Parsing/Shunting-yard algorithm

From Rosetta Code
Task
Parsing/Shunting-yard algorithm
You are encouraged to solve this task according to the task description, using any language you may know.

Given the operator characteristics and input from the Shunting-yard algorithm page and tables Use the algorithm to show the changes in the operator stack and RPN output as each individual token is processed.

  • Assume an input of a correct, space separated, string of tokens representing an infix expression
  • Generate a space separated output string representing the RPN
  • Test with the input string '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3' then print and display the output here.
  • Operator precedence is given in this table:
operator precedence associativity
^ 4 Right
* 3 Left
/ 3 Left
+ 2 Left
- 2 Left
Extra credit
  • Add extra text explaining the actions and an optional comment for the action on receipt of each token.
Note
  • the handling of functions and arguments is not required.
See also



AutoHotkey[edit]

Works with: AutoHotkey_L
SetBatchLines -1
#NoEnv
 
expr := "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
 
output := "Testing string '" expr "'`r`n`r`nToken`tOutput Queue"
. Space(StrLen(expr)-StrLen("Output Queue")+2) "OP Stack"
 
; define a stack with semantic .push() and .pop() funcs
stack := {push: func("ObjInsert"), pop: func("ObjRemove"), peek: func("Peek")}
 
Loop Parse, expr, %A_Space%
{
token := A_LoopField
if token is number
Q .= token A_Space
if isOp(token){
o1 := token
while isOp(o2 := stack.peek())
and ((isLeft(o1) and Precedence(o1) <= Precedence(o2))
or (isRight(o1) and Precedence(o1) < Precedence(o2)))
Q .= stack.pop() A_Space
stack.push(o1)
}
If ( token = "(" )
stack.push(token)
If ( token = ")" )
{
While ((t := stack.pop()) != "(") && (t != "")
Q .= t A_Space
if (t = "")
throw Exception("Unmatched parenthesis. "
. "Character number " A_Index)
}
output .= "`r`n" token Space(7) Q Space(StrLen(expr)+2-StrLen(Q))
. Disp(stack)
}
output .= "`r`n(empty stack to output)"
While (t := stack.pop()) != ""
if InStr("()", t)
throw Exception("Unmatched parenthesis.")
else Q .= t A_Space, output .= "`r`n" Space(8) Q
. Space(StrLen(expr)+2-StrLen(Q)) Disp(stack)
output .= "`r`n`r`nFinal string: '" Q "'"
clipboard := output
 
isOp(t){
return (!!InStr("+-*/^", t) && t)
}
Peek(this){
r := this.Remove(), this.Insert(r)
return r
}
IsLeft(o){
return !!InStr("*/+-", o)
}
IsRight(o){
return o = "^"
}
Precedence(o){
return (InStr("+-/*^", o)+3)//2
}
Disp(obj){
for each, val in obj
o := val . o
return o
}
Space(n){
return n>0 ? A_Space Space(n-1) : ""
}
Output
Testing string '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3'

Token	Output Queue                   OP Stack
3       3                              
+       3                              +
4       3 4                            +
*       3 4                            *+
2       3 4 2                          *+
/       3 4 2 *                        /+
(       3 4 2 *                        (/+
1       3 4 2 * 1                      (/+
-       3 4 2 * 1                      -(/+
5       3 4 2 * 1 5                    -(/+
)       3 4 2 * 1 5 -                  /+
^       3 4 2 * 1 5 -                  ^/+
2       3 4 2 * 1 5 - 2                ^/+
^       3 4 2 * 1 5 - 2                ^^/+
3       3 4 2 * 1 5 - 2 3              ^^/+
(empty stack to output)
        3 4 2 * 1 5 - 2 3 ^            ^/+
        3 4 2 * 1 5 - 2 3 ^ ^          /+
        3 4 2 * 1 5 - 2 3 ^ ^ /        +
        3 4 2 * 1 5 - 2 3 ^ ^ / +      

Final string: '3 4 2 * 1 5 - 2 3 ^ ^ / + '

C[edit]

Requires a functioning ANSI terminal and Enter key.

#include <sys/types.h>
#include <regex.h>
#include <stdio.h>
 
typedef struct {
const char *s;
int len, prec, assoc;
} str_tok_t;
 
typedef struct {
const char * str;
int assoc, prec;
regex_t re;
} pat_t;
 
enum assoc { A_NONE, A_L, A_R };
pat_t pat_eos = {"", A_NONE, 0};
 
pat_t pat_ops[] = {
{"^\\)", A_NONE, -1},
{"^\\*\\*", A_R, 3},
{"^\\^", A_R, 3},
{"^\\*", A_L, 2},
{"^/", A_L, 2},
{"^\\+", A_L, 1},
{"^-", A_L, 1},
{0}
};
 
pat_t pat_arg[] = {
{"^[-+]?[0-9]*\\.?[0-9]+([eE][-+]?[0-9]+)?"},
{"^[a-zA-Z_][a-zA-Z_0-9]*"},
{"^\\(", A_L, -1},
{0}
};
 
str_tok_t stack[256]; /* assume these are big enough */
str_tok_t queue[256];
int l_queue, l_stack;
#define qpush(x) queue[l_queue++] = x
#define spush(x) stack[l_stack++] = x
#define spop() stack[--l_stack]
 
void display(const char *s)
{
int i;
printf("\033[1;1H\033[JText | %s", s);
printf("\nStack| ");
for (i = 0; i < l_stack; i++)
printf("%.*s ", stack[i].len, stack[i].s); // uses C99 format strings
printf("\nQueue| ");
for (i = 0; i < l_queue; i++)
printf("%.*s ", queue[i].len, queue[i].s);
puts("\n\n<press enter>");
getchar();
}
 
int prec_booster;
 
#define fail(s1, s2) {fprintf(stderr, "[Error %s] %s\n", s1, s2); return 0;}
 
int init(void)
{
int i;
pat_t *p;
 
for (i = 0, p = pat_ops; p[i].str; i++)
if (regcomp(&(p[i].re), p[i].str, REG_NEWLINE|REG_EXTENDED))
fail("comp", p[i].str);
 
for (i = 0, p = pat_arg; p[i].str; i++)
if (regcomp(&(p[i].re), p[i].str, REG_NEWLINE|REG_EXTENDED))
fail("comp", p[i].str);
 
return 1;
}
 
pat_t* match(const char *s, pat_t *p, str_tok_t * t, const char **e)
{
int i;
regmatch_t m;
 
while (*s == ' ') s++;
*e = s;
 
if (!*s) return &pat_eos;
 
for (i = 0; p[i].str; i++) {
if (regexec(&(p[i].re), s, 1, &m, REG_NOTEOL))
continue;
t->s = s;
*e = s + (t->len = m.rm_eo - m.rm_so);
return p + i;
}
return 0;
}
 
int parse(const char *s) {
pat_t *p;
str_tok_t *t, tok;
 
prec_booster = l_queue = 0;
display(s);
while (*s) {
p = match(s, pat_arg, &tok, &s);
if (!p || p == &pat_eos) fail("parse arg", s);
 
/* Odd logic here. Don't actually stack the parens: don't need to. */
if (p->prec == -1) {
prec_booster += 100;
continue;
}
qpush(tok);
display(s);
 
re_op: p = match(s, pat_ops, &tok, &s);
if (!p) fail("parse op", s);
 
tok.assoc = p->assoc;
tok.prec = p->prec;
 
if (p->prec > 0)
tok.prec = p->prec + prec_booster;
else if (p->prec == -1) {
if (prec_booster < 100)
fail("unmatched )", s);
tok.prec = prec_booster;
}
 
while (l_stack) {
t = stack + l_stack - 1;
if (!(t->prec == tok.prec && t->assoc == A_L)
&& t->prec <= tok.prec)
break;
qpush(spop());
display(s);
}
 
if (p->prec == -1) {
prec_booster -= 100;
goto re_op;
}
 
if (!p->prec) {
display(s);
if (prec_booster)
fail("unmatched (", s);
return 1;
}
 
spush(tok);
display(s);
}
 
return 1;
}
 
int main()
{
int i;
const char *tests[] = {
"3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3", /* RC mandated: OK */
"123", /* OK */
"3+4 * 2 / ( 1 - 5 ) ^ 2 ^ 3.14", /* OK */
"(((((((1+2+3**(4 + 5))))))", /* bad parens */
"a^(b + c/d * .1e5)!", /* unknown op */
"(1**2)**3", /* OK */
0
};
 
if (!init()) return 1;
for (i = 0; tests[i]; i++) {
printf("Testing string `%s' <enter>\n", tests[i]);
getchar();
 
printf("string `%s': %s\n\n", tests[i],
parse(tests[i]) ? "Ok" : "Error");
}
 
return 0;
}
Output

Note: This cannot give a flavour of the true interactive output where tokens are shuffled around every time the enter key is pressed.

Testing string `3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3'   <enter>

Text | 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
Stack| 
Queue| 

<press enter>

Text |  + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
Stack| 
Queue| 3 

<press enter>

Text |  4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
Stack| + 
Queue| 3 

<press enter>

Text |  * 2 / ( 1 - 5 ) ^ 2 ^ 3
Stack| + 
Queue| 3 4 

<press enter>

Text |  2 / ( 1 - 5 ) ^ 2 ^ 3
Stack| + * 
Queue| 3 4 

<press enter>

Text |  / ( 1 - 5 ) ^ 2 ^ 3
Stack| + * 
Queue| 3 4 2 

<press enter>

Text |  ( 1 - 5 ) ^ 2 ^ 3
Stack| + 
Queue| 3 4 2 * 

<press enter>

Text |  ( 1 - 5 ) ^ 2 ^ 3
Stack| + / 
Queue| 3 4 2 * 

<press enter>

Text |  - 5 ) ^ 2 ^ 3
Stack| + / 
Queue| 3 4 2 * 1 

<press enter>

Text |  5 ) ^ 2 ^ 3
Stack| + / - 
Queue| 3 4 2 * 1 

<press enter>

Text |  ) ^ 2 ^ 3
Stack| + / - 
Queue| 3 4 2 * 1 5 

<press enter>

Text |  ^ 2 ^ 3
Stack| + / 
Queue| 3 4 2 * 1 5 - 

<press enter>

Text |  2 ^ 3
Stack| + / ^ 
Queue| 3 4 2 * 1 5 - 

<press enter>

Text |  ^ 3
Stack| + / ^ 
Queue| 3 4 2 * 1 5 - 2 

<press enter>

Text |  3
Stack| + / ^ ^ 
Queue| 3 4 2 * 1 5 - 2 

<press enter>

Text | 
Stack| + / ^ ^ 
Queue| 3 4 2 * 1 5 - 2 3 

<press enter>

Text | 
Stack| + / ^ 
Queue| 3 4 2 * 1 5 - 2 3 ^ 

<press enter>

Text | 
Stack| + / 
Queue| 3 4 2 * 1 5 - 2 3 ^ ^ 

<press enter>

Text | 
Stack| + 
Queue| 3 4 2 * 1 5 - 2 3 ^ ^ / 

<press enter>

Text | 
Stack| 
Queue| 3 4 2 * 1 5 - 2 3 ^ ^ / + 

<press enter>

Text | 
Stack| 
Queue| 3 4 2 * 1 5 - 2 3 ^ ^ / + 

<press enter>

string `3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3': Ok

Testing string `123'   <enter>
^C

Ceylon[edit]

