Parsing/RPN calculator algorithm
You are encouraged to solve this task according to the task description, using any language you may know.
Create a stack-based evaluator for an expression in reverse Polish notation that also shows the changes in the stack as each individual token is processed as a table.
- Assume an input of a correct, space separated, string of tokens of an RPN expression
- Test with the RPN expression generated from the Parsing/Shunting-yard algorithm task
'3 4 2 * 1 5 - 2 3 ^ ^ / +'then print and display the output here.
- Note
- '^' means exponentiation in the expression above.
- See also
- Parsing/Shunting-yard algorithm for a method of generating an RPN from an infix expression.
- Several solutions to 24 game/Solve make use of RPN evaluators (although tracing how they work is not a part of that task).
- Parsing/RPN to infix conversion.
- Arithmetic evaluation.
Ada
<lang Ada>with Ada.Text_IO, Ada.Containers.Vectors;
procedure RPN_Calculator is
package IIO is new Ada.Text_IO.Float_IO(Float);
package Float_Vec is new Ada.Containers.Vectors
(Index_Type => Positive, Element_Type => Float);
Stack: Float_Vec.Vector;
Input: String := Ada.Text_IO.Get_Line; Cursor: Positive := Input'First; New_Cursor: Positive;
begin
loop
-- read spaces
while Cursor <= Input'Last and then Input(Cursor)=' ' loop
Cursor := Cursor + 1;
end loop;
exit when Cursor > Input'Last;
New_Cursor := Cursor;
while New_Cursor <= Input'Last and then Input(New_Cursor) /= ' ' loop
New_Cursor := New_Cursor + 1;
end loop;
-- try to read a number and push it to the stack
declare
Last: Positive;
Value: Float;
X, Y: Float;
begin
IIO.Get(From => Input(Cursor .. New_Cursor - 1),
Item => Value,
Last => Last);
Stack.Append(Value);
Cursor := New_Cursor;
exception -- if reading the number fails, try to read an operator token
when others =>
Y := Stack.Last_Element; Stack.Delete_Last; -- pick two elements
X := Stack.Last_Element; Stack.Delete_Last; -- from the stack
case Input(Cursor) is
when '+' => Stack.Append(X+Y);
when '-' => Stack.Append(X-Y);
when '*' => Stack.Append(X*Y);
when '/' => Stack.Append(X/Y);
when '^' => Stack.Append(X ** Integer(Float'Rounding(Y)));
when others => raise Program_Error with "unecpected token '"
& Input(Cursor) & "' at column" & Integer'Image(Cursor);
end case;
Cursor := New_Cursor;
end;
for I in Stack.First_Index .. Stack.Last_Index loop
Ada.Text_IO.Put(" ");
IIO.Put(Stack.Element(I), Aft => 5, Exp => 0);
end loop;
Ada.Text_IO.New_Line;
end loop;
Ada.Text_IO.Put("Result = ");
IIO.Put(Item => Stack.Last_Element, Aft => 5, Exp => 0);
end RPN_Calculator;</lang>
Output:
3 4 2 * 1 5 - 2 3 ^ ^ / + 3.00000 3.00000 4.00000 3.00000 4.00000 2.00000 3.00000 8.00000 3.00000 8.00000 1.00000 3.00000 8.00000 1.00000 5.00000 3.00000 8.00000 -4.00000 3.00000 8.00000 -4.00000 2.00000 3.00000 8.00000 -4.00000 2.00000 3.00000 3.00000 8.00000 -4.00000 8.00000 3.00000 8.00000 65536.00000 3.00000 0.00012 3.00012 Result = 3.00012
ANTLR
Java
<lang java> grammar rpnC ; // // rpn Calculator // // Nigel Galloway - April 7th., 2012 // @members { Stack<Double> s = new Stack<Double>(); } rpn : (WS* (num|op) (WS | WS* NEWLINE {System.out.println(s.pop());}))*; num : '-'? Digit+ ('.' Digit+)? {s.push(Double.parseDouble($num.text));}; Digit : '0'..'9'; op : '-' {double x = s.pop(); s.push(s.pop() - x);} | '/' {double x = s.pop(); s.push(s.pop() / x);} | '*' {s.push(s.pop() * s.pop());} | '^' {double x = s.pop(); s.push(Math.pow(s.pop(), x));} | '+' {s.push(s.pop() + s.pop());}; WS : (' ' | '\t'){skip()}; NEWLINE : '\r'? '\n'; </lang> Produces:
>java Test 3 4 2 * 1 5 - 2 3 ^ ^ / + ^Z 3.0001220703125
AutoHotkey
