, 4, 6, 8, 10, 6, 2]
for (i in 0..9) r[i] = Resistor.new("r", resistances[i], 0, null, null)
var node = ((((r[7]+r[9])*r[8]+r[6])*r[5]+r[4])*r[3]+r[2])*r[1] + r[0]
node.voltage = 18
System.print(" Ohm Volt Ampere Watt Network tree")
node.report("")
- Output:
Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r
RPN
Additonally:
import "./fmt" for Fmt
import "./seq" for Stack
class Resistor {
construct new(symbol, resistance, voltage, a, b) {
_symbol = symbol
_resistance = resistance
_voltage = voltage
_a = a
_b = b
}
symbol { _symbol }
resistance { _resistance }
voltage { _voltage}
res {
if (_symbol == "+") return _a.res + _b.res
if (_symbol == "*") return 1 / (1/_a.res + 1/_b.res)
return _resistance
}
current { _voltage / res }
effect { current * _voltage }
voltage=(v) {
if (_symbol == "+") {
var ra = _a.res
var rb = _b.res
_a.voltage = ra / (ra + rb) * v
_b.voltage = rb / (ra + rb) * v
} else if (_symbol == "*") {
_a.voltage = v
_b.voltage = v
}
_voltage = v
}
report(level) {
Fmt.lprint("$8.3f $8.3f $8.3f $8.3f $s$s", [res, _voltage, current, effect, level, symbol])
if (_a != null) _a.report(level + "| ")
if (_b != null) _b.report(level + "| ")
}
+(other) { Resistor.new("+", 0, 0, this, other) }
*(other) { Resistor.new("*", 0, 0, this, other) }
}
var build = Fn.new { |rpn|
var st = Stack.new()
for (token in rpn.split(" ")) {
if (token == "+") {
var b = st.pop()
var a = st.pop()
st.push(Resistor.new("+", 0, 0, a, b))
} else if (token == "*") {
var b = st.pop()
var a = st.pop()
st.push(Resistor.new("*", 0, 0, a, b))
} else {
var r = Num.fromString(token)
st.push(Resistor.new("r", r, 0, null, null))
}
}
return st.pop()
}
var node = build.call("10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +")
node.voltage = 18
System.print(" Ohm Volt Ampere Watt Network tree")
node.report("")
- Output:
Same as Infix version
Zig
Zig requires more "code" than dynamic languages. The following three items account for a good portion of the "extra code".
- There are no hidden memory allocations. Manual memory management.
- Errors are values, and may not be ignored.
- Generic data structures and functions.
Postfix (RPN)
// postfix.zig
const std = @import("std");
const Allocator = std.mem.Allocator;
const Node = @import("common.zig").Node;
const PostfixToken = @import("common.zig").PostfixToken;
const calculate = @import("common.zig").calculate;
pub fn main() !void {
var gpa = std.heap.GeneralPurposeAllocator(.{}){};
defer _ = gpa.deinit();
const allocator = gpa.allocator();
const stdout = std.io.getStdOut().writer();
const node = try postfix(allocator, stdout, 18, "10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +");
std.debug.assert(10 == node.res());
std.debug.assert(18 == node.voltage);
std.debug.assert(1.8 == node.current());
std.debug.assert(@abs(32.4 - node.effect()) < 0.05);
std.debug.assert(.serial == node.node_type);
node.destroyDescendants(allocator);
allocator.destroy(node);
}
/// Also know as RPN (Reverse Polish Notation)
fn postfix(allocator: Allocator, writer: anytype, voltage: f32, s: []const u8) !*Node {
const tokens = try parse(allocator, s);
defer allocator.free(tokens);
return try calculate(allocator, writer, voltage, tokens);
}
const PostfixParseError = error{
UnexpectedCharacter,
};
/// Parse postfix expression 's' to give a slice of PostfixToken.
/// Caller owns slice memory on return.
/// There are no Zig language semantics to indicate ownership or transferal thereof.
fn parse(allocator: Allocator, s: []const u8) ![]PostfixToken {
var tokens = std.ArrayList(PostfixToken).init(allocator);
// defer tokens.deinit(); // not needed, toOwnedSlice() owns memory.
var slice_start: ?usize = null;
// convert the string to a list of Token
for (s, 0..) |ch, i| {
const token: PostfixToken = switch (ch) {
'+' => PostfixToken.serial,
'*' => PostfixToken.parallel,
'0'...'9' => {
// Add digits to 'resistor' value.