import ceylon.collection {
 
ArrayList
}
 
abstract class Token(String|Integer data) of IntegerLiteral | Operator | leftParen | rightParen {
string => data.string;
}
class IntegerLiteral(shared Integer integer) extends Token(integer) {}
class Operator extends Token {
 
shared Integer precedence;
shared Boolean rightAssoc;
 
shared new plus extends Token("+") {
precedence = 2;
rightAssoc = false;
}
shared new minus extends Token("-") {
precedence = 2;
rightAssoc = false;
}
shared new times extends Token("*") {
precedence = 3;
rightAssoc = false;
}
shared new divides extends Token("/") {
precedence = 3;
rightAssoc = false;
}
shared new power extends Token("^") {
precedence = 4;
rightAssoc = true;
}
 
shared Boolean below(Operator other) =>
!rightAssoc && precedence <= other.precedence || rightAssoc && precedence < other.precedence;
}
object leftParen extends Token("(") {}
object rightParen extends Token(")") {}
 
 
shared void run() {
 
function shunt(String input) {
 
function tokenize(String input) =>
input.split().map((String element) =>
switch(element.trimmed)
case("(") leftParen
case(")") rightParen
case("+") Operator.plus
case("-") Operator.minus
case("*") Operator.times
case("/") Operator.divides
case("^") Operator.power
else IntegerLiteral(parseInteger(element) else 0)); // no error handling
 
value outputQueue = ArrayList<Token>();
value operatorStack = ArrayList<Token>();
 
void report(String action) {
print("``action.padTrailing(22)`` | ``" ".join(outputQueue).padTrailing(25)`` | ``" ".join(operatorStack).padTrailing(10)``");
}
 
print("input is ``input``\n");
print("Action | Output Queue | Operators' Stack
-----------------------|---------------------------|-----------------");
 
for(token in tokenize(input)) {
switch(token)
case(is IntegerLiteral) {
outputQueue.offer(token);
report("``token`` from input to queue");
}
case(leftParen) {
operatorStack.push(token);
report("``token`` from input to stack");
}
case(rightParen){
while(exists top = operatorStack.pop(), top != leftParen) {
outputQueue.offer(top);
report("``top`` from stack to queue");
}
}
case(is Operator) {
while(exists top = operatorStack.top, is Operator top, token.below(top)) {
operatorStack.pop();
outputQueue.offer(top);
report("``top`` from stack to queue");
}
operatorStack.push(token);
report("``token`` from input to stack");
}
}
while(exists top = operatorStack.pop()) {
outputQueue.offer(top);
report("``top`` from stack to queue");
}
return " ".join(outputQueue);
}
 
value rpn = shunt("3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3");
assert(rpn == "3 4 2 * 1 5 - 2 3 ^ ^ / +");
print("\nthe result is ``rpn``");
}
Output:
input is 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3

Action                 | Output Queue              | Operators' Stack
-----------------------|---------------------------|-----------------
3 from input to queue  | 3                         |           
+ from input to stack  | 3                         | +         
4 from input to queue  | 3 4                       | +         
* from input to stack  | 3 4                       | + *       
2 from input to queue  | 3 4 2                     | + *       
* from stack to queue  | 3 4 2 *                   | +         
/ from input to stack  | 3 4 2 *                   | + /       
( from input to stack  | 3 4 2 *                   | + / (     
1 from input to queue  | 3 4 2 * 1                 | + / (     
- from input to stack  | 3 4 2 * 1                 | + / ( -   
5 from input to queue  | 3 4 2 * 1 5               | + / ( -   
- from stack to queue  | 3 4 2 * 1 5 -             | + / (     
^ from input to stack  | 3 4 2 * 1 5 -             | + / ^     
2 from input to queue  | 3 4 2 * 1 5 - 2           | + / ^     
^ from input to stack  | 3 4 2 * 1 5 - 2           | + / ^ ^   
3 from input to queue  | 3 4 2 * 1 5 - 2 3         | + / ^ ^   
^ from stack to queue  | 3 4 2 * 1 5 - 2 3 ^       | + / ^     
^ from stack to queue  | 3 4 2 * 1 5 - 2 3 ^ ^     | + /       
/ from stack to queue  | 3 4 2 * 1 5 - 2 3 ^ ^ /   | +         
+ from stack to queue  | 3 4 2 * 1 5 - 2 3 ^ ^ / + |           

the result is 3 4 2 * 1 5 - 2 3 ^ ^ / +

Common Lisp[edit]

Implemented as a state machine. The current state is the top of both the input queue and the operator stack. A signal function receives the current state and does a lookup to determine the signal to output. Based on the signal, the state (input queue and/or operator stack) is changed. The process iterates until both queue and stack are empty.

;;;; Parsing/infix to RPN conversion
(defconstant operators "^*/+-")
(defconstant precedence '(-4 3 3 2 2))
 
(defun operator-p (op)
"string->integer|nil: Returns operator precedence index or nil if not operator."
(and (= (length op) 1) (position (char op 0) operators)))
 
(defun has-priority (op2 op1)
"(string,string)->boolean: True if op2 has output priority over op1."
(defun prec (op) (nth (operator-p op) precedence))
(or (and (plusp (prec op1)) (<= (prec op1) (abs (prec op2))))
(and (minusp (prec op1)) (< (- (prec op1)) (abs (prec op2))))))
 
(defun string-split (expr)
"string->list: Tokenize a space separated string."
(let* ((p (position #\Space expr))
(tok (if p (subseq expr 0 p) expr)))
(if p (append (list tok) (string-split (subseq expr (1+ p)))) (list tok))))
 
(defun classify (tok)
"nil|string->symbol: Classify a token."
(cond
((null tok) 'NOL)
((operator-p tok) 'OPR)
((string= tok "(") 'LPR)
((string= tok ")") 'RPR)
(t 'LIT)))
 
;;; transitions when op2 is dont care
(defconstant trans1D '((LIT GO) (LPR ENTER)))
;;; transitions when we check op2 also
(defconstant trans2D
'((OPR ((NOL ENTER)
(LPR ENTER)
(OPR (lambda (op1 op2) (if (has-priority op2 op1) 'LEAVE 'ENTER)))))
(RPR ((NOL "mismatched parentheses")
(LPR CLEAR)
(OPR LEAVE)))
(NOL ((NOL nil)
(LPR "mismatched parentheses")
(OPR LEAVE)))))
 
(defun do-signal (op1 op2)
"(nil|string,nil|string)->symbol|string|nil: Emit a signal based on state of inputq and opstack.
A nil return is a successful lookup (on nil,nil) because all input combinations are specified."

(let ((sig (or (cadr (assoc (classify op1) trans1D))
(cadr (assoc (classify op2) (cadr (assoc (classify op1) trans2D)))))))
(if (or (null sig) (symbolp sig) (stringp sig)) sig
(funcall (coerce sig 'function) op1 op2))))
 
(defun rpn (expr)
"string->string: Parse infix expression into rpn."
(format t "TOKEN TOS SIGNAL OPSTACK OUTPUTQ~%")
 
;; iterate until both stacks empty
(do* ((input (string-split expr)) (opstack nil) (outputq "")
(sig (do-signal (first input) (first opstack)) (do-signal (first input) (first opstack))))
((null sig) ; until
;; print last closing frame
(format t "~A~7,T~A~14,T~A~25,T~A~38,T~A~%" nil nil nil opstack outputq)
(subseq outputq 1)) ; return final infix expression
 
;; print opening frame
(format t "~A~7,T~A~14,T" (first input) (first opstack))
(format t (if (stringp sig) "\"~A\"" "~A") sig)
 
;; switch state
(let ((output (case sig
(GO (pop input))
(ENTER (push (pop input) opstack) nil)
(LEAVE (pop opstack))
(CLEAR (pop input) (pop opstack) nil)
(otherwise (pop input) (pop opstack)
(if (stringp sig) sig "unknown signal")))))
(when output (setf outputq (concatenate 'string outputq " " output))))
 
;; print closing frame
(format t "~25,T~A~38,T~A~%" opstack outputq))) ; end-do
 
(defun main (&optional (xtra nil))
"nil->[printed rpn expressions]: Main function."
(let ((expressions '("3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
"( ( 1 + 2 ) ^ ( 3 + 4 ) ) ^ ( 5 + 6 )"
"( ( 3 ^ 4 ) ^ 2 ^ 9 ) ^ 2 ^ 5"
"3 + 4 * ( 5 - 6 ) ) 4 * 9")))
(dolist (expr (if xtra expressions (list (car expressions))))
(format t "~%INFIX:\"~A\"~%" expr)
(format t "RPN:\"~A\"~%" (rpn expr)))))
 
Output:
CL-USER(2): (main)

INFIX:"3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
TOKEN  TOS    SIGNAL     OPSTACK       OUTPUTQ
3      NIL    GO         NIL           3
+      NIL    ENTER      (+)           3
4      +      GO         (+)           3 4
*      +      ENTER      (* +)         3 4
2      *      GO         (* +)         3 4 2
/      *      LEAVE      (+)           3 4 2 *
/      +      ENTER      (/ +)         3 4 2 *
(      /      ENTER      (( / +)       3 4 2 *
1      (      GO         (( / +)       3 4 2 * 1
-      (      ENTER      (- ( / +)     3 4 2 * 1
5      -      GO         (- ( / +)     3 4 2 * 1 5
)      -      LEAVE      (( / +)       3 4 2 * 1 5 -
)      (      CLEAR      (/ +)         3 4 2 * 1 5 -
^      /      ENTER      (^ / +)       3 4 2 * 1 5 -
2      ^      GO         (^ / +)       3 4 2 * 1 5 - 2
^      ^      ENTER      (^ ^ / +)     3 4 2 * 1 5 - 2
3      ^      GO         (^ ^ / +)     3 4 2 * 1 5 - 2 3
NIL    ^      LEAVE      (^ / +)       3 4 2 * 1 5 - 2 3 ^
NIL    ^      LEAVE      (/ +)         3 4 2 * 1 5 - 2 3 ^ ^
NIL    /      LEAVE      (+)           3 4 2 * 1 5 - 2 3 ^ ^ /
NIL    +      LEAVE      NIL           3 4 2 * 1 5 - 2 3 ^ ^ / +
NIL    NIL    NIL        NIL           3 4 2 * 1 5 - 2 3 ^ ^ / +
RPN:"3 4 2 * 1 5 - 2 3 ^ ^ / +"
NIL

EchoLisp[edit]

 
(require 'hash)
(require 'tree)
 
(define OPS (make-hash))
(hash-set OPS "^" '( 4 #f)) ;; right assoc
(hash-set OPS "*" '( 3 #t)) ;; left assoc
(hash-set OPS "/" '( 3 #t))
(hash-set OPS "+" '( 2 #t))
(hash-set OPS "-" '( 2 #t))
 
;; helpers
(define (is-right-par? token) (string=? token ")"))
(define (is-left-par? token) (string=? token "("))
(define (is-num? op) (not (hash-ref OPS op))) ;; crude
(define (is-op? op) (hash-ref OPS op))
(define (is-left? op) (second (hash-ref OPS op)))
(define (is-right? op) (not (is-left? op)))
(define (op-prec op) (first (hash-ref OPS op)))
 