Output is in clipboard. <lang AHK>evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +") evalRPN(s){ stack := [] out := "For RPN expression: '" s "'`r`n`r`nTOKEN`t`tACTION`t`t`tSTACK`r`n" Loop Parse, s If A_LoopField is number t .= A_LoopField else { If t stack.Insert(t) , out .= t "`tPush num onto top of stack`t" stackShow(stack) "`r`n" , t := "" If InStr("+-/*^", l := A_LoopField) { a := stack.Remove(), b := stack.Remove() stack.Insert( l = "+" ? b + a :l = "-" ? b - a :l = "*" ? b * a :l = "/" ? b / a :l = "^" ? b **a :0 ) out .= l "`tApply op " l " to top of stack`t" stackShow(stack) "`r`n" } } r := stack.Remove() out .= "`r`n The final output value is: '" r "'" clipboard := out return r } StackShow(stack){ for each, value in stack out .= A_Space value return subStr(out, 2) }</lang>
- Output
For RPN expression: '3 4 2 * 1 5 - 2 3 ^ ^ / +' TOKEN ACTION STACK 3 Push num onto top of stack 3 4 Push num onto top of stack 3 4 2 Push num onto top of stack 3 4 2 * Apply op * to top of stack 3 8 1 Push num onto top of stack 3 8 1 5 Push num onto top of stack 3 8 1 5 - Apply op - to top of stack 3 8 -4 2 Push num onto top of stack 3 8 -4 2 3 Push num onto top of stack 3 8 -4 2 3 ^ Apply op ^ to top of stack 3 8 -4 8 ^ Apply op ^ to top of stack 3 8 65536 / Apply op / to top of stack 3 0.000122 + Apply op + to top of stack 3.000122 The final output value is: '3.000122'
C
<lang c>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
- include <math.h>
void die(char *msg) { fprintf(stderr, "%s", msg); abort(); }
- define MAX_D 256
double stack[MAX_D]; int depth;
void push(double v) { if (depth >= MAX_D) die("stack overflow\n"); stack[depth++] = v; }
double pop() { if (!depth) die("stack underflow\n"); return stack[--depth]; }
double rpn(char *s) { double a, b; int i; char *e, *w = " \t\n\r\f";
for (s = strtok(s, w); s; s = strtok(0, w)) { a = strtod(s, &e); if (e > s) printf(" :"), push(a);
- define binop(x) printf("%c:", *s), b = pop(), a = pop(), push(x)
else if (*s == '+') binop(a + b); else if (*s == '-') binop(a - b); else if (*s == '*') binop(a * b); else if (*s == '/') binop(a / b); else if (*s == '^') binop(pow(a, b));
- undef binop
else { fprintf(stderr, "'%c': ", *s); die("unknown oeprator\n"); } for (i = depth; i-- || 0 * putchar('\n'); ) printf(" %g", stack[i]); }
if (depth != 1) die("stack leftover\n");
return pop(); }
int main(void) { char s[] = " 3 4 2 * 1 5 - 2 3 ^ ^ / + "; printf("%g\n", rpn(s)); return 0; }</lang>
It's also possible to parse RPN string backwards and recursively; good luck printing out your token stack as a table: there isn't one. <lang c>#include <stdio.h>
- include <stdlib.h>
- include <ctype.h>
- include <string.h>
- include <math.h>
- define die(msg) fprintf(stderr, msg"\n"), abort();
double get(char *s, char *e, char **new_e) { char *t; double a, b;
for (e--; e >= s && isspace(*e); e--); for (t = e; t > s && !isspace(t[-1]); t--);
if (t < s) die("underflow");
- define get2(expr) b = get(s, t, &t), a = get(s, t, &t), a = expr
a = strtod(t, &e); if (e <= t) { if (t[0] == '+') get2(a + b); else if (t[0] == '-') get2(a - b); else if (t[0] == '*') get2(a * b); else if (t[0] == '/') get2(a / b); else if (t[0] == '^') get2(pow(a, b)); else { fprintf(stderr, "'%c': ", t[0]); die("unknown token"); } }
- undef get2
*new_e = t; return a; }
double rpn(char *s) { char *e = s + strlen(s); double v = get(s, e, &e);
while (e > s && isspace(e[-1])) e--; if (e == s) return v;
fprintf(stderr, "\"%.*s\": ", e - s, s); die("front garbage"); }
int main(void) { printf("%g\n", rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +")); return 0; }</lang>
C++
<lang cpp>#include <vector>
- include <string>
- include <sstream>
- include <iostream>
- include <cmath>
- include <algorithm>
- include <iterator>
- include <cstdlib>
double rpn(const std::string &expr){
std::istringstream iss(expr);
std::vector<double> stack;
std::cout << "Input\tOperation\tStack after" << std::endl;
std::string token;
while (iss >> token) {
std::cout << token << "\t";
double tokenNum;
if (std::istringstream(token) >> tokenNum) {
std::cout << "Push\t\t";
stack.push_back(tokenNum);
} else {
std::cout << "Operate\t\t";
double secondOperand = stack.back();