// 'slice_start' determines if any digit(s) have already been parsed.
if (slice_start) |_| _ = tokens.pop() else slice_start = i;
const slice_end = i + 1;
try tokens.append(PostfixToken{ .resistor = s[slice_start.?..slice_end] });
continue;
},
' ', '\t' => {
slice_start = null;
continue;
},
else => return PostfixParseError.UnexpectedCharacter,
};
try tokens.append(token);
// Last token was not a resistor. Reset 'start_slice'.
slice_start = null;
}
return tokens.toOwnedSlice();
}
Infix
// infix.zig
const std = @import("std");
const Allocator = std.mem.Allocator;
const Stack = @import("common.zig").Stack;
const Node = @import("common.zig").Node;
const PostfixToken = @import("common.zig").PostfixToken;
const calculate = @import("common.zig").calculate;
pub fn main() !void {
var gpa = std.heap.GeneralPurposeAllocator(.{}){};
defer _ = gpa.deinit();
const allocator = gpa.allocator();
const stdout = std.io.getStdOut().writer();
const node = try infix(allocator, stdout, 18, "((((10+2)*6+8)*6+4)*8+4)*8+6");
std.debug.assert(10 == node.res());
std.debug.assert(18 == node.voltage);
std.debug.assert(1.8 == node.current());
std.debug.assert(@abs(32.4 - node.effect()) < 0.05);
std.debug.assert(.serial == node.node_type);
node.destroyDescendants(allocator);
allocator.destroy(node);
}
// Zig tagged union.
const InfixToken = union(enum) {
lparen,
rparen,
serial, // +
parallel, // *
// Slice of digits from parent string.
// Do not let the parent string go out of scope while this is in scope.
resistor: []const u8,
};
/// Convert infix expression 's' to postfix and call the postfix calculate()
fn infix(allocator: Allocator, writer: anytype, voltage: f32, s: []const u8) !*Node {
// parse infix expression
const infix_tokens: []InfixToken = try parse(allocator, s);
defer allocator.free(infix_tokens);
// convert infix to postfix
const postfix_tokens: []PostfixToken = try shuntPostfix(allocator, infix_tokens);
defer allocator.free(postfix_tokens);
// use postfix calculate()
return try calculate(allocator, writer, voltage, postfix_tokens);
}
const InfixParseError = error{
UnexpectedCharacter,
};
/// Parse infix expression 's' to give a slice of InfixToken.
/// Caller owns slice memory on return.
/// There are no Zig language semantics to indicate ownership or transferal thereof.
fn parse(allocator: Allocator, s: []const u8) ![]InfixToken {
var tokens = std.ArrayList(InfixToken).init(allocator);
// defer tokens.deinit(); // not needed, toOwnedSlice() owns memory.
var slice_start: ?usize = null;
for (s, 0..) |ch, i| {
const token: InfixToken = switch (ch) {
'(' => InfixToken.lparen,
')' => InfixToken.rparen,
'+' => InfixToken.serial,
'*' => InfixToken.parallel,
'0'...'9' => {
// Add digits to 'resistor' value.
// 'slice_start' determines if any digit(s) have already been parsed.
if (slice_start) |_| _ = tokens.pop() else slice_start = i;
const slice_end = i + 1;
try tokens.append(InfixToken{ .resistor = s[slice_start.?..slice_end] });
continue;
},
' ', '\t' => { // extraneous whitespace
slice_start = null;
continue;
},
else => return InfixParseError.UnexpectedCharacter, // unknown
};
try tokens.append(token);
// Last token was not a resistor. Reset 'start_slice'.
slice_start = null;
}
return tokens.toOwnedSlice();
}
const ShuntPostfixError = error{
LParenNotAllowed,
RParenNotAllowed,
};
/// Input infix (infix tokens) in infix order.
/// Output postfix (postfix tokens) in postfix order.
///
/// Caller owns resultant slice and is responsible for freeing.
fn shuntPostfix(allocator: Allocator, infix_tokens: []InfixToken) ![]PostfixToken {
var result = PostfixTokenArray.init(allocator); // destination storage
var stack = InfixTokenStack.init(allocator); // working storage
defer result.deinit();
defer stack.deinit();
for (infix_tokens) |token| {
switch (token) {
.lparen => try stack.push(token),
.rparen => while (!stack.isEmpty()) {
const op = stack.pop();
if (op == InfixToken.lparen) break;
try result.append(op);
},
.parallel, .serial => {
while (!stack.isEmpty()) {
const op = stack.peek();
if (op != InfixToken.serial and op != InfixToken.parallel) break;
_ = stack.pop();
try result.append(op);
}
try stack.push(token);
},
.resistor => try result.append(token),
}
}
while (!stack.isEmpty())
try result.append(stack.pop());
// array now contains operands and operators in postfix order (no parentheses)
return result.toOwnedSlice();
}
const InfixTokenStack = Stack(InfixToken);
/// Façade to an ArrayList that translates from InfixToken tagged unions to
/// PostfixToken tagged unions in its append() function.
const PostfixTokenArray = struct {
result: std.ArrayList(PostfixToken),
fn init(allocator: Allocator) PostfixTokenArray {
return PostfixTokenArray{
.result = std.ArrayList(PostfixToken).init(allocator),
};
}
fn deinit(self: *PostfixTokenArray) void {
self.result.deinit();
}
/// Convert InfixToken to PostfixToken.
fn append(self: *PostfixTokenArray, infix_token: InfixToken) !void {
const postfix_token: PostfixToken = switch (infix_token) {
.serial => PostfixToken.serial,
.parallel => PostfixToken.parallel,
.resistor => |slice| PostfixToken{ .resistor = slice },
// Postfix does not have parentheses.