;; Wikipedia algorithm, translated as it is
 
(define (shunt tokens S Q)
(for ((token tokens))
(writeln "S: " (stack->list S) "Q: " (queue->list Q) "token: "token)
(cond
[(is-left-par? token) (push S token) ]
[(is-right-par? token)
(while (and (stack-top S) (not (is-left-par? (stack-top S))))
(q-push Q ( pop S)))
(when (stack-empty? S) (error 'misplaced-parenthesis "()" ))
(pop S)] ; // left par
 
[(is-op? token)
(while (and
(is-op? (stack-top S))
(or
(and (is-left? token) (<= (op-prec token) (op-prec (stack-top S))))
(and (is-right? token) (< (op-prec token) (op-prec (stack-top S))))))
(q-push Q (pop S)))
(push S token)]
 
[(is-num? token) (q-push Q token)]
[else (error 'bad-token token)])) ; for
(while (stack-top S) (q-push Q (pop S))))
 
(string-delimiter "")
(define (task infix)
(define S (stack 'S))
(define Q (queue 'Q))
(shunt (text-parse infix) S Q)
(writeln 'infix infix)
(writeln 'RPN (queue->list Q)))
 
Output:
(task  "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3")

S:      null     Q:      null     token:      3    
S:      null     Q:      (3)     token:      +    
S:      (+)     Q:      (3)     token:      4    
S:      (+)     Q:      (3 4)     token:      *    
S:      (+ *)     Q:      (3 4)     token:      2    
S:      (+ *)     Q:      (3 4 2)     token:      /    
S:      (+ /)     Q:      (3 4 2 *)     token:      (    
S:      (+ / ()     Q:      (3 4 2 *)     token:      1    
S:      (+ / ()     Q:      (3 4 2 * 1)     token:      -    
S:      (+ / (-)     Q:      (3 4 2 * 1)     token:      5    
S:      (+ / (-)     Q:      (3 4 2 * 1 5)     token:      )    
S:      (+ /)       Q:      (3 4 2 * 1 5 -)     token:      ^    
S:      (+ / ^)     Q:      (3 4 2 * 1 5 -)     token:      2    
S:      (+ / ^)     Q:      (3 4 2 * 1 5 - 2)     token:      ^    
S:      (+ / ^ ^)     Q:      (3 4 2 * 1 5 - 2)     token:      3   
 
infix     3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3    
RPN     (3 4 2 * 1 5 - 2 3 ^ ^ / +)    

Fortran[edit]

The plan[edit]

The basic idea comes from noting that operands and operators alternate, so the plan is to flip-flop between two states. Similarly, the "shunting" aspect comes from shunting incoming operators to a stack providing that higher-precedence operators already in the stack are passed on first. Notice that stacked operators are sent forth if their precedence is greater than or equal to the incoming operator. This means that a sequence such as 1 + 2 + 3 will be handled as (1 + 2) + 3 rather than first stacking up all the adds. In other words, this is the tie-breaker rule of left-to-right for sequences of equal precedence. Similarly, when the end of the expression is reached, a space is treated as if it were an operator but one with very low precedence so that all stacked operators are rolled forth. Otherwise, the scan would have to be followed by code to flush the stack, an annoying duplication.

To handle the special behaviour for exponentiation whereby 1^2^3 is evaluated right-to-left as 1^(2^3) - contrary to the tiebreaker rule - when the ^ operator is stacked its stacked precedence is made one lower than its precedence when encountered. Thus, if a second ^ is encountered it will not cause its predecessor to be sent forth by the "greater than or equal to" scheme; only later, lesser operators will do that. Unfortunately this means that the stack of deferred operators can grow without limit, as for the case of 1^2^3^4^... since the left-to-right rule will not be keeping it down. Otherwise, the height of the stack would be limited by the number of different precedences involved - were it not for bracketing: a sequence such as {[(...)]} will cause escalation too. A different approach to evaluation, and one often followed by humans (especially by those who have used a HP calculator) is to dive into the deepest part of the expression first then back out. For the example 3 + 4*2/(1 - 5)^2^3 that would mean starting with the (1 - 5) and not having the early + waiting on a stack - and, when actually evaluating, the 3 being in the data stack with a long wait for its use. This can be useful on computers calculating with a hardware stack where say the top two elements are in registers (as with the B6700) because less up&down means that more can be done via the registers without the delays of memory access. In doing this it is helpful to have divide-reverse and subtract-reverse operations, or an operation to exchange the top two stack elements. But the resulting sequence of actions would not be RPN style.

A similar trick with the precedences attends the stacking of open brackets as a pseudo-operator with a lower stacked precedence so that when later a closing bracket is found all subsequent operators on the stack (genuine ones, such as +-*/^) will be rolled, and then BALANCEBRA can compare the closing bracket to the possibly long-ago opening bracket. If all is well, the stacked operator will be vanished and the incoming closing bracket not stacked, nor will EMIT be invoked. Further, neither the opening nor closing bracket (encountered when expecting an operand), change the state of expecting an operand next: there is to be no alternation for them.

The task specification is that each token in the text is bounded by spaces. This means that a sequence such as -6 cannot appear so there is no confusion over unary minus versus dyadic minus (as in a - b) and whether or not the hyphen used for both should be interpreted as a part of the number or as an operator applied to a number. Thus, -6^2 might be (-6)^2 or -(6^2) instead. Following the source style of Fortran, this scanner disregards all spaces nor does it require spaces between tokens.

The example expression uses only single-digit numbers, so there was a temptation to employ a DO-loop stepping through the text, but that would require a special flush stage after reaching the end of the text. This could be avoided by having the loop run DO L = 1,LEN(TEXT) + 1 for the extra step, but that would require annoying checks within the loop for L > LEN(TEXT) to prevent out-of-bounds accessing. So, abandon the DO-loop approach and instead allow for surges forward such as for multi-digit numbers - or for multi-character operators (such as <=) or even, for names of variables. However, only integers are allowed for here. The syntax of allowable floating-point numbers is quite complex and a logical function EATREAL(V) requires over a hundred lines, which would swamp the source more directly devoted to the project. It would of course be smaller if no errors were checked for nor complaints made, but testing the backwards logic of the algorithm is quite tricky when it is not working correctly because of mistakes or omissions, so statements of affront were helpful, and would belong in a "production" version anyway.

Having abandoned the idea of a scan-in-place via the introduction of FORASIGN to span the next token, having two calls is not troublesome so the token processing can be done in two successive stages: one for operands, then after the second FORASIGN, another for operators. This in turn allows a GO TO to retry the appropriate stage should bracketing be encountered. Alternatively, the GO TO could be avoided by having a state WANTOPERAND plus a test to select which of the two states is required, followed by a state flip. And for brackets, the state would have to be flipped so that the subsequent flip would not change it. This is too much to pay for the approval of those disliking GO TO statements.

F90 style has been used, in part because of the convenience of shared data and data aggregates such as SYMBOL however, these could be replaced by suitable COMMON statements and data structures can be replaced by a collection of separate variables whose names are structured. The ability to place a subroutine inside another subroutine so as to share local context is likewise a mere convenience.

Source[edit]

      MODULE COMPILER	!At least of arithmetic expressions.
INTEGER KBD,MSG !I/O units.
 
INTEGER ENUFF !How long s a piece of string?
PARAMETER (ENUFF = 66) !This long.
CHARACTER*(ENUFF) RP !Holds the Reverse Polish Notation.
INTEGER LR !And this is its length.
 
INTEGER OPSYMBOLS !Recognised operator symbols.
PARAMETER (OPSYMBOLS = 11) !There are also some associates.
TYPE SYMB !To recognise symbols and carry associated information.
CHARACTER*1 IS !Its text. Careful with the trailing space and comparisons.
INTEGER*1 PRECEDENCE !Controls the order of evaluation.
CHARACTER*48 USAGE !Description.
END TYPE SYMB !The cross-linkage of precedences is tricky.
TYPE(SYMB) SYMBOL(0:OPSYMBOLS) !Righto, I'll have some.
PARAMETER (SYMBOL =(/ !Note that "*" is not to be seen as a match to "**".
o SYMB(" ", 0,"Not recognised as an operator's symbol."),
1 SYMB(" ", 1,"separates symbols and aids legibility."),
2 SYMB(")", 4,"opened with ( to bracket a sub-expression."),
3 SYMB("]", 4,"opened with [ to bracket a sub-expression."),
4 SYMB("}", 4,"opened with { to bracket a sub-expression."),
5 SYMB("+",11,"addition, and unary + to no effect."),
6 SYMB("-",11,"subtraction, and unary - for neg. numbers."),
7 SYMB("*",12,"multiplication."),
8 SYMB("×",12,"multiplication, if you can find this."),
9 SYMB("/",12,"division."),
o SYMB("÷",12,"division for those with a fancy keyboard."),
C 13 is used so that stacked ^ will have lower priority than incoming ^, thus delivering right-to-left evaluation.
1 SYMB("^",14,"raise to power. Not recognised is **.")/))
CHARACTER*3 BRAOPEN,BRACLOSE !Three types are allowed.
PARAMETER (BRAOPEN = "([{", BRACLOSE = ")]}") !These.
INTEGER BRALEVEL !In and out, in and out. That's the game.
INTEGER PRBRA,PRPOW !Special double values.
PARAMETER (PRBRA = SYMBOL( 3).PRECEDENCE) !Bracketing
PARAMETER (PRPOW = SYMBOL(11).PRECEDENCE) !And powers refer leftwards.
 
CHARACTER*10 DIGIT !Numberish is a bit more complex.
PARAMETER (DIGIT = "0123456789") !But this will do for integers.
 
INTEGER STACKLIMIT !How high is a stack?
PARAMETER (STACKLIMIT = 66) !This should suffice.
TYPE DEFERRED !I need a siding for lower-precedence operations.
CHARACTER*1 OPC !The operation code.
INTEGER*1 PRECEDENCE !Its precedence in the siding may differ.
END TYPE DEFERRED !Anyway, that's enough.
TYPE(DEFERRED) OPSTACK(0:STACKLIMIT) !One siding, please.
INTEGER OSP !The operation stack pointer.
 
INTEGER INCOMING,TOKENTYPE,NOTHING,ANUMBER,OPENBRA,HUH !Some mnemonics.
PARAMETER (NOTHING = 0, ANUMBER = -1, OPENBRA = -2, HUH = -3) !The ordering is not arbitrary.
CONTAINS !Now to mess about.
SUBROUTINE EMIT(STUFF) !The objective is to produce some RPN text.
CHARACTER*(*) STUFF !The term of the moment.
INTEGER L !A length.
WRITE (MSG,1) STUFF !Announce.
1 FORMAT ("Emit ",A) !Whatever it is.
IF (STUFF.EQ."") RETURN !Ha ha.
L = LEN(STUFF) !So, how much is there to append?
IF (LR + L.GE.ENUFF) STOP "Too much RPN for RP!" !Perhaps too much.
IF (LR.GT.0) THEN !Is there existing stuff?
LR = LR + 1 !Yes. Advance one,
RP(LR:LR) = " " !And place a space.
END IF !So much for separators.
RP(LR + 1:LR + L) = STUFF !Place the stuff.
LR = LR + L !Count it in.
END SUBROUTINE EMIT !Simple enough, if a bit finicky.
 