stack.pop_back();
double firstOperand = stack.back();
stack.pop_back();
if (token == "*")
stack.push_back(firstOperand * secondOperand);
else if (token == "/")
stack.push_back(firstOperand / secondOperand);
else if (token == "-")
stack.push_back(firstOperand - secondOperand);
else if (token == "+")
stack.push_back(firstOperand + secondOperand);
else if (token == "^")
stack.push_back(std::pow(firstOperand, secondOperand));
else { //just in case
std::cerr << "Error" << std::endl; std::exit(1);
} } std::copy(stack.begin(), stack.end(), std::ostream_iterator<double>(std::cout, " ")); std::cout << std::endl; } return stack.back();
}
int main() {
std::string s = " 3 4 2 * 1 5 - 2 3 ^ ^ / + "; std::cout << "Final answer: " << rpn(s) << std::endl; return 0;
}</lang>
- Output:
Input Operation Stack after 3 Push 3 4 Push 3 4 2 Push 3 4 2 * Operate 3 8 1 Push 3 8 1 5 Push 3 8 1 5 - Operate 3 8 -4 2 Push 3 8 -4 2 3 Push 3 8 -4 2 3 ^ Operate 3 8 -4 8 ^ Operate 3 8 65536 / Operate 3 0.00012207 + Operate 3.00012 Final answer: 3.00012
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq; using System.Globalization; using System.Threading;
namespace RPNEvaluator {
class RPNEvaluator
{
static void Main(string[] args)
{
Thread.CurrentThread.CurrentCulture = CultureInfo.InvariantCulture;
string rpn = "3 4 2 * 1 5 - 2 3 ^ ^ / +";
Console.WriteLine("{0}\n", rpn);
decimal result = CalculateRPN(rpn);
Console.WriteLine("\nResult is {0}", result);
}
static decimal CalculateRPN(string rpn)
{
string[] rpnTokens = rpn.Split(' ');
Stack<decimal> stack = new Stack<decimal>();
decimal number = decimal.Zero;
foreach (string token in rpnTokens)
{
if (decimal.TryParse(token, out number))
{
stack.Push(number);
}
else
{
switch (token)
{
case "^":
case "pow":
{
number = stack.Pop();
stack.Push((decimal)Math.Pow((double)stack.Pop(), (double)number));
break;
}
case "ln":
{
stack.Push((decimal)Math.Log((double)stack.Pop(), Math.E));
break;
}
case "sqrt":
{
stack.Push((decimal)Math.Sqrt((double)stack.Pop()));
break;
}
case "*":
{
stack.Push(stack.Pop() * stack.Pop());
break;
}
case "/":
{
number = stack.Pop();
stack.Push(stack.Pop() / number);
break;
}
case "+":
{
stack.Push(stack.Pop() + stack.Pop());
break;
}
case "-":
{
number = stack.Pop();
stack.Push(stack.Pop() - number);
break;
}
default:
Console.WriteLine("Error in CalculateRPN(string) Method!");
break;
}
}
PrintState(stack);
}
return stack.Pop();
}
static void PrintState(Stack<decimal> stack)
{
decimal[] arr = stack.ToArray();
for (int i = arr.Length - 1; i >= 0; i--)
{
Console.Write("{0,-8:F3}", arr[i]);
}
Console.WriteLine();
}
}
}</lang> Output:
3 4 2 * 1 5 - 2 3 ^ ^ / + 3.000 3.000 4.000 3.000 4.000 2.000 3.000 8.000 3.000 8.000 1.000 3.000 8.000 1.000 5.000 3.000 8.000 -4.000 3.000 8.000 -4.000 2.000 3.000 8.000 -4.000 2.000 3.000 3.000 8.000 -4.000 8.000 3.000 8.000 65536.000 3.000 0.000 3.000 Result is 3.0001220703125
Ela
<lang ela>open string console list format read
eval str = writen "Input\tOperation\tStack after" $
eval' (split " " str) []
where eval' [] (s::_) = printfn "Result: {0}" s
eval' (x::xs) sta | "+"? = eval' xs <| op (+)
| "-"? = eval' xs <| op (-)
| "^"? = eval' xs <| op (**)
| "/"? = eval' xs <| op (/)
| "*"? = eval' xs <| op (*)
| else = eval' xs <| conv x
where c? = x == c
op (^) = out "Operate" st' $ st'
where st' = (head ss ^ s) :: tail ss
conv x = out "Push" st' $ st'
where st' = readStr x :: sta
(s,ss) | sta == [] = ((),[])
| else = (head sta,tail sta)
out op st' = printfn "{0}\t{1}\t\t{2}" x op st'
eval "3 4 2 * 1 5 - 2 3 ^ ^ / +"</lang>
Output:
Input Operation Stack after 3 Push [3] 4 Push [4,3] 2 Push [2,4,3] * Operate [8,3] 1 Push [1,8,3] 5 Push [5,1,8,3] - Operate [-4,8,3] 2 Push [2,-4,8,3] 3 Push [3,2,-4,8,3] ^ Operate [8,-4,8,3] ^ Operate [65536,8,3] / Operate [0.0001220703125,3] + Operate [3.0001220703125] Result: 3.0001220703125
D
<lang d>import std.stdio, std.string, std.conv, std.typetuple;
