Reverse Polish notation

Question

You must evaluate a string written in Reverse Polish notation and output the result.

The program must accept an input and return the output. For programming languages that do not have functions to receive input/output, you can assume functions like readLine/print.

You are not allowed to use any kind of "eval" in the program.

Numbers and operators are separated by one or more spaces.

You must support at least the +, -, * and / operators.

You need to add support to negative numbers (for example, -4 is not the same thing as 0 4 -) and floating point numbers.

You can assume the input is valid and follows the rules above

Test Cases

Input:

-4 5 +

Output:

1

---

Input:

5 2 /

Output:

2.5

---

Input:

5 2.5 /

Output:

2

---

Input:

5 1 2 + 4 * 3 - +

Output:

14

---

Input:

4 2 5 * + 1 3 2 * + /

Output:

2

Answer 1

Ruby - 95 77 characters

a=[]
gets.split.each{|b|a<<(b=~/\d/?b.to_f: (j,k=a.pop 2;j.send b,k))}
p a[0]

Takes input on stdin.

Testing code

[
  "-4 5 +",
  "5 2 /",
  "5 2.5 /",
  "5 1 2 + 4 * 3 - +",
  "4 2 5 * + 1 3 2 * + /",
  "12 8 3 * 6 / - 2 + -20.5 "
].each do |test|
  puts "[#{test}] gives #{`echo '#{test}' | ruby golf-polish.rb`}"
end

gives

[-4 5 +] gives 1.0
[5 2 /] gives 2.5
[5 2.5 /] gives 2.0
[5 1 2 + 4 * 3 - +] gives 14.0
[4 2 5 * + 1 3 2 * + /] gives 2.0
[12 8 3 * 6 / - 2 + -20.5 ] gives 10.0

Unlike the C version this returns the last valid result if there are extra numbers appended to the input it seems.

Answer 2

Python - 124 chars

s=[1,1]
for i in raw_input().split():b,a=map(float,s[:2]);s[:2]=[[a+b],[a-b],[a*b],[a/b],[i,b,a]]["+-*/".find(i)]
print s[0]

Python - 133 chars

s=[1,1]
for i in raw_input().split():b,a=map(float,s[:2]);s={'+':[a+b],'-':[a-b],'*':[a*b],'/':[a/b]}.get(i,[i,b,a])+s[2:]
print s[0]

Answer 3

Scheme, 162 chars

(Line breaks added for clarity—all are optional.)

(let l((s'()))(let((t(read)))(cond((number? t)(l`(,t,@s)))((assq t
`((+,+)(-,-)(*,*)(/,/)))=>(lambda(a)(l`(,((cadr a)(cadr s)(car s))
,@(cddr s)))))(else(car s)))))

Fully-formatted (ungolfed) version:

(let loop ((stack '()))
  (let ((token (read)))
    (cond ((number? token) (loop `(,token ,@stack)))
          ((assq token `((+ ,+) (- ,-) (* ,*) (/ ,/)))
           => (lambda (ass) (loop `(,((cadr ass) (cadr stack) (car stack))
                                    ,@(cddr stack)))))
          (else (car stack)))))

---

Selected commentary

`(,foo ,@bar) is the same as (cons foo bar) (i.e., it (effectively^†) returns a new list with foo prepended to bar), except it's one character shorter if you compress all the spaces out.

Thus, you can read the iteration clauses as (loop (cons token stack)) and (loop (cons ((cadr ass) (cadr stack) (car stack)) (cddr stack))) if that's easier on your eyes.

`((+ ,+) (- ,-) (* ,*) (/ ,/)) creates an association list with the symbol + paired with the procedure +, and likewise with the other operators. Thus it's a simple symbol lookup table (bare words are (read) in as symbols, which is why no further processing on token is necessary). Association lists have O(n) lookup, and thus are only suitable for short lists, as is the case here. :-P

† This is not technically accurate, but, for non-Lisp programmers, it gets a right-enough idea across.