SUBROUTINE STACKOP(C,P) !Push an item into the siding.
CHARACTER*1 C !The operation code.
INTEGER P !Its precedence.
OSP = OSP + 1 !Stacking up...
IF (OSP.GT.STACKLIMIT) STOP "OSP overtopped!" !Perhaps not.
OPSTACK(OSP).OPC = C !Righto,
OPSTACK(OSP).PRECEDENCE = P !The deed is simple.
WRITE (MSG,1) C,OPSTACK(1:OSP) !Announce.
1 FORMAT ("Stack ",A1,9X,",OpStk=",33(A1,I2:","))
END SUBROUTINE STACKOP !So this is more for mnemonic ease.
 
LOGICAL FUNCTION COMPILE(TEXT) !A compiler confronts a compiler!
CHARACTER*(*) TEXT !To be inspected.
INTEGER L1,L2 !Fingers for the scan.
CHARACTER*1 C !Character of the moment.
INTEGER HAPPY !Ah, shades of mood.
LR = 0 !No output yet.
OSP = 0 !Nothing stacked.
OPSTACK(0).OPC = "" !Prepare a bouncer.
OPSTACK(0).PRECEDENCE = 0 !So that loops won't go past.
BRALEVEL = 0 !None seen.
HAPPY = +1 !Nor any problems.
L2 = 1 !Syncopation: one past the end of the previous token.
Chew into an operand, possibly obstructed by an open bracket.
100 CALL FORASIGN !Find something to inspect.
IF (TOKENTYPE.EQ.NOTHING) THEN !Run off the end?
IF (OSP.GT.0) CALL GRUMP("Another operand or one of " !E.g. "1 +".
1 //BRAOPEN//" is expected.") !Give a hint, because stacked stuff awaits.
ELSE IF (TOKENTYPE.EQ.ANUMBER) THEN !If a number,
CALL EMIT(TEXT(L1:L2 - 1)) !Roll all its digits.
ELSE IF (TOKENTYPE.EQ.OPENBRA) THEN !Starting a sub-expression?
CALL STACKOP(C,PRBRA - 1) !Thus ( has less precedence than ).
GO TO 100 !And I still want an operand.
C ELSE IF (TOKENTYPE.EQ.ANAME) THEN !Name of something?
C CALL EMIT(TEXT(L1:L2 - 1)) !Roll it.
ELSE !No further options.
CALL GRUMP("Huh? Unexpected "//C) !Probably something like "1 + +"
END IF !Righto, finished with operands.
Chase after an operator, possibly interrupted by a close bracket,.
200 CALL FORASIGN !Find something to inspect.
IF (TOKENTYPE.LT.0) THEN !But, have I an operand-like token instead?
CALL GRUMP("Operator expected, not "//C) !It seems so.
ELSE !Normally, an operator is to hand. Possibly a NOTHING, though.
WRITE (MSG,201) C,INCOMING,OPSTACK(1:OSP) !Document it.
201 FORMAT ("Oprn=>",A1,"< Prec=",I2, !Try to align with other output.
1 ",OpStk=",33(A1,I2:",")) !So as not to clutter the display.
DO WHILE(OPSTACK(OSP).PRECEDENCE .GE. INCOMING) !Shunt higher-precedence stuff out.
IF (OPSTACK(OSP).PRECEDENCE .EQ. PRBRA - 1) !Only opening brackets have this precedence.
1 CALL GRUMP("Unbalanced "//OPSTACK(OSP).OPC) !And they vanish only when meeting their closing bracket.
CALL EMIT(OPSTACK(OSP).OPC) !Otherwise we have an operator.
OSP = OSP - 1 !It has gone forth.
END DO !On to the next.
IF (TOKENTYPE.GT.NOTHING) THEN !Now, only lower-precedence items are still in the stack.
IF (INCOMING.EQ.PRBRA) THEN !And this is a special arrival.
CALL BALANCEBRA(C) !It should match an earlier entry.
BRALEVEL = BRALEVEL - 1 !Count it out.
GO TO 200 !And I still haven't got an operator.
ELSE !All others are normal operators.
IF (C.EQ."^") INCOMING = PRPOW - 1 !Special trick to cause leftwards association of x^2^3.
CALL STACKOP(C,INCOMING) !Shunt aside, to await the next arrival.
END IF !So much for that operator.
END IF !Providing it was not just an end-of-input flusher.
END IF !And not a misplaced operand.
Carry on?
IF (HAPPY .GT. 0) GO TO 100 !No problems, and not a nothing from the end of the text.
Completed.
COMPILE = HAPPY.GE.0 !One hopes so.
CONTAINS !Now for some assistants.
SUBROUTINE GRUMP(GROWL) !There might be a problem.
CHARACTER*(*) GROWL !The fault.
WRITE (MSG,1) GROWL !Say it.
IF (L1.GT. 1) WRITE (MSG,1) "Tasty:",TEXT( 1:L1 - 1) !Now explain the context.
IF (L2.GT.L1) WRITE (MSG,1) "Nasty:",TEXT(L1:L2 - 1) !This is the token when trouble was found.
IF (L2.LE.LEN(TEXT)) WRITE (MSG,1) "Misty:",TEXT(L2:) !And this remains to be seen.
1 FORMAT (4X,A,1X,A) !A simple layout works nicely for reasonable-length texts.
HAPPY = -1 . !Just so.
END SUBROUTINE GRUMP !Enuogh said.
 
SUBROUTINE BALANCEBRA(B) !Perhaps a happy meeting.
CHARACTER*1 B !The closer.
CHARACTER*1 O !The putative opener.
INTEGER IT,L !Fingers.
CHARACTER*88 GROWL !A scratchpad.
O = OPSTACK(OSP).OPC !This should match B.
WRITE (MSG,1) O,B !Perhaps.
1 FORMAT ("Match ",2A) !Show what I've got, anyway.
IT = INDEX(BRAOPEN,O) !So, what sort did I save?
IF (IT .EQ. INDEX(BRACLOSE,B)) THEN !A friend?
OSP = OSP - 1 !Yes. They vanish together.
ELSE !Otherwise, something is out of place.
GROWL = "Unbalanced {[(...)]} bracketing! The closing " !Alas.
1 //B//" is unmatched." !So, a mess.
IF (IT.GT.0) GROWL(62:) = "A "//BRACLOSE(IT:IT) !Perhaps there had been no opening bracket.
1 //" would be better." !But if there had, this would be its friend.
CALL GRUMP(GROWL) !Take that!
END IF !So much for discrepancies.
END SUBROUTINE BALANCEBRA !But, hopefully, amity prevails.
 
SUBROUTINE FORASIGN !See what comes next.
INTEGER I !A stepper.
L1 = L2 !Pick up where the previous scan left off.
10 IF (L1.GT.LEN(TEXT)) THEN !Are we off the end yet?
C = "" !Yes. Scrub the marker.
L2 = L1 !TEXT(L1:L2 - 1) will be null.
TOKENTYPE = NOTHING !But this is to be checked first.
INCOMING = SYMBOL(1).PRECEDENCE !For flushing sidetracked operators.
HAPPY = 0 !Fading away.
ELSE !Otherwise, there is grist.
Check for spaces and move past them.
C = TEXT(L1:L1) !Grab the first character of the prospective token.
IF (C.LE." ") THEN !Boring?
L1 = L1 + 1 !Yes. Step past it.
GO TO 10 !And look afresh.
END IF !Otherwise, L1 now fingers the start.
Caught something to inspect.
L2 = L1 + 1 !This is one beyond. Just for digit strings.
IF (INDEX(DIGIT,C).GT.0) THEN !So, has one started?
TOKENTYPE = ANUMBER !Yep.
20 IF (L2.LE.LEN(TEXT)) THEN !Probe ahead.
IF (INDEX(DIGIT,TEXT(L2:L2)).GT.0) THEN !Another digit?
L2 = L2 + 1 !Yes. Leaving L1 fingering its start,
GO TO 20 !Chase its end.
END IF !So much for another digit.
END IF !And checking against the end.
C ELSE IF (INDEX(LETTERS,C).GT.0) THEN !Some sort of name?
C advance L2 while in NAMEISH.
ELSE IF (INDEX(BRAOPEN,C).GT.0) THEN !An open bracket?
TOKENTYPE = OPENBRA !Yep.
ELSE !Otherwise, anything else.
DO I = OPSYMBOLS,1,-1 !Scan backwards, to find ** before *, if present.
IF (SYMBOL(I).IS .EQ. C) EXIT !Found?
END DO !On to the next. A linear search will do.
IF (I.LE.0) THEN !Is it identified?
TOKENTYPE = HUH !No.
INCOMING = SYMBOL(0).PRECEDENCE !And this might provoke a flush.
ELSE !If it is identified,
TOKENTYPE = I !Then this is a positive number.
INCOMING = SYMBOL(I).PRECEDENCE !And this is of interest.
END IF !Righto, anything has been identified, possibly as HUH.
END IF !So much for classification.
END IF !If there is something to see.
WRITE (MSG,30) C,INCOMING,TOKENTYPE !Announce.
30 FORMAT ("Next=>",A1,"< Prec=",I2,",Ttype=",I2) !C might be blank.
END SUBROUTINE FORASIGN !I call for a sign, and I see what?
END FUNCTION COMPILE !That's the main activity.
END MODULE COMPILER !So, enough of this.
 
PROGRAM POKE
USE COMPILER
CHARACTER*66 TEXT
LOGICAL HIC
MSG = 6
KBD = 5
WRITE (MSG,1)
1 FORMAT ("Produce RPN from infix...",/)
 
10 WRITE (MSG,11)
11 FORMAT("Infix: ",$)
READ(KBD,12) TEXT
12 FORMAT (A)
IF (TEXT.EQ."") STOP "Enough."
HIC = COMPILE(TEXT)
WRITE (MSG,13) HIC,RP(1:LR)
13 FORMAT (L6," RPN: >",A,"<")
GO TO 10
END

Results[edit]

So that spaces can be seen, texts are marked off via >...< The operator stack is shown as a list of elements upwards, each element being the operator followed by its precedence. Notably, the ( has precedence 3, while ) has 4, while ^ in-the-text has precedence 14 but once on the stack it has precedence 13...

Produce RPN from infix...