void main() {
auto input = "3 4 2 * 1 5 - 2 3 ^ ^ / +";
writeln("For postfix expression: ", input);
writeln("\nToken Action Stack");
real[] stack;
foreach (tok; input.split()) {
auto action = "Apply op to top of stack";
switch (tok) {
foreach (o; TypeTuple!("+", "-", "*", "/", "^")) {
case o:
mixin("stack[$ - 2]" ~
(o == "^" ? "^^" : o) ~ "=stack[$ - 1];");
stack.length--;
break;
}
break;
default:
action = "Push num onto top of stack";
stack ~= to!real(tok);
}
writefln("%3s %-26s %s", tok, action, stack);
}
writeln("\nThe final value is ", stack[0]);
}</lang>
- Output:
For postfix expression: 3 4 2 * 1 5 - 2 3 ^ ^ / + Token Action Stack 3 Push num onto top of stack [3] 4 Push num onto top of stack [3, 4] 2 Push num onto top of stack [3, 4, 2] * Apply op to top of stack [3, 8] 1 Push num onto top of stack [3, 8, 1] 5 Push num onto top of stack [3, 8, 1, 5] - Apply op to top of stack [3, 8, -4] 2 Push num onto top of stack [3, 8, -4, 2] 3 Push num onto top of stack [3, 8, -4, 2, 3] ^ Apply op to top of stack [3, 8, -4, 8] ^ Apply op to top of stack [3, 8, 65536] / Apply op to top of stack [3, 0.00012207] + Apply op to top of stack [3.00012] The final value is 3.00012
Go
No error checking. <lang go>package main
import (
"fmt" "math" "strconv" "strings"
)
var input = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
func main() {
fmt.Printf("For postfix %q\n", input)
fmt.Println("\nToken Action Stack")
var stack []float64
for _, tok := range strings.Fields(input) {
action := "Apply op to top of stack"
switch tok {
case "+":
stack[len(stack)-2] += stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "-":
stack[len(stack)-2] -= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "*":
stack[len(stack)-2] *= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "/":
stack[len(stack)-2] /= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "^":
stack[len(stack)-2] =
math.Pow(stack[len(stack)-2], stack[len(stack)-1])
stack = stack[:len(stack)-1]
default:
action = "Push num onto top of stack"
f, _ := strconv.ParseFloat(tok, 64)
stack = append(stack, f)
}
fmt.Printf("%3s %-26s %v\n", tok, action, stack)
}
fmt.Println("\nThe final value is", stack[0])
}</lang> Output:
For postfix "3 4 2 * 1 5 - 2 3 ^ ^ / +" Token Action Stack 3 Push num onto top of stack [3] 4 Push num onto top of stack [3 4] 2 Push num onto top of stack [3 4 2] * Apply op to top of stack [3 8] 1 Push num onto top of stack [3 8 1] 5 Push num onto top of stack [3 8 1 5] - Apply op to top of stack [3 8 -4] 2 Push num onto top of stack [3 8 -4 2] 3 Push num onto top of stack [3 8 -4 2 3] ^ Apply op to top of stack [3 8 -4 8] ^ Apply op to top of stack [3 8 65536] / Apply op to top of stack [3 0.0001220703125] + Apply op to top of stack [3.0001220703125] The final value is 3.0001220703125
Groovy
<lang groovy>def evaluateRPN(expression) {
def stack = [] as Stack
def binaryOp = { action -> return { action.call(stack.pop(), stack.pop()) } }
def actions = [
'+': binaryOp { a, b -> b + a },
'-': binaryOp { a, b -> b - a },
'*': binaryOp { a, b -> b * a },
'/': binaryOp { a, b -> b / a },
'^': binaryOp { a, b -> b ** a }
]
expression.split(' ').each { item ->
def action = actions[item] ?: { item as BigDecimal }
stack.push(action.call())
println "$item: $stack" } assert stack.size() == 1 : "Unbalanced Expression: $expression ($stack)" stack.pop()
}</lang> Test <lang groovy>println evaluateRPN('3 4 2 * 1 5 - 2 3 ^ ^ / +')</lang> Output:
3: [3] 4: [3, 4] 2: [3, 4, 2] *: [3, 8] 1: [3, 8, 1] 5: [3, 8, 1, 5] -: [3, 8, -4] 2: [3, 8, -4, 2] 3: [3, 8, -4, 2, 3] ^: [3, 8, -4, 8] ^: [3, 8, 65536] /: [3, 0.0001220703125] +: [3.0001220703125] 3.0001220703125
Haskell
<lang Haskell>import Data.List (elemIndex)
-- Show results main = mapM_ (\(x, y) -> putStrLn $ x ++ " ==> " ++ show y) $ reverse $ zip b (a:c)
where (a, b, c) = solve "3 4 2 * 1 5 - 2 3 ^ ^ / +"
-- Solve and report RPN solve = foldl reduce ([], [], []) . words reduce (xs, ps, st) w =