.lparen => return ShuntPostfixError.LParenNotAllowed,
.rparen => return ShuntPostfixError.RParenNotAllowed,
};
try self.result.append(postfix_token);
}
fn toOwnedSlice(self: *PostfixTokenArray) !std.ArrayList(PostfixToken).Slice {
return try self.result.toOwnedSlice();
}
};
// common.zig
const std = @import("std");
const Allocator = std.mem.Allocator;
// Zig "enum"
const NodeType = enum {
serial,
parallel,
resistor,
fn repr(self: NodeType) u8 {
return switch (self) {
.serial => '+',
.parallel => '*',
.resistor => 'r',
};
}
};
// Zig "tagged union"
pub const PostfixToken = union(NodeType) {
serial, // '+'
parallel, // '*'
// Slice of digits from parent string.
// Do not let the parent string go out of scope while this is in scope.
resistor: []const u8, // 'r'
};
// Zig "struct"
pub const Node = struct {
node_type: NodeType,
resistance: ?f32 = null, // optional float, either value or null
voltage: ?f32 = null,
a: ?*Node = null, // optional pointer to Node, either value or null
b: ?*Node = null,
pub fn res(self: *Node) f32 {
return switch (self.node_type) {
.serial => self.a.?.res() + self.b.?.res(),
.parallel => 1 / (1 / self.a.?.res() + 1 / self.b.?.res()),
.resistor => if (self.resistance) |resistance| resistance else unreachable,
};
}
pub fn current(self: *Node) f32 {
if (self.voltage) |voltage| return voltage / self.res() else unreachable;
}
pub fn effect(self: *Node) f32 {
if (self.voltage) |voltage| return self.current() * voltage else unreachable;
}
pub fn setVoltage(self: *Node, voltage: f32) void {
self.voltage = voltage;
switch (self.node_type) {
.serial => {
const ra: f32 = self.a.?.res();
const rb: f32 = self.b.?.res();
self.a.?.setVoltage(ra / (ra + rb) * voltage);
self.b.?.setVoltage(rb / (ra + rb) * voltage);
},
.parallel => {
self.a.?.setVoltage(voltage);
self.b.?.setVoltage(voltage);
},
.resistor => {},
}
}
pub fn report(self: *Node, allocator: Allocator, writer: anytype, level: []const u8) !void {
if (self.voltage) |voltage| {
try writer.print("{d:8.3} {d:8.3} {d:8.3} {d:8.3} {s}{c}\n", .{
self.res(), voltage, self.current(),
self.effect(), level, self.node_type.repr(),
});
} else unreachable;
// iterate though 'a' and 'b' optional nodes
for ([2]?*Node{ self.a, self.b }) |optional_node| {
if (optional_node) |node| {
const next_level = try std.fmt.allocPrint(allocator, "{s}| ", .{level});
defer allocator.free(next_level);
try node.report(allocator, writer, next_level);
}
}
}
/// Free memory allocated to Node descendants and Node itself.
pub fn destroyDescendants(self: *Node, allocator: Allocator) void {
if (self.a) |a| {
self.a = null;
a.destroyDescendants(allocator);
allocator.destroy(a);
}
if (self.b) |b| {
self.b = null;
b.destroyDescendants(allocator);
allocator.destroy(b);
}
}
};
fn build(allocator: Allocator, tokens: []PostfixToken) !*Node {
var stack = Stack(*Node).init(allocator);
defer stack.deinit();
for (tokens) |token| {
const node = try allocator.create(Node);
// 'token' is a tagged union.
// note the extraction of the '.resistor' variable via |r|
node.* = switch (token) {
.serial => Node{ .node_type = NodeType.serial, .b = stack.pop(), .a = stack.pop() },
.parallel => Node{ .node_type = NodeType.parallel, .b = stack.pop(), .a = stack.pop() },
.resistor => |r| Node{ .node_type = NodeType.resistor, .resistance = try std.fmt.parseFloat(f32, r) },
};
try stack.push(node);
}
std.debug.assert(stack.hasOne()); // stack length should be 1.
return stack.pop();
}
pub fn calculate(allocator: Allocator, writer: anytype, voltage: f32, tokens: []PostfixToken) !*Node {
try writer.print(" Ohm Volt Ampere Watt Network tree\n", .{});
var node = try build(allocator, tokens);
node.setVoltage(voltage);
try node.report(allocator, writer, "");
return node;
}
// Zig "Generic Data Structure"
// An ad hoc generic stack implementation.