Infix: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
Next=>3< Prec= 0,Ttype=-1
Emit  3
Next=>+< Prec=11,Ttype= 5
Oprn=>+< Prec=11,OpStk=
Stack +         ,OpStk=+11
Next=>4< Prec=11,Ttype=-1
Emit  4
Next=>*< Prec=12,Ttype= 7
Oprn=>*< Prec=12,OpStk=+11
Stack *         ,OpStk=+11,*12
Next=>2< Prec=12,Ttype=-1
Emit  2
Next=>/< Prec=12,Ttype= 9
Oprn=>/< Prec=12,OpStk=+11,*12
Emit  *
Stack /         ,OpStk=+11,/12
Next=>(< Prec=12,Ttype=-2
Stack (         ,OpStk=+11,/12,( 3
Next=>1< Prec=12,Ttype=-1
Emit  1
Next=>-< Prec=11,Ttype= 6
Oprn=>-< Prec=11,OpStk=+11,/12,( 3
Stack -         ,OpStk=+11,/12,( 3,-11
Next=>5< Prec=11,Ttype=-1
Emit  5
Next=>)< Prec= 4,Ttype= 2
Oprn=>)< Prec= 4,OpStk=+11,/12,( 3,-11
Emit  -
Match ()
Next=>^< Prec=14,Ttype=11
Oprn=>^< Prec=14,OpStk=+11,/12
Stack ^         ,OpStk=+11,/12,^13
Next=>2< Prec=13,Ttype=-1
Emit  2
Next=>^< Prec=14,Ttype=11
Oprn=>^< Prec=14,OpStk=+11,/12,^13
Stack ^         ,OpStk=+11,/12,^13,^13
Next=>3< Prec=13,Ttype=-1
Emit  3
Next=> < Prec= 1,Ttype= 0
Oprn=> < Prec= 1,OpStk=+11,/12,^13,^13
Emit  ^
Emit  ^
Emit  /
Emit  +
     T RPN: >3 4 2 * 1 5 - 2 3 ^ ^ / +<
Infix:
Enough.

A fuller symbol table[edit]

The odd values for the precedences of the operators is driven by the model source being for a compiler able to handle much more complex arithmetic statements involving logical operations, variables, functions (some, like Max(a,b,c,...) with an arbitrary number of parameters), assignment within an expression, and conditionals such as IF condition THEN exp1 ELSE exp2 OWISE exp3 FI - a three-value logic is employed. Similarly, ? stands for a "not a number" and ! for "Infinity". The fuller symbol table is...

Caution! The apparent gaps in the sequence of precedence values in this table are *not* unused!
Cunning ploys with precedence allow parameter evaluation, and right-to-left order as in x**y**z.
INTEGER OPSYMBOLS !Recognised operator symbols.
PARAMETER (OPSYMBOLS = 25) !There are also some associates.
TYPE SYMB !To recognise symbols and carry associated information.
CHARACTER*2 IS !Its text. Careful with the trailing space and comparisons.
INTEGER*1 PRECEDENCE !Controls the order of evaluation.
INTEGER*1 POPCOUNT !Stack activity: a+b means + requires two in.
CHARACTER*48 USAGE !Description.
END TYPE SYMB !The cross-linkage of precedences is tricky.
CHARACTER*5 IFPARTS(0:4) !These appear when an operator would otherwise be expected.
PARAMETER (IFPARTS = (/"IF","THEN","ELSE","OWISE","FI"/)) !So, bend the usage of "operator".
TYPE(SYMB) SYMBOL(-4:OPSYMBOLS) !Righto, I'll have some.
PARAMETER (SYMBOL =(/ !Note that "*" is not to be seen as a match to "**".
4 SYMB("FI", 2,0,"the FI that ends an IF-statement."), !These negative entries are not for name matching
3 SYMB("Ow", 3,0,"the OWISE part of an IF-statement."), !Which is instead done via IFPARTS
2 SYMB("El", 3,0,"the ELSE part of an IF-statement."), !But are here to take advantage of the structure in place.
1 SYMB("Th", 3,0,"the THEN part of an IF-statement."), !The IF is recognised separately, when expecting an operand.
o SYMB(" ", 0,0,"Not recognised as an operator's symbol."),
1 SYMB(" ", 1,0,"separates symbols and aids legibility."),
C 2 and 3 are used for the parts of an IF-statement. See PRIF.
C 3 These precedences ensure the desired order of evaluation.
2 SYMB(") ", 4,0,"opened with ( to bracket a sub-expression."),
3 SYMB("] ", 4,0,"opened with [ to bracket a sub-expression."),
4 SYMB("} ", 4,0,"opened with { to bracket a sub-expression."),
5 SYMB(", ", 5,0,"continues a list of parameters to a function."),
C SYMB(":=", 6,0,"marks an on-the-fly assignment of a result"), Identified differently... see PRREF.
6 SYMB("| ", 7,2,"logical OR, similar to addition."),
7 SYMB("& ", 8,2,"logical AND, similar to multiplication."),
8 SYMB("¬ ", 9,0,"logical NOT, similar to negation."),
9 SYMB("= ",10,2,"tests for equality (beware decimal fractions)"),
o SYMB("< ",10,2,"tests strictly less than."),
1 SYMB("> ",10,2,"tests strictly greater than."),
2 SYMB("<>",10,2,"tests not equal (there is no 'not' key!)"),
3 SYMB("¬=",10,2,"tests not equal if you can find a ¬ !"),
4 SYMB("<=",10,2,"tests less than or equal."),
5 SYMB(">=",10,2,"tests greater than or equal."),
6 SYMB("+ ",11,2,"addition, and unary + to no effect."),
7 SYMB("- ",11,2,"subtraction, and unary - for neg. numbers."),
8 SYMB("* ",12,2,"multiplication."),
9 SYMB("× ",12,2,"multiplication, if you can find this."),
o SYMB("/ ",12,2,"division."),
1 SYMB("÷ ",12,2,"division for those with a fancy keyboard."),
2 SYMB("\ ",12,2,"remainder a\b = a - truncate(a/b)*b; 11\3 = 2"),
C 13 is used so that stacked ** will have lower priority than incoming **, thus delivering right-to-left evaluation.
3 SYMB("^ ",14,2,"raise to power: also recognised is **."), !Uses the previous precedence level also!
4 SYMB("**",14,2,"raise to power: also recognised is ^."),
5 SYMB("! ",15,1,"factorial, sortof, just for fun.")/))

The USAGE field is for when there is a request for help, and the response uses the scanner's actual symbol table entries to formulate its assistance, rather than roll forth a separately-prepared wad of text.

Go[edit]

No error checking. No extra credit output, but there are some comments in the code.

package main
 
import (
"fmt"
"strings"
)
 
var input = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
 
var opa = map[string]struct {
prec int
rAssoc bool
}{
"^": {4, true},
"*": {3, false},
"/": {3, false},
"+": {2, false},
"-": {2, false},
}
 
func main() {
fmt.Println("infix: ", input)
fmt.Println("postfix:", parseInfix(input))
}
 
func parseInfix(e string) (rpn string) {
var stack []string // holds operators and left parenthesis
for _, tok := range strings.Fields(e) {
switch tok {
case "(":
stack = append(stack, tok) // push "(" to stack
case ")":
var op string
for {
// pop item ("(" or operator) from stack
op, stack = stack[len(stack)-1], stack[:len(stack)-1]
if op == "(" {
break // discard "("
}
rpn += " " + op // add operator to result
}
default:
if o1, isOp := opa[tok]; isOp {
// token is an operator
for len(stack) > 0 {
// consider top item on stack
op := stack[len(stack)-1]
if o2, isOp := opa[op]; !isOp || o1.prec > o2.prec ||
o1.prec == o2.prec && o1.rAssoc {
break
}
// top item is an operator that needs to come off
stack = stack[:len(stack)-1] // pop it
rpn += " " + op // add it to result
}
// push operator (the new one) to stack
stack = append(stack, tok)
} else { // token is an operand
if rpn > "" {
rpn += " "
}
rpn += tok // add operand to result
}
}
}
// drain stack to result
for len(stack) > 0 {
rpn += " " + stack[len(stack)-1]
stack = stack[:len(stack)-1]
}
return
}

Output:

infix:   3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / +

Haskell[edit]

Simple with zero error handling; some extra credit.

import Text.Printf
 
prec "^" = 4
prec "*" = 3
prec "/" = 3
prec "+" = 2
prec "-" = 2
 
leftAssoc "^" = False
leftAssoc _ = True
 
isOp (t:[]) = t `elem` "-+/*^"
isOp _ = False
 
simSYA xs = final ++ [lastStep]
where final = scanl f ([],[],"") xs
lastStep = (\(x,y,_) -> (reverse y ++ x, [], "")) $ last final
f (out,st,_) t | isOp t =
(reverse (takeWhile testOp st) ++ out
, (t:) $ (dropWhile testOp st), t)
| t == "(" = (out, "(":st, t)
| t == ")" = (reverse (takeWhile (/="(") st) ++ out,
tail $ dropWhile (/="(") st, t)
| otherwise = (t:out, st, t)
where testOp x = isOp x && (leftAssoc t && prec t == prec x
|| prec t < prec x)
 
main = do
a <- getLine
printf "%30s%20s%7s" "Output" "Stack" "Token"
mapM_ (\(x,y,z) -> printf "%30s%20s%7s\n"
(unwords $ reverse x) (unwords y) z) $ simSYA $ words a

Output:

>main
3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                        Output               Stack  Token                                                         
                             3                          3
                             3                   +      +
                           3 4                   +      4
                           3 4                 * +      *
                         3 4 2                 * +      2
                       3 4 2 *                 / +      /
                       3 4 2 *               ( / +      (
                     3 4 2 * 1               ( / +      1
                     3 4 2 * 1             - ( / +      -
                   3 4 2 * 1 5             - ( / +      5
                 3 4 2 * 1 5 -                 / +      )
                 3 4 2 * 1 5 -               ^ / +      ^
               3 4 2 * 1 5 - 2               ^ / +      2
               3 4 2 * 1 5 - 2             ^ ^ / +      ^
             3 4 2 * 1 5 - 2 3             ^ ^ / +      3
     3 4 2 * 1 5 - 2 3 ^ ^ / +                           

A more complete version with typed input, output and stack; StateT + Control.Lens for stateful actions; Either for both invalid tokens on parsing and unmatched parens when converting; readLine support.

{-# LANGUAGE LambdaCase #-}
import Control.Applicative
import Control.Lens
import Control.Monad
import Control.Monad.Error
import Control.Monad.State
import System.Console.Readline
 
data InToken = InOp Op | InVal Int | LParen | RParen deriving (Show)
data OutToken = OutOp Op | OutVal Int
data StackElem = StOp Op | Paren deriving (Show)
data Op = Pow | Mul | Div | Add | Sub deriving (Show)
data Assoc = L | R deriving (Eq)
 
type Env = ([OutToken], [StackElem])
type RPNComp = StateT Env (Either String)
 
instance Show OutToken where
show (OutOp x) = snd $ opInfo x
show (OutVal v) = show v
 
opInfo = \case
Pow -> (4, "^")
Mul -> (3, "*")
Div -> (3, "/")
Add -> (2, "+")
Sub -> (2, "-")
 
prec = fst . opInfo
leftAssoc Pow = False
leftAssoc _ = True
 
--Stateful actions
processToken :: InToken -> RPNComp ()
processToken = \case
(InVal z) -> pushVal z
(InOp op) -> pushOp op
LParen -> pushParen
RParen -> pushTillParen
 
pushTillParen :: RPNComp ()
pushTillParen = use _2 >>= \case
[] -> throwError "Unmatched right parenthesis"
(s:st) -> case s of
StOp o -> _1 %= (OutOp o:) >> _2 %= tail >> pushTillParen
Paren -> _2 %= tail
 
pushOp :: Op -> RPNComp ()
pushOp o = use _2 >>= \case
[] -> _2 .= [StOp o]
(s:st) -> case s of
(StOp o2) -> if leftAssoc o && prec o == prec o2
|| prec o < prec o2
then _1 %= (OutOp o2:) >> _2 %= tail >> pushOp o
else _2 %= (StOp o:)
Paren -> _2 %= (StOp o:)
 
pushVal :: Int -> RPNComp ()
pushVal n = _1 %= (OutVal n:)
 
pushParen :: RPNComp ()
pushParen = _2 %= (Paren:)
 