if i == Nothing
then (read w:xs, ("Pushing " ++ w):ps, xs:st)
else (([(*),(+),(-),(/),(**)]!!o) a b:zs, ("Performing " ++ w):ps, xs:st)
where i = elemIndex (head w) "*+-/^"
Just o = i
(b:a:zs) = xs
</lang> Output:
*Main> main Pushing 3 ==> [3.0] Pushing 4 ==> [4.0,3.0] Pushing 2 ==> [2.0,4.0,3.0] Performing * ==> [8.0,3.0] Pushing 1 ==> [1.0,8.0,3.0] Pushing 5 ==> [5.0,1.0,8.0,3.0] Performing - ==> [-4.0,8.0,3.0] Pushing 2 ==> [2.0,-4.0,8.0,3.0] Pushing 3 ==> [3.0,2.0,-4.0,8.0,3.0] Performing ^ ==> [8.0,-4.0,8.0,3.0] Performing ^ ==> [65536.0,8.0,3.0] Performing / ==> [1.220703125e-4,3.0] Performing + ==> [3.0001220703125] *Main>
Icon and Unicon
<lang Icon>procedure main()
EvalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
end
link printf invocable all
procedure EvalRPN(expr) #: evaluate (and trace stack) an RPN string
stack := []
expr ? until pos(0) do {
tab(many(' ')) # consume previous seperator
token := tab(upto(' ')|0) # get token
if token := numeric(token) then { # ... numeric
push(stack,token)
printf("pushed numeric %i : %s\n",token,list2string(stack))
}
else { # ... operator
every b|a := pop(stack) # pop & reverse operands
case token of {
"+"|"-"|"*"|"^" : push(stack,token(a,b))
"/" : push(stack,token(real(a),b))
default : runerr(205,token)
}
printf("applied operator %s : %s\n",token,list2string(stack))
}
}
end
procedure list2string(L) #: format list as a string
every (s := "[ ") ||:= !L || " " return s || "]"
end</lang>
printf.icn provides formatting
Output:
pushed numeric 3 : [ 3 ] pushed numeric 4 : [ 4 3 ] pushed numeric 2 : [ 2 4 3 ] applied operator * : [ 8 3 ] pushed numeric 1 : [ 1 8 3 ] pushed numeric 5 : [ 5 1 8 3 ] applied operator - : [ -4 8 3 ] pushed numeric 2 : [ 2 -4 8 3 ] pushed numeric 3 : [ 3 2 -4 8 3 ] applied operator ^ : [ 8 -4 8 3 ] applied operator ^ : [ 65536 8 3 ] applied operator / : [ 0.0001220703125 3 ] applied operator + : [ 3.0001220703125 ]
J
Offered operations are all dyadic - having two argument. So on each step we may either "shift" a number to the stack or "reduce" two topmost stack items to one.
The final verb is monad - it takes single argument, which contains both the input and accumulated stack. First, create initial state of the input: <lang J> a: , <;._1 ' ' , '3 4 2 * 1 5 - 2 3 ^ ^ / +' ┌┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┐ ││3│4│2│*│1│5│-│2│3│^│^│/│+│ └┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┘</lang> As an example, let's add monadic operation _ which inverses the sign of the stack top element.
We're going to read tokens from input one by one. Each time we read a token, we're checking if it's a number - in this case we put the number to the stack - or an operation - in this case we apply the operation to the stack. The monad which returns 1 for operation and 0 otherwise is "isOp". Dyad, moving input token to the stack, is "doShift", and applying the operation to the stack is "doApply".
There are 6 operations - one monadic "_" and five dyadic "+", "-", "*", "/", "^". For operation, we need to translate input token into operation and apply it to the stack. The dyad which converts the input token to the operation is "dispatch". It uses two miscellaneous adverbs, one for monadic operations - "mo" - and another for dyadic - "dy".
The RPN driver is monad "consume", which handles one token. The output is the state of the program after the token was consumed - stack in the 0th box, and remaining input afterwards. As a side effect, "consume" is going to print the resulting stack, so running "consume" once for each token will produce intermediate states of the stack. <lang J> isOp=: '_+-*/^' e.~ {.@>@{.
mo=: 1 :'(}: , u@{:) @ ['
dy=: 1 :'(_2&}. , u/@(_2&{.)) @ ['
dispatch=: (-mo)`(+dy)`(-dy)`(*dy)`(%dy)`(^dy)@.('_+-*/^' i. {.@>@])
doShift=: (<@, ".@>@{.) , }.@]
doApply=: }.@] ,~ [ <@dispatch {.@]
consume=: [: ([ smoutput@>@{.) >@{. doShift`doApply@.(isOp@]) }.