Answer 4

c -- 424 necessary character

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define O(X) g=o();g=o() X g;u(g);break;
char*p=NULL,*b;size_t a,n=0;float g,s[99];float o(){return s[--n];};
void u(float v){s[n++]=v;};int main(){getdelim(&p,&a,EOF,stdin);for(;;){
b=strsep(&p," \n\t");if(3>p-b){if(*b>='0'&&*b<='9')goto n;switch(*b){case 0:
case EOF:printf("%f\n",o());return 0;case'+':O(+)case'-':O(-)case'*':O(*)
case'/':O(/)}}else n:u(atof(b));}}

Assumes that you have a new enough libc to include getdelim in stdio.h. The approach is straight ahead, the whole input is read into a buffer, then we tokenize with strsep and use length and initial character to determine the class of each. There is no protection against bad input. Feed it "+ - * / + - ...", and it will happily pop stuff off the memory "below" the stack until it seg faults. All non-operators are interpreted as floats by atof which means zero value if they don't look like numbers.

Readable and commented:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

char *p=NULL,*b;
size_t a,n=0;
float g,s[99];
float o(){        /* pOp */
  //printf("\tpoping '%f'\n",s[n-1]);
  return s[--n];
};
void u(float v){  /* pUsh */
  //printf("\tpushing '%f'\n",v);
  s[n++]=v;
};
int main(){
  getdelim(&p,&a,EOF,stdin); /* get all the input */
  for(;;){
    b=strsep(&p," \n\t"); /* now *b though *(p-1) is a token and p
                 points at the rest of the input */
    if(3>p-b){
      if (*b>='0'&&*b<='9') goto n;
      //printf("Got 1 char token '%c'\n",*b);
      switch (*b) {
      case 0:
      case EOF: printf("%f\n",o()); return 0;
      case '+': g=o(); g=o()+g; u(g); break;
      case '-': g=o(); g=o()-g; u(g); break;
      case '*': g=o(); g=o()*g; u(g); break;
      case '/': g=o(); g=o()/g; u(g); break;
    /* all other cases viciously ignored */
      } 
    } else { n:
      //printf("Got token '%s' (%f)\n",b,atof(b));
      u(atof(b));
    }
  }
}

Validation:

 $ gcc -c99 rpn_golf.c 
 $ wc rpn_golf.c
  9  34 433 rpn_golf.c
 $ echo -4 5 + | ./a.out
1.000000
 $ echo 5 2 / | ./a.out
2.500000
 $ echo 5 2.5 / | ./a.out
2.000000

Heh! Gotta quote anything with * in it...

 $ echo "5 1 2 + 4 * 3 - +" | ./a.out
14.000000
 $ echo "4 2 5 * + 1 3 2 * + /" | ./a.out
2.000000

and my own test case

 $ echo "12 8 3 * 6 / - 2 + -20.5 " | ./a.out
-20.500000

Answer 5

Haskell (155)

f#(a:b:c)=b`f`a:c
(s:_)![]=print s
s!("+":v)=(+)#s!v
s!("-":v)=(-)#s!v
s!("*":v)=(*)#s!v
s!("/":v)=(/)#s!v
s!(n:v)=(read n:s)!v
main=getLine>>=([]!).words

Answer 6

Perl (134)

@a=split/\s/,<>;/\d/?push@s,$_:($x=pop@s,$y=pop@s,push@s,('+'eq$_?$x+$y:'-'eq$_?$y-$x:'*'eq$_?$x*$y:'/'eq$_?$y/$x:0))for@a;print pop@s

Next time, I'm going to use the recursive regexp thing.

Ungolfed:

@a = split /\s/, <>;
for (@a) {
    /\d/
  ? (push @s, $_)
  : ( $x = pop @s,
      $y = pop @s,
      push @s , ( '+' eq $_ ? $x + $y
                : '-' eq $_ ? $y - $x
                : '*' eq $_ ? $x * $y
                : '/' eq $_ ? $y / $x
                : 0 )
      )
}
print(pop @s);

I though F# is my only dream programming language...

Answer 7

Windows PowerShell, 152 181 192

In readable form, because by now it's only two lines with no chance of breaking them up:

$s=@()
switch -r(-split$input){
  '\+'        {$s[1]+=$s[0]}
  '-'         {$s[1]-=$s[0]}
  '\*'        {$s[1]*=$s[0]}
  '/'         {$s[1]/=$s[0]}
  '-?[\d.]+'  {$s=0,+$_+$s}
  '.'         {$s=$s[1..($s.count)]}}
$s

2010-01-30 11:07 (192) – First attempt.

2010-01-30 11:09 (170) – Turning the function into a scriptblock solves the scope issues. Just makes each invocation two bytes longer.

2010-01-30 11:19 (188) – Didn't solve the scope issue, the test case just masked it. Removed the index from the final output and removed a superfluous line break, though. And changed double to float.