--Run StateT
toRPN :: [InToken] -> Either String [OutToken]
toRPN xs = evalStateT process ([],[])
where process = mapM_ processToken xs
>> get >>= \(a,b) -> (reverse a++) <$> (mapM toOut b)
toOut :: StackElem -> RPNComp OutToken
toOut (StOp o) = return $ OutOp o
toOut Paren = throwError "Unmatched left parenthesis"
 
--Parsing
readTokens :: String -> Either String [InToken]
readTokens = mapM f . words
where f = let g = return . InOp in \case {
"^" -> g Pow; "*" -> g Mul; "/" -> g Div;
"+" -> g Add; "-" -> g Sub; "(" -> return LParen;
")" -> return RParen;
a -> case reads a of
[] -> throwError $ "Invalid token `" ++ a ++ "`"
[(_,x:[])] -> throwError $ "Invalid token `" ++ a ++ "`"
[(v,[])] -> return $ InVal v }
 
--Showing
showOutput (Left msg) = msg
showOutput (Right xs) = unwords $ map show xs
 
main = do
a <- readline "Enter expression: "
case a of
Nothing -> putStrLn "Please enter a line" >> main
Just "exit" -> return ()
Just l -> addHistory l >> case readTokens l of
Left msg -> putStrLn msg >> main
Right ts -> putStrLn (showOutput (toRPN ts)) >> main
 
Enter expression: 3 + ( ( 4 + 5 )
Unmatched left parenthesis
Enter expression: 3 + ( 4 + 5 ) )
Unmatched right parenthesis
Enter expression: 3 + ( alan + 5 )
Invalid token `alan`
Enter expression: 3 + ( 4 + 5 )
3 4 5 + +
Enter expression: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
3 4 2 * 1 5 - 2 3 ^ ^ / +

Icon and Unicon[edit]

procedure main()        
infix := "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
printf("Infix = %i\n",infix)
printf("RPN = %i\n",Infix2RPN(infix))
end
 
link printf
 
record op_info(pr,as) # p=precedence, a=associativity (left=null)
 
procedure Infix2RPN(expr) #: Infix to RPN parser - shunting yard
static oi
initial {
oi := table() # precedence & associativity
every oi[!"+-"] := op_info(2) # 2L
every oi[!"*/"] := op_info(3) # 3L
oi["^"] := op_info(4,1) # 4R
}
 
ostack := [] # operator stack
rpn := "" # rpn
 
pat := sprintf("%%5s  :  %%-%ds  :  %%s\n",*expr) # fmt
printf(pat,"Token","Output","Op Stack") # header
 
expr ? until pos(0) do { # while tokens
tab(many(' ')) # consume any seperator
token := tab(upto(' ')|0) # get token
printf(pat,token,rpn,list2string(ostack)) # report
if token := numeric(token) then # ... numeric
rpn ||:= token || " "
else
if member(oi,token) then { # ... operator
while member(oi,op2 := ostack[1]) &
( /oi[token].as & oi[token].pr <= oi[op2].pr ) |
( \oi[token].as & oi[token].pr < oi[op2].pr ) do
rpn ||:= pop(ostack) || " "
push(ostack,token)
}
else # ... parenthesis
if token == "(" then
push(ostack,token)
else if token == ")" then {
until ostack[1] == "(" do
rpn ||:= pop(ostack) || " " |
stop("Unbalanced parenthesis")
pop(ostack) # discard "("
}
}
 
while token := pop(ostack) do # ... input exhausted
if token == ("("|")") then stop("Unbalanced parenthesis")
else {
rpn ||:= token || " "
printf(pat,"",rpn,list2string(ostack))
}
 
return rpn
end
 
procedure list2string(L) #: format list as a string
every (s := "[ ") ||:= !L || " "
return s || "]"
end

printf.icn provides formatting

Output:
Infix = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
Token  :  Output                         :  Op Stack
    3  :                                 :  [ ]
    +  :  3                              :  [ ]
    4  :  3                              :  [ + ]
    *  :  3 4                            :  [ + ]
    2  :  3 4                            :  [ * + ]
    /  :  3 4 2                          :  [ * + ]
    (  :  3 4 2 *                        :  [ / + ]
    1  :  3 4 2 *                        :  [ ( / + ]
    -  :  3 4 2 * 1                      :  [ ( / + ]
    5  :  3 4 2 * 1                      :  [ - ( / + ]
    )  :  3 4 2 * 1 5                    :  [ - ( / + ]
    ^  :  3 4 2 * 1 5 -                  :  [ / + ]
    2  :  3 4 2 * 1 5 -                  :  [ ^ / + ]
    ^  :  3 4 2 * 1 5 - 2                :  [ ^ / + ]
    3  :  3 4 2 * 1 5 - 2                :  [ ^ ^ / + ]
       :  3 4 2 * 1 5 - 2 3 ^            :  [ ^ / + ]
       :  3 4 2 * 1 5 - 2 3 ^ ^          :  [ / + ]
       :  3 4 2 * 1 5 - 2 3 ^ ^ /        :  [ + ]
       :  3 4 2 * 1 5 - 2 3 ^ ^ / +      :  [ ]
RPN   = "3 4 2 * 1 5 - 2 3 ^ ^ / + "

J[edit]

Code

 
NB. j does not have a verb based precedence.
NB. j evaluates verb noun sequences from right to left.
NB. Seriously. 18 precedence levels in C++ .
 
display=: ([: : (smoutput@:(, [: ; ' '&,&.>@:{:@:|:))) :: empty
 
Display=: adverb define
:
m display^:(0 -.@:-: x)y
)
 
NB. Queue, Stack, Pop: m literal name of vector to use. verbose unless x is 0.
NB. Implementation includes display, group push and pop not available in the RC FIFO & LIFO pages
NB. As adverbs, these definitions work with any global variable.
NB. Pop needs the feature, and it helps with display as well.
Queue=: adverb define NB. enqueue y
('m'~)=: y ,~ (m~)
EMPTY
:
x (m,' queue')Display y
m Queue y
)
 
Stack=: adverb define NB. Stack y
('m'~)=: (|.y) , (m~)
EMPTY
:
x (m,' stack')Display y
m Stack y
)
 
Pop=: adverb define NB. Pop y items
0 m Pop y
:
y=. 0 {:@:, y NB. if y is empty use 0 instead
rv=. y {. (m~)
('m'~)=: y }. (m~)
x (m,' pop') Display rv
rv
)
 
NB. tests
TEST=: ''
'TEST'Stack'abc'
'TEST'Stack'de'
assert 'edc' -: 'TEST'Pop 3
assert 'ba' -: 'TEST'Pop 2
assert 0 (= #) TEST
'TEST'Queue'abc'
'TEST'Queue'de'
assert 'ab' -: 'TEST'Pop 2
assert 'cde' -: 'TEST'Pop 3
assert 0 (= #) TEST
 
any=: +./
 
DIGITS=: a. {~ 48+i.10 NB. ASCII 48--57
precedence_oppression=: <;._1' +- */ ^ ( ) ',DIGITS
associativity=: 'xLLRxxL'
 
classify=: {:@:I.@:(1 , [email protected]&>)&precedence_oppression
 
NB. The required tokens are also tokens in j.
NB. Use the default sequential machine ;: for lexical analysis.
rclex=: (;~ classify)"0@:;:
 
 
NB. numbers can be treated as highest precedence operators
number=: Q Queue NB. put numbers onto the output queue
left=: S Stack NB. push left paren onto the stack
 
NB. Until the token at the top of the stack is (, pop
NB. operators off the stack onto the output queue.
NB. Pop the left parenthesis from the stack, but not onto the output queue.
right=: 4 : 0 NB. If the token is a right parenthesis:
i=. (S~) (i. rclex) '('
if. i (= #) S~ do.
smoutput'Check your parens!'
throw.
end.
x Q Queue x S Pop i
x S Pop 1
EMPTY
)
 
NB. If the token is an operator, o1, then:
NB.
NB. while there is an operator token, o2, at the top of the stack, and
NB. either o1 is [[left-associative and its precedence is less than or
NB. equal to that of o2]]"L*.<:", or o1 is [[right-associative and its precedence
NB. is less than that of o2]]"R*.<", pop o2 off the stack, onto the output queue;
NB. [[the tally of adjacent leading truths]]"NCT"
NB.
NB. push o1 onto the stack.
o=: 4 : 0
P=. 0 0 {:: y
L=. 'L' = P { associativity
operators=. ({.~ i.&(rclex'(')) S~
NB. NCT L*.<: or R*.<
i=. (+/@:(*./\)@:((L *. P&<:) +. ((-.L) *. P&<))@:(0&{::"1)) :: 0: operators
x Q Queue x S Pop i
x (S Stack) y
EMPTY
)
 
NB. terminating version of invalid
invalid=: 4 : 0
smoutput 'invalid token ',0 1 {:: y
throw.
)
 
NB. demonstrated invalid
invalid=: [: smoutput 'discarding invalid token ' , 0 1 {:: ]
 
NB. shunt_yard is a verb to implement shunt-yard parsing.
NB. verbose defaults to 0. (quiet)
NB. use: verbosity shunt_yard_parse algebraic_string
shunt_yard_parse=: 0&$: : (4 : 0)
 
NB. j's data structure is array. Rank 1 arrays (vectors)
NB. are just right for the stack and output queue.
 
'S Q'=: ;: 'OPERATOR OUTPUT'
('S'~)=:('Q'~)=: i.0 2
 
NB. Follow agenda for all tokens, result saved on global OUTPUT variable
x (invalid`o`o`o`left`right`number@.(0 0 {:: ])"2 ,:"1@:rclex) y
NB. x (invalid`o`o`o`left`right`o@.(0 0 {:: ])"2 ,:"1@:rclex) y NB. numbers can be treated as operators
NB. check for junk on stack
if. (rclex'(') e. S~ do.
smoutput'Check your other parens!'
throw.
end.
 