consume ^: (<:@#) a: , <;._1 ' ' , '3 4 2 * 1 5 - 2 3 ^ ^ / +'
3 3 4 3 4 2 3 8 3 8 1 3 8 1 5 3 8 _4 3 8 _4 2 3 8 _4 2 3 3 8 _4 8 3 8 65536 3 0.00012207 3.00012 ┌───────┐ │3.00012│ └───────┘
consume ^: (<:@#) a: , <;._1 ' ' , '3 _ 4 +'
3 _3 _3 4 1 ┌─┐ │1│ └─┘</lang>
Java
Supports multi-digit numbers and negative numbers. <lang java5>import java.util.LinkedList;
public class RPN{ public static void evalRPN(String expr){ String cleanExpr = cleanExpr(expr); LinkedList<Double> stack = new LinkedList<Double>(); System.out.println("Input\tOperation\tStack after"); for(String token:cleanExpr.split("\\s")){ System.out.print(token+"\t"); Double tokenNum = null; try{ tokenNum = Double.parseDouble(token); }catch(NumberFormatException e){} if(tokenNum != null){ System.out.print("Push\t\t"); stack.push(Double.parseDouble(token+"")); }else if(token.equals("*")){ System.out.print("Operate\t\t"); double secondOperand = stack.pop(); double firstOperand = stack.pop(); stack.push(firstOperand * secondOperand); }else if(token.equals("/")){ System.out.print("Operate\t\t"); double secondOperand = stack.pop(); double firstOperand = stack.pop(); stack.push(firstOperand / secondOperand); }else if(token.equals("-")){ System.out.print("Operate\t\t"); double secondOperand = stack.pop(); double firstOperand = stack.pop(); stack.push(firstOperand - secondOperand); }else if(token.equals("+")){ System.out.print("Operate\t\t"); double secondOperand = stack.pop(); double firstOperand = stack.pop(); stack.push(firstOperand + secondOperand); }else if(token.equals("^")){ System.out.print("Operate\t\t"); double secondOperand = stack.pop(); double firstOperand = stack.pop(); stack.push(Math.pow(firstOperand, secondOperand)); }else{//just in case System.out.println("Error"); return; } System.out.println(stack); } System.out.println("Final answer: " + stack.pop()); }
private static String cleanExpr(String expr){ //remove all non-operators, non-whitespace, and non digit chars return expr.replaceAll("[^\\^\\*\\+\\-\\d/\\s]", ""); }
public static void main(String[] args){ evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +"); } }</lang> Output:
Input Operation Stack after 3 Push [3.0] 4 Push [4.0, 3.0] 2 Push [2.0, 4.0, 3.0] * Operate [8.0, 3.0] 1 Push [1.0, 8.0, 3.0] 5 Push [5.0, 1.0, 8.0, 3.0] - Operate [-4.0, 8.0, 3.0] 2 Push [2.0, -4.0, 8.0, 3.0] 3 Push [3.0, 2.0, -4.0, 8.0, 3.0] ^ Operate [8.0, -4.0, 8.0, 3.0] ^ Operate [65536.0, 8.0, 3.0] / Operate [1.220703125E-4, 3.0] + Operate [3.0001220703125] Final answer: 3.0001220703125
Objeck
<lang objeck> use IO; use Struct;
bundle Default {
class RpnCalc {
function : Main(args : String[]) ~ Nil {
Caculate("3 4 2 * 1 5 - 2 3 ^ ^ / +");
}
function : native : Caculate(rpn : String) ~ Nil {
rpn->PrintLine();
tokens := rpn->Split(" ");
stack := FloatVector->New();
each(i : tokens) {
token := tokens[i]->Trim();
if(token->Size() > 0) {
if(token->Get(0)->IsDigit()) {
stack->AddBack(token->ToFloat());
}
else {
right := stack->Get(stack->Size() - 1); stack->RemoveBack();
left := stack->Get(stack->Size() - 1); stack->RemoveBack();
select(token->Get(0)) {
label '+': {
stack->AddBack(left + right);
}
label '-': {
stack->AddBack(left - right);
}
label '*': {
stack->AddBack(left * right);
}
label '/': {
stack->AddBack(left / right);
}
label '^': {
stack->AddBack(right->Power(left));
}
};
};
PrintStack(stack);
};
};
Console->Print("result: ")->PrintLine(stack->Get(0));
}
function : PrintStack(stack : FloatVector) ~ Nil {
" ["->Print();
each(i : stack) {
stack->Get(i)->Print();
if(i + 1< stack->Size()) {
", "->Print();
};
};
']'->PrintLine();
}
}
} </lang>
Output
3 4 2 * 1 5 - 2 3 ^ ^ / + [3] [3, 4] [3, 4, 2] [3, 8] [3, 8, 1] [3, 8, 1, 5] [3, 8, -4] [3, 8, -4, 2] [3, 8, -4, 2, 3] [3, 8, -4, 8] [3, 8, 65536] [3, 0.00012207] [3.00012] result: 3.00012
Perl
<lang Perl>
- RPN calculator
- Nigel Galloway April 2nd., 2012