2010-01-30 11:19 (181) – Can't even remember my own advice. Casting to a numeric type can be done in a single char.

2010-01-30 11:39 (152) – Greatly reduced by using regex matching in the switch. Completely solves the previous scope issues with accessing the stack to pop it.

Answer 8

MATLAB – 158, 147

C=strsplit(input('','s'));D=str2double(C);q=[];for i=1:numel(D),if isnan(D(i)),f=str2func(C{i});q=[f(q(2),q(1)) q(3:end)];else q=[D(i) q];end,end,q

(input is read from user input, output printed out).

---

Below is the code prettified and commented, it pretty much implements the postfix algorithm described (with the assumption that expressions are valid):

C = strsplit(input('','s'));         % prompt user for input and split string by spaces
D = str2double(C);                   % convert to numbers, non-numeric are set to NaN
q = [];                              % initialize stack (array)
for i=1:numel(D)                     % for each value
    if isnan(D(i))                   % if it is an operator
        f = str2func(C{i});          % convert op to a function
        q = [f(q(2),q(1)) q(3:end)]; % pop top two values, apply op and push result
    else
        q = [D(i) q];                % else push value on stack
    end
end
q                                    % show result

---

Bonus:

In the code above, we assume operators are always binary (+, -, *, /). We can generalize it by using nargin(f) to determine the number of arguments the operand/function requires, and pop the right amount of values from the stack accordingly, as in:

f = str2func(C{i});
n = nargin(f);
args = num2cell(q(n:-1:1));
q = [f(args{:}) q(n+1:end)];

That way we can evaluate expressions like:

str = '6 5 1 2 mean_of_three 1 + 4 * +'

where mean_of_three is a user-defined function with three inputs:

function d = mean_of_three(a,b,c)
    d = (a+b+c)/3;
end

Answer 9

Racket 131:

(let l((s 0))(define t(read))(cond[(real? t)
(l`(,t,@s))][(memq t'(+ - * /))(l`(,((eval t)(cadr s)
(car s)),@(cddr s)))][0(car s)]))

Line breaks optional.

Based on Chris Jester-Young's solution for Scheme.

Answer 10

Python, 166 characters

import os,operator as o
S=[]
for i in os.read(0,99).split():
 try:S=[float(i)]+S
 except:S=[{'+':o.add,'-':o.sub,'/':o.div,'*':o.mul}[i](S[1],S[0])]+S[2:]
print S[0]

Answer 11

Python 3, 119 bytes

s=[]
for x in input().split():
 try:s+=float(x),
 except:o='-*+'.find(x);*s,a,b=s;s+=(a+b*~-o,a*b**o)[o%2],
print(s[0])

Input: 5 1 1 - -7 0 * + - 2 /

Output: 2.5

(You can find a 128-character Python 2 version in the edit history.)

Answer 12

JavaScript (157)

This code assumes there are these two functions: readLine and print

a=readLine().split(/ +/g);s=[];for(i in a){v=a[i];if(isNaN(+v)){f=s.pop();p=s.pop();s.push([p+f,p-f,p*f,p/f]['+-*/'.indexOf(v)])}else{s.push(+v)}}print(s[0])

Answer 13

Perl, 128

This isn't really competitive next to the other Perl answer, but explores a different (suboptimal) path.

perl -plE '@_=split" ";$_=$_[$i],/\d||
do{($a,$b)=splice@_,$i-=2,2;$_[$i--]=
"+"eq$_?$a+$b:"-"eq$_?$a-$b:"*"eq$_?
$a*$b:$a/$b;}while++$i<@_'

Characters counted as diff to a simple perl -e '' invocation.

Answer 14

Python, 161 characters:

from operator import*;s=[];i=raw_input().split(' ')
q="*+-/";o=[mul,add,0,sub,0,div]
for c in i:
 if c in q:s=[o[ord(c)-42](*s[1::-1])]+s 
 else:s=[float(c)]+s
print(s[0])

Answer 15

PHP, 439 265 263 262 244 240 characters

<? $c=fgets(STDIN);$a=array_values(array_filter(explode(" ",$c)));$s[]=0;foreach($a as$b){if(floatval($b)){$s[]=$b;continue;}$d=array_pop($s);$e=array_pop($s);$s[]=$b=="+"?$e+$d:($b=="-"?$e-$d:($b=="*"?$e*$d:($b=="/"?$e/$d:"")));}echo$s[1];

This code should work with stdin, though it is not tested with stdin.