// 'pub' is the Zig way of giving visibility outside module scope.
pub fn Stack(comptime T: type) type {
return struct {
const Self = @This();
stack: std.ArrayList(T),
pub fn init(allocator: Allocator) Self {
return Self{
.stack = std.ArrayList(T).init(allocator),
};
}
pub fn deinit(self: *Self) void {
self.stack.deinit();
}
pub fn push(self: *Self, node: T) !void {
return try self.stack.append(node);
}
pub fn pop(self: *Self) T {
return self.stack.pop();
}
pub fn peek(self: *const Self) T {
return self.stack.items[self.stack.items.len - 1];
}
pub fn isEmpty(self: *const Self) bool {
return self.stack.items.len == 0;
}
// no 'pub' - private to this module
fn hasOne(self: *Self) bool {
return self.stack.items.len == 1;
}
};
}
zkl
class Resistor{
fcn init(resistance_,symbol_="r", a_=Void, b_=Void){
var resistance,a,b,symbol, voltage=Void;
resistance,symbol,a,b = vm.arglist;
resistance=resistance.toFloat(); // deal with strings/ints
}
fcn res{
if (symbol=="+") a.res() + b.res();
else if(symbol=="*") 1.0/(1.0/a.res() + 1.0/b.res());
else resistance
}
fcn setVoltage(voltage){
if(symbol=="+"){
ra,rb := a.res(), b.res();
a.setVoltage(ra/(ra + rb)*voltage);
b.setVoltage(rb/(ra + rb)*voltage);
}
else if(symbol=="*") T(a,b).apply2("setVoltage",voltage);
self.voltage = voltage.toFloat();
}
fcn current{ voltage/res() }
fcn effect { current()*voltage }
fcn report(level=""){
println("%8.3f %8.3f %8.3f %8.3f %s%s".fmt(res(),voltage,current(),effect(),level,symbol));
T(a,b).apply2("report",level + "| "); // noop if Void
}
fcn __opAdd(other){ Resistor(0,"+",self,other) }
fcn __opMul(other){ Resistor(0,"*",self,other) }
}
Infix
R1,R2,R3,R4,R5,R6,R7,R8,R9,R10 := T(6,8,4,8,4,6,8,10,6,2].apply(Resistor);
node:=((((R8 + R10)*R9 + R7)*R6 + R5)*R4 + R3)*R2 + R1;
node.setVoltage(18);
println(" Ohm Volt Ampere Watt Network tree");
node.report();
- Output:
Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r
RPN
fcn build(rpnStr){
stack:=List();
foreach symbol in (rpnStr.split()){
if(symbol=="+"){
a,b:=stack.pop(),stack.pop();
stack.append(Resistor(0,"+",b,a))
}
else if(symbol=="*"){
a,b:=stack.pop(),stack.pop();
stack.append(Resistor(0,"*",b,a))
}
else stack.append(Resistor(symbol,"r"));
}
stack.pop() // unevaluated top of circuit
}
node:=build("10 2 + 6 * 8 + 6 * 4 + 8 * 4 + 8 * 6 +");
node.setVoltage(18);
println(" Ohm Volt Ampere Watt Network tree");
node.report();
- Output:
Ohm Volt Ampere Watt Network tree 10.000 18.000 1.800 32.400 + 4.000 7.200 1.800 12.960 | * 8.000 7.200 0.900 6.480 | | + 4.000 3.600 0.900 3.240 | | | * 8.000 3.600 0.450 1.620 | | | | + 4.000 1.800 0.450 0.810 | | | | | * 12.000 1.800 0.150 0.270 | | | | | | + 4.000 0.600 0.150 0.090 | | | | | | | * 12.000 0.600 0.050 0.030 | | | | | | | | + 10.000 0.500 0.050 0.025 | | | | | | | | | r 2.000 0.100 0.050 0.005 | | | | | | | | | r 6.000 0.600 0.100 0.060 | | | | | | | | r 8.000 1.200 0.150 0.180 | | | | | | | r 6.000 1.800 0.300 0.540 | | | | | | r 4.000 1.800 0.450 0.810 | | | | | r 8.000 3.600 0.450 1.620 | | | | r 4.000 3.600 0.900 3.240 | | | r 8.000 7.200 0.900 6.480 | | r 6.000 10.800 1.800 19.440 | r