$WSb = '(?:^|\s+)'; $WSa = '(?:\s+|$)'; $num = '([+-/]?(?:\.\d+|\d+(?:\.\d*)?))'; $op = '([-+*/^])'; sub myE {
my $a = '('.$1.')'.$3.'('.$2.')';
$a =~ s/\^/**/;
return eval($a);
} while (<>) {
while (s/$WSb$num\s+$num\s+$op$WSa/' '.myE().' '/e) {}
print ($_, "\n");
} </lang> Produces:
>rpnC.pl 3 4 2 * 1 5 - 2 3 ^ ^ / + 3.0001220703125
Perl 6
<lang perl6>my $proggie = '3 4 2 * 1 5 - 2 3 ^ ^ / +';
class RPN is Array {
method binop(&infix:<op>) { self.push: self.pop Rop self.pop }
method run($p) {
for $p.words {
say "$_ ({self})";
when /\d/ { self.push: $_ }
when '+' { self.binop: &[+] }
when '-' { self.binop: &[-] }
when '*' { self.binop: &[*] }
when '/' { self.binop: &[/] }
when '^' { self.binop: &[**] }
default { die "$_ is bogus" }
}
say self;
}
}
RPN.new.run($proggie);</lang>
- Output:
3 () 4 (3) 2 (3 4) * (3 4 2) 1 (3 8) 5 (3 8 1) - (3 8 1 5) 2 (3 8 -4) 3 (3 8 -4 2) ^ (3 8 -4 2 3) ^ (3 8 -4 8) / (3 8 65536) + (3 0.0001220703125) 3.0001220703125
PHP
<lang php> <?php // RPN Calculator // // Nigel Galloway - April 3rd., 2012 // $WSb = '(?:^|\s+)'; $WSa = '(?:\s+|$)'; $num = '([+-]?(?:\.\d+|\d+(?:\.\d*)?))'; $op = '([-+*\/^])';
function myE($m) {
return $m[3] == '^' ? ' ' . pow($m[1], $m[2]) . ' ' : ' ' . eval("return " . $m[1] . $m[3] . $m[2] . ";") . ' ';
}
while (!feof(STDIN)) {
$s = trim(fgets(STDIN));
if ($s == )
continue;
do {
$s = preg_replace_callback("/$WSb$num\\s+$num\\s+$op$WSa/", "myE", $s, -1, $n);
} while ($n);
echo floatval($s) . "\n";
} ?> </lang> Produces:
3 4 2 * 1 5 - 2 3 ^ ^ / + 3.0001220703125
PicoLisp
This is an integer-only calculator: <lang PicoLisp>(de rpnCalculator (Str)
(let (^ ** Stack) # Define '^' from the built-in '**'
(prinl "Token Stack")
(for Token (str Str "*+-/\^")
(if (num? Token)
(push 'Stack @)
(set (cdr Stack)
(Token (cadr Stack) (pop 'Stack)) ) )
(prin Token)
(space 6)
(println Stack) )
(println (car Stack)) ) )</lang>
Test (note that the top-of-stack is in the left-most position): <lang PicoLisp>: (rpnCalculator "3 4 2 * 1 5 - 2 3 \^ \^ / +") Token Stack 3 (3) 4 (4 3) 2 (2 4 3)
- (8 3)
1 (1 8 3) 5 (5 1 8 3) - (-4 8 3) 2 (2 -4 8 3) 3 (3 2 -4 8 3) ^ (8 -4 8 3) ^ (65536 8 3) / (0 3) + (3) 3 -> 3</lang>
Prolog
Works with SWI-Prolog. <lang Prolog>rpn(L) :- writeln('Token Action Stack'), parse(L, [],[X] ,[]), format('~nThe final output value is ~w~n', [X]).
% skip spaces parse([X|L], St) --> {char_type(X, white)}, parse(L, St).
% detect operators parse([Op|L], [Y, X | St]) --> { is_op(Op, X, Y, V), writef(' %s', Op), with_output_to(atom(Str2), writef('Apply %s on top of stack', Op)), writef(' %35l', [Str2]), writef('%w\n', St)}, parse(L, [V | St]).
% detect number parse([N|L], St) --> {char_type(N, digit)}, parse_number(L, [N], St).
% string is finished parse([], St) --> St.
% compute numbers parse_number([N|L], NC, St) --> {char_type(N, digit)}, parse_number(L, [N|NC], St).
parse_number(S, NC, St) --> { reverse(NC, RNC), number_chars(V, RNC), writef('%5r', [V]), with_output_to(atom(Str2), writef('Push num %w on top of stack', [V])), writef(' %35l', [Str2]), writef('%w\n', St)}, parse(S, [V|St]).
% defining operations is_op(42, X, Y, V) :- V is X*Y. is_op(43, X, Y, V) :- V is X+Y. is_op(45, X, Y, V) :- V is X-Y. is_op(47, X, Y, V) :- V is X/Y. is_op(94, X, Y, V) :- V is X**Y.</lang> Output :
5 ?- rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +").
Token Action Stack
3 'Push num 3 on top of stack' [3]
4 'Push num 4 on top of stack' [4,3]
2 'Push num 2 on top of stack' [2,4,3]
* 'Apply * on top of stack' [8,3]
1 'Push num 1 on top of stack' [1,8,3]
5 'Push num 5 on top of stack' [5,1,8,3]
- 'Apply - on top of stack' [-4,8,3]
2 'Push num 2 on top of stack' [2,-4,8,3]
3 'Push num 3 on top of stack' [3,2,-4,8,3]
^ 'Apply ^ on top of stack' [8,-4,8,3]
^ 'Apply ^ on top of stack' [65536,8,3]
/ 'Apply / on top of stack' [0.0001220703125,3]
+ 'Apply + on top of stack' [3.0001220703125]
The final output value is 3.0001220703125
true .