It has been tested on all of the cases, the output (and code) for the last one is here:
http://codepad.viper-7.com/fGbnv6

Ungolfed, 314 330 326 characters

<?php
$c = fgets(STDIN);
$a = array_values(array_filter(explode(" ", $c)));
$s[] = 0;
foreach($a as $b){
    if(floatval($b)){
        $s[] = $b;
        continue;
    }
    $d = array_pop($s);
    $e = array_pop($s);
    $s[] = $b == "+" ? $e + $d : ($b == "-" ? $e - $d : ($b == "*" ? $e * $d : ($b == "/" ? $e / $d :"")));
}
echo $s[1];

Answer 16

flex - 157

%{
float b[100],*s=b;
#define O(o) s--;*(s-1)=*(s-1)o*s;
%}
%%
-?[0-9.]+ *s++=strtof(yytext,0);
\+ O(+)
- O(-)
\* O(*)
\/ O(/)
\n printf("%g\n",*--s);
.
%%

If you aren't familiar, compile with flex rpn.l && gcc -lfl lex.yy.c

Answer 17

Python, 130 characters

Would be 124 characters if we dropped b and (which some of the Python answers are missing). And it incorporates 42!

s=[]
for x in raw_input().split():
 try:s=[float(x)]+s
 except:b,a=s[:2];s[:2]=[[a*b,a+b,0,a-b,0,b and a/b][ord(x)-42]]
print s[0]

Answer 18

Python 3, 126 132 chars

s=[2,2]
for c in input().split():
    a,b=s[:2]
    try:s[:2]=[[a+b,b-a,a*b,a and b/a]["+-*/".index(c)]]
    except:s=[float(c)]+s
print(s[0])

There have been better solutions already, but now that I had written it (without having read the prior submissions, of course - even though I have to admit that my code looks as if I had copypasted them together), I wanted to share it, too.

Answer 19

c99 gcc 235

This works for me (with warnings):

#include <stdlib.h>
#define O(x):--d;s[d]=s[d]x s[d+1];break;
float s[99];main(c,v)char**v;{for(int i=1,d=0;i<c;i++)switch(!v[i][1]?*v[i]:' '){case'+'O(+)case'-'O(-)case'*'O(*)case'/'O(/)default:s[++d]=atof(v[i]);}printf("%f\n",s[1]);}

But if you are compiling it with mingw32 you need to turn off globbing (see https://www.cygwin.com/ml/cygwin/1999-11/msg00052.html) by compiling like this:

gcc -std=c99 x.c C:\Applications\mingw32\i686-w64-mingw32\lib\CRT_noglob.o

If you don't * is automatically expanded by the mingw32 CRT.

Does anybody know how to turn break;case'*':s[--d]*=s[d+1]; into a macro that accepts the character + as a parameter because then all four cases would just be O(+)O(-)O(*)O(/)

H:\Desktop>gcc -std=c99 x.c C:\Applications\mingw32\i686-w64-mingw32\lib\CRT_noglob.o
x.c:3:13: warning: return type defaults to 'int'
 float s[99];main(c,v)char**v;{for(int i=1,d=0;i<c;i++)switch(!v[i][1]?*v[i]:' '){case'+'O(+)case'-'O(-)case'*'O(*)case'/'O(/)default:s[++d]=atof(v[i]);}printf("%f\n",s[1]);}
x.c: In function 'main':
x.c:3:13: warning: type of 'c' defaults to 'int'
x.c:3:1: warning: implicit declaration of function 'atof' [-Wimplicit-function-declaration]
 float s[99];main(c,v)char**v;{for(int i=1,d=0;i<c;i++)switch(!v[i][1]?*v[i]:' '){case'+'O(+)case'-'O(-)case'*'O(*)case'/'O(/)default:s[++d]=atof(v[i]);}printf("%f\n",s[1]);}
x.c:3:1: warning: implicit declaration of function 'printf' [-Wimplicit-function-declaration]
x.c:3:153: warning: incompatible implicit declaration of built-in function 'printf'
 float s[99];main(c,v)char**v;{for(int i=1,d=0;i<c;i++)switch(!v[i][1]?*v[i]:' '){case'+'O(+)case'-'O(-)case'*'O(*)case'/'O(/)default:s[++d]=atof(v[i]);}printf("%f\n",s[1]);}
H:\Desktop>a -4 5 +
1.000000
H:\Desktop>a 5 2 /
2.500000
H:\Desktop>a 5 2.5 /
2.000000
H:\Desktop>a 5 1 2 + 4 * 3 - +
14.000000
H:\Desktop>a 4 2 5 * + 1 3 2 * + /
2.000000

Answer 20

C, 232 229 bytes

Fun with recursion.