NB. shift remaining operators onto the output queue
x Q Queue x S Pop # S~
 
NB. return the output queue
Q~
)
 
algebra_to_rpn=: {:@:|:@:shunt_yard_parse
 
fulfill_requirement=: ;@:(' '&,&.>)@:algebra_to_rpn
 

Demonstration

 
fulfill_requirement '3+4*2/(1-5)^2^3'
3 4 2 * 1 5 - 2 3 ^ ^ / +
 
shunt_yard_parse'3*)2+4)'
Check your parens!
 
shunt_yard_parse'3*(2+4'
Check your other parens!
 
algebra_to_rpn'1+x*(3+x)'
discarding invalid token x
discarding invalid token x
┌─┬─┬─┬─┬─┐
13│+│*│+│
└─┴─┴─┴─┴─┘
 
NB. Boxed form useful for evaluation
algebra_to_rpn'0+666*(1+666*(2+666*(3)))' NB. polynomial evaluation.
┌─┬───┬─┬───┬─┬───┬─┬─┬─┬─┬─┬─┬─┐
0666166626663│*│+│*│+│*│+│
└─┴───┴─┴───┴─┴───┴─┴─┴─┴─┴─┴─┴─┘
 
1 fulfill_requirement'3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3'
OUTPUT queue 3
OPERATOR pop
OUTPUT queue
OPERATOR stack +
OUTPUT queue 4
OPERATOR pop
OUTPUT queue
OPERATOR stack *
OUTPUT queue 2
OPERATOR pop *
OUTPUT queue *
OPERATOR stack /
OPERATOR stack (
OUTPUT queue 1
OPERATOR pop
OUTPUT queue
OPERATOR stack -
OUTPUT queue 5
OPERATOR pop -
OUTPUT queue -
OPERATOR pop (
OPERATOR pop
OUTPUT queue
OPERATOR stack ^
OUTPUT queue 2
OPERATOR pop
OUTPUT queue
OPERATOR stack ^
OUTPUT queue 3
OPERATOR pop ^ ^ / +
OUTPUT queue ^ ^ / +
3 4 2 * 1 5 - 2 3 ^ ^ / +
 

Java[edit]

Works with: Java version 7
import java.util.Stack;
 
public class ShuntingYard {
 
public static void main(String[] args) {
String infix = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3";
System.out.printf("infix:  %s%n", infix);
System.out.printf("postfix: %s%n", infixToPostfix(infix));
}
 
static String infixToPostfix(String infix) {
final String ops = "-+/*^";
StringBuilder sb = new StringBuilder();
Stack<Integer> s = new Stack<>();
 
for (String token : infix.split("\\s")) {
if (token.isEmpty())
continue;
char c = token.charAt(0);
int idx = ops.indexOf(c);
 
// check for operator
if (idx != -1) {
if (s.isEmpty())
s.push(idx);
 
else {
while (!s.isEmpty()) {
int prec2 = s.peek() / 2;
int prec1 = idx / 2;
if (prec2 > prec1 || (prec2 == prec1 && c != '^'))
sb.append(ops.charAt(s.pop())).append(' ');
else break;
}
s.push(idx);
}
}
else if (c == '(') {
s.push(-2); // -2 stands for '('
}
else if (c == ')') {
// until '(' on stack, pop operators.
while (s.peek() != -2)
sb.append(ops.charAt(s.pop())).append(' ');
s.pop();
}
else {
sb.append(token).append(' ');
}
}
while (!s.isEmpty())
sb.append(ops.charAt(s.pop())).append(' ');
return sb.toString();
}
}

Output:

infix:   3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / + 

JavaScript[edit]

function Stack() {
this.dataStore = [];
this.top = 0;
this.push = push;
this.pop = pop;
this.peek = peek;
this.length = length;
}
 
function push(element) {
this.dataStore[this.top++] = element;
}
 
function pop() {
return this.dataStore[--this.top];
}
 
function peek() {
return this.dataStore[this.top-1];
}
 
function length() {
return this.top;
}
 
var infix = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3";
infix = infix.replace(/\s+/g, ''); // remove spaces, so infix[i]!=" "
 
var s = new Stack();
var ops = "-+/*^";
var precedence = {"^":4, "*":3, "/":3, "+":2, "-":2};
var associativity = {"^":"Right", "*":"Left", "/":"Left", "+":"Left", "-":"Left"};
var token;
var postfix = "";
var o1, o2;
 
for (var i = 0; i < infix.length; i++) {
token = infix[i];
if (token >= "0" && token <= "9") { // if token is operand (here limited to 0 <= x <= 9)
postfix += token + " ";
}
else if (ops.indexOf(token) != -1) { // if token is an operator
o1 = token;
o2 = s.peek();
while (ops.indexOf(o2)!=-1 && ( // while operator token, o2, on top of the stack
// and o1 is left-associative and its precedence is less than or equal to that of o2
(associativity[o1] == "Left" && (precedence[o1] <= precedence[o2]) ) ||
// the algorithm on wikipedia says: or o1 precedence < o2 precedence, but I think it should be
// or o1 is right-associative and its precedence is less than that of o2
(associativity[o1] == "Right" && (precedence[o1] < precedence[o2]))
)){
postfix += o2 + " "; // add o2 to output queue
s.pop(); // pop o2 of the stack
o2 = s.peek(); // next round
}
s.push(o1); // push o1 onto the stack
}
else if (token == "(") { // if token is left parenthesis
s.push(token); // then push it onto the stack
}
else if (token == ")") { // if token is right parenthesis
while (s.peek() != "("){ // until token at top is (
postfix += s.pop() + " ";
}
s.pop(); // pop (, but not onto the output queue
}
}
while (s.length()>0){
postfix += s.pop() + " ";
}
print(postfix);

Output:

infix:   3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / + 

Liberty BASIC[edit]

 
global stack$,queue$
stack$=""
queue$=""
 
in$ = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
print "Input:"
print in$
 
token$ = "#"
print "No", "token", "stack", "queue"
 
while 1
i=i+1
token$ = word$(in$, i)
if token$ = "" then i=i-1: exit while
print i, token$, reverse$(stack$), queue$
 
select case
case token$ = "("
call stack.push token$
 
case token$ = ")"
while stack.peek$() <> "("
'if stack is empty
if stack$="" then print "Error: no matching '(' for token ";i: end
call queue.push stack.pop$()
wend
discard$=stack.pop$() 'discard "("
 
case isOperator(token$)
op1$=token$
while(isOperator(stack.peek$()))
op2$=stack.peek$()
select case
case op2$<>"^" and precedence(op1$) = precedence(op2$)
'"^" is the only right-associative operator
call queue.push stack.pop$()
case precedence(op1$) < precedence(op2$)
call queue.push stack.pop$()
case else
exit while
end select
wend
call stack.push op1$
 
case else 'number
'actually, wrong operator could end up here, like say %
'If the token is a number, then add it to the output queue.
call queue.push token$
end select
 
wend
 
while stack$<>""
if stack.peek$() = "(" then print "no matching ')'": end
call queue.push stack.pop$()
wend
 
print "Output:"
while queue$<>""
print queue.pop$();" ";
wend
print
 
end
 
'------------------------------------------
function isOperator(op$)
isOperator = instr("+-*/^", op$)<>0 AND len(op$)=1
end function
 
function precedence(op$)
if isOperator(op$) then
precedence = 1 _
+ (instr("+-*/^", op$)<>0) _
+ (instr("*/^", op$)<>0) _
+ (instr("^", op$)<>0)
end if
end function
 
'------------------------------------------
sub stack.push s$
stack$=s$+"|"+stack$
end sub
 
sub queue.push s$
queue$=queue$+s$+"|"
end sub
 
function queue.pop$()
'it does return empty on empty stack or queue
queue.pop$=word$(queue$,1,"|")
queue$=mid$(queue$,instr(queue$,"|")+1)
end function
 
function stack.pop$()
'it does return empty on empty stack or queue
stack.pop$=word$(stack$,1,"|")
stack$=mid$(stack$,instr(stack$,"|")+1)
end function
 
function stack.peek$()
'it does return empty on empty stack or queue
stack.peek$=word$(stack$,1,"|")
end function
 
function reverse$(s$)
reverse$ = ""
token$="#"
while token$<>""
i=i+1
token$=word$(s$,i,"|")
reverse$ = token$;" ";reverse$
wend
end function
 
Output:
Input:
3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
No            token         stack         queue
1             3
2             +                           3|
3             4              +            3|
4             *              +            3|4|
5             2              + *          3|4|
6             /              + *          3|4|2|
7             (              + /          3|4|2|*|
8             1              + / (        3|4|2|*|
9             -              + / (        3|4|2|*|1|
10            5              + / ( -      3|4|2|*|1|
11            )              + / ( -      3|4|2|*|1|5|
12            ^              + /          3|4|2|*|1|5|-|
13            2              + / ^        3|4|2|*|1|5|-|
14            ^              + / ^        3|4|2|*|1|5|-|2|
15            3              + / ^ ^      3|4|2|*|1|5|-|2|
Output:
3 4 2 * 1 5 - 2 3 ^ ^ / +

Mathematica[edit]

rpn[str_] := 
StringRiffle[
ToString /@
Module[{in = StringSplit[str], stack = {}, out = {}, next},
While[in != {}, next = in[[1]]; in = in[[2 ;;]];
Which[DigitQ[next], AppendTo[out, next], LetterQ[next],
AppendTo[stack, next], next == ",",
While[stack[[-1]] != "(", AppendTo[out, stack[[-1]]];
stack = stack[[;; -2]]], next == "^", AppendTo[stack, "^"],
next == "*",
While[stack != {} && MatchQ[stack[[-1]], "^" | "*" | "/"],
AppendTo[out, stack[[-1]]]; stack = stack[[;; -2]]];
AppendTo[stack, "*"], next == "/",
While[stack != {} && MatchQ[stack[[-1]], "^" | "*" | "/"],
AppendTo[out, stack[[-1]]]; stack = stack[[;; -2]]];
AppendTo[stack, "/"], next == "+",
While[stack != {} &&
MatchQ[stack[[-1]], "^" | "*" | "/" | "+" | "-"],
AppendTo[out, stack[[-1]]]; stack = stack[[;; -2]]];
AppendTo[stack, "+"], next == "-",
While[stack != {} &&
MatchQ[stack[[-1]], "^" | "*" | "/" | "+" | "-"],
AppendTo[out, stack[[-1]]]; stack = stack[[;; -2]]];
AppendTo[stack, "-"], next == "(", AppendTo[stack, "("],
next == ")",
While[stack[[-1]] =!= "(", AppendTo[out, stack[[-1]]];
stack = stack[[;; -2]]]; stack = stack[[;; -2]];
If[StringQ[stack[[-1]]], AppendTo[out, stack[[-1]]];
stack = stack[[;; -2]]]]];
While[stack != {}, AppendTo[out, stack[[-1]]];
stack = stack[[;; -2]]]; out]];
Print[rpn["3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"]];
Output:
3 4 2 * 1 5 - / 2 3 ^ ^ +

Perl[edit]

Translation of: Perl 6
my %prec = (
'^' => 4,
'*' => 3,
'/' => 3,
'+' => 2,
'-' => 2,
'(' => 1
);
 
my %assoc = (
'^' => 'right',
'*' => 'left',
'/' => 'left',
'+' => 'left',
'-' => 'left'
);
 
sub shunting_yard {
my @inp = split ' ', $_[0];
my @ops;
my @res;
 
my $report = sub { printf "%25s  %-7s %10s %s\n", "@res", "@ops", $_[0], "@inp" };
my $shift = sub { $report->("shift @_"); push @ops, @_ };
my $reduce = sub { $report->("reduce @_"); push @res, @_ };
 
while (@inp) {
my $token = shift @inp;
if ( $token =~ /\d/ ) { $reduce->($token) }
elsif ( $token eq '(' ) { $shift->($token) }
elsif ( $token eq ')' ) {
while ( @ops and "(" ne ( my $x = pop @ops ) ) { $reduce->($x) }
} else {
my $newprec = $prec{$token};
while (@ops) {
my $oldprec = $prec{ $ops[-1] };
last if $newprec > $oldprec;
last if $newprec == $oldprec and $assoc{$token} eq 'right';
$reduce->( pop @ops );
}
$shift->($token);
}
}
$reduce->( pop @ops ) while @ops;
@res;
}
 
local $, = " ";
print shunting_yard '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3';
 