Python
<lang python>def op_pow(stack):
b = stack.pop(); a = stack.pop() stack.append( a ** b )
def op_mul(stack):
b = stack.pop(); a = stack.pop() stack.append( a * b )
def op_div(stack):
b = stack.pop(); a = stack.pop() stack.append( a / b )
def op_add(stack):
b = stack.pop(); a = stack.pop() stack.append( a + b )
def op_sub(stack):
b = stack.pop(); a = stack.pop() stack.append( a - b )
def op_num(stack, num):
stack.append( num )
ops = {
'^': op_pow, '*': op_mul, '/': op_div, '+': op_add, '-': op_sub, }
def get_input(inp = None):
'Inputs an expression and returns list of tokens'
if inp is None:
inp = input('expression: ')
tokens = inp.strip().split()
return tokens
def rpn_calc(tokens):
stack = []
table = ['TOKEN,ACTION,STACK'.split(',')]
for token in tokens:
if token in ops:
action = 'Apply op to top of stack'
ops[token](stack)
table.append( (token, action, ' '.join(str(s) for s in stack)) )
else:
action = 'Push num onto top of stack'
op_num(stack, eval(token))
table.append( (token, action, ' '.join(str(s) for s in stack)) )
return table
if __name__ == '__main__':
rpn = '3 4 2 * 1 5 - 2 3 ^ ^ / +'
print( 'For RPN expression: %r\n' % rpn )
rp = rpn_calc(get_input(rpn))
maxcolwidths = [max(len(y) for y in x) for x in zip(*rp)]
row = rp[0]
print( ' '.join('{cell:^{width}}'.format(width=width, cell=cell) for (width, cell) in zip(maxcolwidths, row)))
for row in rp[1:]:
print( ' '.join('{cell:<{width}}'.format(width=width, cell=cell) for (width, cell) in zip(maxcolwidths, row)))
print('\n The final output value is: %r' % rp[-1][2])</lang>
- Output
For RPN expression: '3 4 2 * 1 5 - 2 3 ^ ^ / +' TOKEN ACTION STACK 3 Push num onto top of stack 3 4 Push num onto top of stack 3 4 2 Push num onto top of stack 3 4 2 * Apply op to top of stack 3 8 1 Push num onto top of stack 3 8 1 5 Push num onto top of stack 3 8 1 5 - Apply op to top of stack 3 8 -4 2 Push num onto top of stack 3 8 -4 2 3 Push num onto top of stack 3 8 -4 2 3 ^ Apply op to top of stack 3 8 -4 8 ^ Apply op to top of stack 3 8 65536 / Apply op to top of stack 3 0.0001220703125 + Apply op to top of stack 3.0001220703125 The final output value is: '3.0001220703125'
Ruby
See Parsing/RPN/Ruby <lang ruby>rpn = RPNExpression("3 4 2 * 1 5 - 2 3 ^ ^ / +") value = rpn.eval</lang> outputs
for RPN expression: 3 4 2 * 1 5 - 2 3 ^ ^ / + Term Action Stack 3 PUSH [3] 4 PUSH [3, 4] 2 PUSH [3, 4, 2] * MUL [3, 8] 1 PUSH [3, 8, 1] 5 PUSH [3, 8, 1, 5] - SUB [3, 8, -4] 2 PUSH [3, 8, -4, 2] 3 PUSH [3, 8, -4, 2, 3] ^ EXP [3, 8, -4, 8] ^ EXP [3, 8, 65536] / DIV [3, 0.0001220703125] + ADD [3.0001220703125] Value = 3.0001220703125
Run BASIC
<lang runbasic>prn$ = "3 4 2 * 1 5 - 2 3 ^ ^ / + "
j = 0 while word$(prn$,i + 1," ") <> "" i = i + 1
n$ = word$(prn$,i," ") if n$ < "0" or n$ > "9" then num1 = val(word$(stack$,s," ")) num2 = val(word$(stack$,s-1," ")) n = op(n$,num2,num1) s = s - 1 stack$ = stk$(stack$,s -1,str$(n)) print "Push Opr ";n$;" to stack: ";stack$ else s = s + 1 stack$ = stack$ + n$ + " " print "Push Num ";n$;" to stack: ";stack$
end if wend
function stk$(stack$,s,a$) for i = 1 to s
stk$ = stk$ + word$(stack$,i," ") + " "
next i stk$ = stk$ + a$ + " " end function
FUNCTION op(op$,a,b) if op$ = "*" then op = a * b if op$ = "/" then op = a / b if op$ = "^" then op = a ^ b if op$ = "+" then op = a + b if op$ = "-" then op = a - b end function</lang>
Push Num 3 to stack: 3 Push Num 4 to stack: 3 4 Push Num 2 to stack: 3 4 2 Push Opr * to stack: 3 8 Push Num 1 to stack: 3 8 1 Push Num 5 to stack: 3 8 1 5 Push Opr - to stack: 3 8 -4 Push Num 2 to stack: 3 8 -4 2 Push Num 3 to stack: 3 8 -4 2 3 Push Opr ^ to stack: 3 8 -4 8 Push Opr ^ to stack: 3 8 65536 Push Opr / to stack: 3 1.22070312e-4 Push Opr + to stack: 3.00012207
Tcl
<lang tcl># Helper proc pop stk {
upvar 1 $stk s set val [lindex $s end] set s [lreplace $s end end] return $val
}
proc evaluate rpn {
set stack {}
foreach token $rpn {
set act "apply" switch $token { "^" { # Non-commutative operation set a [pop stack] lappend stack [expr {[pop stack] ** $a}] } "/" { # Non-commutative, special float handling set a [pop stack] set b [expr {[pop stack] / double($a)}] if {$b == round($b)} {set b [expr {round($b)}]} lappend stack $b } "*" { # Commutative operation lappend stack [expr {[pop stack] * [pop stack]}] } "-" { # Non-commutative operation set a [pop stack] lappend stack [expr {[pop stack] - $a}] } "+" { # Commutative operation lappend stack [expr {[pop stack] + [pop stack]}] } default { set act "push" lappend stack $token } } puts "$token\t$act\t$stack"
} return [lindex $stack end]
}
puts [evaluate {3 4 2 * 1 5 - 2 3 ^ ^ / +}]</lang> Output:
3 push 3 4 push 3 4 2 push 3 4 2 * apply 3 8 1 push 3 8 1 5 push 3 8 1 5 - apply 3 8 -4 2 push 3 8 -4 2 3 push 3 8 -4 2 3 ^ apply 3 8 -4 8 ^ apply 3 8 65536 / apply 3 0.0001220703125 + apply 3.0001220703125 3.0001220703125