#include <stdlib.h>
#define b *p>47|*(p+1)>47
char*p;float a(float m){float n=strtof(p,&p);b?n=a(n):0;for(;*++p==32;);m=*p%43?*p%45?*p%42?m/n:m*n:m-n:m+n;return*++p&&b?a(m):m;}main(c,v)char**v;{printf("%f\n",a(strtof(v[1],&p)));}

Ungolfed:

#include <stdlib.h>

/* Detect if next char in buffer is a number */
#define b *p > 47 | *(p+1) > 47

char*p; /* the buffer */

float a(float m)
{
    float n = strtof(p, &p); /* parse the next number */

    /* if the next thing is another number, recursively evaluate */
    b ? n = a(n) : 0;

    for(;*++p==32;); /* skip spaces */

    /* Perform the arithmetic operation */
    m = *p%'+' ? *p%'-' ? *p%'*' ? m/n : m*n : m-n : m+n;

    /* If there's more stuff, recursively parse that, otherwise return the current computed value */
    return *++p && b ? a(m) : m;
}

int main(int c, char **v)
{
    printf("%f\n", a(strtof(v[1], &p)));
}

Test Cases:

$ ./a.out "-4 5 +"
1.000000
$ ./a.out "5 2 /"
2.500000
$ ./a.out "5 2.5 /"
2.000000
$ ./a.out "5 1 2 + 4 * 3 - +"
14.000000
$ ./a.out "4 2 5 * + 1 3 2 * + /"
2.000000

Answer 21

JavaScript ES7, 119 bytes

I'm getting a bug with array comprehensions so I've used .map

(s,t=[])=>(s.split` `.map(i=>+i?t.unshift(+i):t.unshift((r=t.pop(),o=t.pop(),[r+o,r-o,r*o,r/o]['+-*/'.indexOf(i)]))),t)

Try it online at ESFiddle

Answer 22

PHP - 259 characters

$n=explode(" ",$_POST["i"]);$s=array();for($i=0;$i<count($n);$s=$d-->0?array_merge($s,!$p?array($b,$a,$c):array($p)):$s){if($c=$n[$i++]){$d=1;$a=array_pop($s);$b=array_pop($s);$p=$c=="+"?$b+$a:($c=="-"?$b-$a:($c=="*"?$b*$a:($c=="/"?$b/$a:false)));}}echo$s[2];

Assuming input in POST variable i.

Answer 23

C# - 392 characters

namespace System.Collections.Generic{class P{static void Main(){var i=Console.ReadLine().Split(' ');var k=new Stack<float>();float o;foreach(var s in i)switch (s){case "+":k.Push(k.Pop()+k.Pop());break;case "-":o=k.Pop();k.Push(k.Pop()-o);break;case "*":k.Push(k.Pop()*k.Pop());break;case "/":o=k.Pop();k.Push(k.Pop()/o);break;default:k.Push(float.Parse(s));break;}Console.Write(k.Pop());}}}

However, if arguments can be used instead of standard input, we can bring it down to

C# - 366 characters

namespace System.Collections.Generic{class P{static void Main(string[] i){var k=new Stack<float>();float o;foreach(var s in i)switch (s){case "+":k.Push(k.Pop()+k.Pop());break;case "-":o=k.Pop();k.Push(k.Pop()-o);break;case "*":k.Push(k.Pop()*k.Pop());break;case "/":o=k.Pop();k.Push(k.Pop()/o);break;default:k.Push(float.Parse(s));break;}Console.Write(k.Pop());}}}

Answer 24

Scala 412 376 349 335 312:

object P extends App{
def p(t:List[String],u:List[Double]):Double={
def a=u drop 2
t match{
case Nil=>u.head
case x::y=>x match{
case"+"=>p(y,u(1)+u(0)::a)
case"-"=>p(y,u(1)-u(0)::a)
case"*"=>p(y,u(1)*u(0)::a)
case"/"=>p(y,u(1)/u(0)::a)
case d=>p(y,d.toDouble::u)}}}
println(p((readLine()split " ").toList,Nil))}

Answer 25

Python - 206

import sys;i=sys.argv[1].split();s=[];a=s.append;b=s.pop
for t in i:
 if t=="+":a(b()+b())
 elif t=="-":m=b();a(b()-m)
 elif t=="*":a(b()*b())
 elif t=="/":m=b();a(b()/m)
 else:a(float(t))
print(b())

Ungolfed version:

# RPN

import sys

input = sys.argv[1].split()
stack = []

# Eval postfix notation
for tkn in input:
    if tkn == "+":
        stack.append(stack.pop() + stack.pop())
    elif tkn == "-":
        tmp = stack.pop()
        stack.append(stack.pop() - tmp)
    elif tkn == "*":
        stack.append(stack.pop() * stack.pop())
    elif tkn == "/":
        tmp = stack.pop()
        stack.append(stack.pop()/tmp)
    else:
        stack.append(float(tkn))

print(stack.pop())

Input from command-line argument; output on standard output.

Answer 26

ECMAScript 6 (131)

Just typed together in a few seconds, so it can probably be golfed further or maybe even approached better. I might revisit it tomorrow:

f=s=>(p=[],s.split(/\s+/).forEach(t=>+t==t?p.push(t):(b=+p.pop(),a=+p.pop(),p.push(t=='+'?a+b:t=='-'?a-b:t=='*'?a*b:a/b))),p.pop())

Answer 27

C# - 323 284 241

class P{static void Main(string[] i){int x=0;var a=new float[i.Length];foreach(var s in i){var o="+-*/".IndexOf(s);if(o>-1){float y=a[--x],z=a[--x];a[x++]=o>3?z/y:o>2?z*y:o>1?z-y:y+z;}else a[x++]=float.Parse(s);}System.Console.Write(a[0]);}}

Edit: Replacing the Stack with an Array is way shorter

Edit2: Replaced the ifs with a ternary expression

Answer 28

Python 2

I've tried out some different approaches to the ones published so far. None of these is quite as short as the best Python solutions, but they might still be interesting to some of you.

Using recursion, 146

def f(s):
 try:x=s.pop();r=float(x)
 except:b,s=f(s);a,s=f(s);r=[a+b,a-b,a*b,b and a/b]['+-*'.find(x)]
 return r,s
print f(raw_input().split())[0]

Using list manipulation, 149

s=raw_input().split()
i=0
while s[1:]:
 o='+-*/'.find(s[i])
 if~o:i-=2;a,b=map(float,s[i:i+2]);s[i:i+3]=[[a+b,a-b,a*b,b and a/b][o]]
 i+=1
print s[0]

Using reduce(), 145

print reduce(lambda s,x:x in'+-*/'and[(lambda b,a:[a+b,a-b,a*b,b and a/b])(*s[:2])['+-*'.find(x)]]+s[2:]or[float(x)]+s,raw_input().split(),[])[0]

Answer 29

Matlab, 228

F='+-/*';f={@plus,@minus,@rdivide,@times};t=strsplit(input('','s'),' ');i=str2double(t);j=~isnan(i);t(j)=num2cell(i(j));while numel(t)>1
n=find(cellfun(@(x)isstr(x),t),1);t{n}=bsxfun(f{t{n}==F},t{n-2:n-1});t(n-2:n-1)=[];end
t{1}

Ungolfed:

F = '+-/*'; %// possible operators
f = {@plus,@minus,@rdivide,@times}; %// to be used with bsxfun
t = strsplit(input('','s'),' '); %// input string and split by one or multiple spaces
i = str2double(t); %// convert each split string to number
j =~ isnan(i); %// these were operators, not numbers ...
t(j) = num2cell(i(j)); %// ... so restore them
while numel(t)>1
    n = find(cellfun(@(x)isstr(x),t),1); %// find left-most operator
    t{n} = bsxfun(f{t{n}==F}, t{n-2:n-1}); %// apply it to preceding numbers and replace
    t(n-2:n-1)=[]; %// remove used numbers
end
t{1} %// display result

Answer 30

K5, 70 bytes

`0:*{$[-9=@*x;((*(+;-;*;%)@"+-*/"?y).-2#x;x,.y)@47<y;(.x;.y)]}/" "\0:`

I'm not sure when K5 was released, so this might not count. Still awesome!