Output:
                                       reduce 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                        3               shift + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                        3    +         reduce 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                      3 4    +          shift * 2 / ( 1 - 5 ) ^ 2 ^ 3
                      3 4    + *       reduce 2 / ( 1 - 5 ) ^ 2 ^ 3
                    3 4 2    +         reduce * ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    +          shift / ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    + /        shift ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    + / (     reduce 1 - 5 ) ^ 2 ^ 3
                3 4 2 * 1    + / (      shift - 5 ) ^ 2 ^ 3
                3 4 2 * 1    + / ( -   reduce 5 ) ^ 2 ^ 3
              3 4 2 * 1 5    + / (     reduce - ^ 2 ^ 3
            3 4 2 * 1 5 -    + /        shift ^ 2 ^ 3
            3 4 2 * 1 5 -    + / ^     reduce 2 ^ 3
          3 4 2 * 1 5 - 2    + / ^      shift ^ 3
          3 4 2 * 1 5 - 2    + / ^ ^   reduce 3
        3 4 2 * 1 5 - 2 3    + / ^     reduce ^
      3 4 2 * 1 5 - 2 3 ^    + /       reduce ^
    3 4 2 * 1 5 - 2 3 ^ ^    +         reduce /
  3 4 2 * 1 5 - 2 3 ^ ^ /              reduce +
3 4 2 * 1 5 - 2 3 ^ ^ / +

Perl 6[edit]

my %prec =
'^' => 4,
'*' => 3,
'/' => 3,
'+' => 2,
'-' => 2,
'(' => 1;
 
my %assoc =
'^' => 'right',
'*' => 'left',
'/' => 'left',
'+' => 'left',
'-' => 'left';
 
sub shunting-yard ($prog) {
my @inp = $prog.words;
my @ops;
my @res;
 
sub report($op) { printf "%25s  %-7s %10s %s\n", ~@res, ~@ops, $op, ~@inp }
sub shift($t) { report( "shift $t"); @ops.push: $t }
sub reduce($t) { report("reduce $t"); @res.push: $t }
 
while @inp {
given @inp.shift {
when /\d/ { reduce $_ };
when '(' { shift $_ }
when ')' { while @ops and (my $x = @ops.pop and $x ne '(') { reduce $x } }
default {
my $newprec = %prec{$_};
while @ops {
my $oldprec = %prec{@ops[*-1]};
last if $newprec > $oldprec;
last if $newprec == $oldprec and %assoc{$_} eq 'right';
reduce @ops.pop;
}
shift $_;
}
}
}
reduce @ops.pop while @ops;
@res;
}
 
say shunting-yard '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3';
Output:
                                       reduce 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                        3               shift + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                        3    +         reduce 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                      3 4    +          shift * 2 / ( 1 - 5 ) ^ 2 ^ 3
                      3 4    + *       reduce 2 / ( 1 - 5 ) ^ 2 ^ 3
                    3 4 2    +         reduce * ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    +          shift / ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    + /        shift ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    + / (     reduce 1 - 5 ) ^ 2 ^ 3
                3 4 2 * 1    + / (      shift - 5 ) ^ 2 ^ 3
                3 4 2 * 1    + / ( -   reduce 5 ) ^ 2 ^ 3
              3 4 2 * 1 5    + / (     reduce - ^ 2 ^ 3
            3 4 2 * 1 5 -    + /        shift ^ 2 ^ 3
            3 4 2 * 1 5 -    + / ^     reduce 2 ^ 3
          3 4 2 * 1 5 - 2    + / ^      shift ^ 3
          3 4 2 * 1 5 - 2    + / ^ ^   reduce 3 
        3 4 2 * 1 5 - 2 3    + / ^     reduce ^ 
      3 4 2 * 1 5 - 2 3 ^    + /       reduce ^ 
    3 4 2 * 1 5 - 2 3 ^ ^    +         reduce / 
  3 4 2 * 1 5 - 2 3 ^ ^ /              reduce + 
3 4 2 * 1 5 - 2 3 ^ ^ / +

PicoLisp[edit]

Note: "^" is a meta-character and must be escaped in strings

(de operator (Op)
(member Op '("\^" "*" "/" "+" "-")) )
 
(de leftAssoc (Op)
(member Op '("*" "/" "+" "-")) )
 
(de precedence (Op)
(case Op
("\^" 4)
(("*" "/") 3)
(("+" "-") 2) ) )
 
(de shuntingYard (Str)
(make
(let (Fmt (-7 -30 -4) Stack)
(tab Fmt "Token" "Output" "Stack")
(for Token (str Str "_")
(cond
((num? Token) (link @))
((= "(" Token) (push 'Stack Token))
((= ")" Token)
(until (= "(" (car Stack))
(unless Stack
(quit "Unbalanced Stack") )
(link (pop 'Stack)) )
(pop 'Stack) )
(T
(while
(and
(operator (car Stack))
((if (leftAssoc (car Stack)) <= <)
(precedence Token)
(precedence (car Stack)) ) )
(link (pop 'Stack)) )
(push 'Stack Token) ) )
(tab Fmt Token (glue " " (made)) Stack) )
(while Stack
(when (= "(" (car Stack))
(quit "Unbalanced Stack") )
(link (pop 'Stack))
(tab Fmt NIL (glue " " (made)) Stack) ) ) ) )

Output:

: (shuntingYard "3 + 4 * 2 / (1 - 5) \^ 2 \^ 3")
Token Output Stack
3 3
+ 3 +
4 3 4 +
* 3 4 *+
2 3 4 2 *+
/ 3 4 2 * /+
( 3 4 2 * (/+
1 3 4 2 * 1 (/+
- 3 4 2 * 1 -(/+
5 3 4 2 * 1 5 -(/+
) 3 4 2 * 1 5 - /+
^ 3 4 2 * 1 5 - ^/+
2 3 4 2 * 1 5 - 2 ^/+
^ 3 4 2 * 1 5 - 2 ^^/+
3 3 4 2 * 1 5 - 2 3 ^^/+
3 4 2 * 1 5 - 2 3 ^ ^/+
3 4 2 * 1 5 - 2 3 ^ ^ /+
3 4 2 * 1 5 - 2 3 ^ ^ / +
3 4 2 * 1 5 - 2 3 ^ ^ / +
-> (3 4 2 "*" 1 5 "-" 2 3 "\^" "\^" "/" "+")

PL/I[edit]

 
cvt: procedure options (main); /* 15 January 2012. */
declare (in, stack, out) character (100) varying;
declare (ch, chs) character (1);
declare display bit (1) static initial ('0'b);
 
in = '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3';
 
in = '(' || in || ' ) '; /* Initialize with parentheses */
 
put skip edit ('INPUT', 'STACK', 'OUTPUT') (a, col(37), a, col(47), a);
 
stack = ' '; out = ''; /* Initialize */
do while (length (in) > 0);
ch = substr(in, 1, 1);
select (ch);
when (' ') ;
 
when ('+', '-', '*', '/', '^')
do;
/* Copy any equal or higher-priority operators from the stack */
/* to the output string */
chs = substr(stack, 1, 1);
do while ((spriority(chs) >= priority(ch)) & ( chs ^= ')' ) );
if display then put skip list ('unstacking: ' || chs);
out = out || ' ' || chs;
stack = substr(stack, 2);
chs = substr(stack, 1, 1);
end;
/* Now copy the input to the TOS. */
if display then put skip list ('copying ' || ch || ' to TOS');
stack = ch || stack;
end;
when ( '(' )
do;
stack = '(' || stack;
if display then put skip list ('stacking the (' );
end;
when ( ')' )
do; /* copy all operators from the stack to the output, */
/* until a '(' is encountered. */
chs = substr(stack, 1, 1);
do while (chs ^= '(' );
if display then put skip list ('copying stack ' || chs || ' to output');
put skip edit (stack, out) (col(37), a, col(47), a);
out = out || ' ' || chs;
stack = substr(stack, 2);
chs = substr(stack, 1, 1);
end;
/* Now delete the '(' from the input and */
/* the ')' from the top of the stack. */
if display then put skip edit ('Deleting ( from TOS') (col(30), a);
stack = substr(stack, 2);
/* The '(' on the input is removed at the end of the loop. */
end;
otherwise /* it's an operand. */
do;
out = out || ' ';
do while (ch ^= ' ');
if display then put skip list ('copying ' || ch || ' to output');
out = out || ch;
in = substr(in, 2);
ch = substr(in, 1, 1);
end;
end;
end;
in = substr(in, 2); /* Remove one character from the input */
put skip edit (in, stack, out) (a, col(37), a, col(47), a);
end;
 
priority: procedure (ch) returns (character(1));
declare ch character (1);
 
return ( translate(ch, '1122335', '()+-*/^' ) );
end priority;
 
spriority: procedure (ch) returns (character(1));
declare ch character (1);
 
return ( translate(ch, '1122334', '()+-*/^' ) );
end spriority;
 
end cvt;
 

Output:

 
INPUT STACK OUTPUT
3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 ) (
+ 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 ) ( 3
4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 ) +( 3
4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 ) +( 3
* 2 / ( 1 - 5 ) ^ 2 ^ 3 ) +( 3 4
2 / ( 1 - 5 ) ^ 2 ^ 3 ) *+( 3 4
2 / ( 1 - 5 ) ^ 2 ^ 3 ) *+( 3 4
/ ( 1 - 5 ) ^ 2 ^ 3 ) *+( 3 4 2
( 1 - 5 ) ^ 2 ^ 3 ) /+( 3 4 2 *
( 1 - 5 ) ^ 2 ^ 3 ) /+( 3 4 2 *
1 - 5 ) ^ 2 ^ 3 ) (/+( 3 4 2 *
1 - 5 ) ^ 2 ^ 3 ) (/+( 3 4 2 *
- 5 ) ^ 2 ^ 3 ) (/+( 3 4 2 * 1
5 ) ^ 2 ^ 3 ) -(/+( 3 4 2 * 1
5 ) ^ 2 ^ 3 ) -(/+( 3 4 2 * 1
) ^ 2 ^ 3 ) -(/+( 3 4 2 * 1 5
-(/+( 3 4 2 * 1 5
^ 2 ^ 3 ) /+( 3 4 2 * 1 5 -
^ 2 ^ 3 ) /+( 3 4 2 * 1 5 -
2 ^ 3 ) ^/+( 3 4 2 * 1 5 -
2 ^ 3 ) ^/+( 3 4 2 * 1 5 -
^ 3 ) ^/+( 3 4 2 * 1 5 - 2
3 ) ^^/+( 3 4 2 * 1 5 - 2
3 ) ^^/+( 3 4 2 * 1 5 - 2
) ^^/+( 3 4 2 * 1 5 - 2 3
^^/+( 3 4 2 * 1 5 - 2 3
^/+( 3 4 2 * 1 5 - 2 3 ^
/+( 3 4 2 * 1 5 - 2 3 ^ ^
+( 3 4 2 * 1 5 - 2 3 ^ ^ /
3 4 2 * 1 5 - 2 3 ^ ^ / +
3 4 2 * 1 5 - 2 3 ^ ^ / +
 

Python[edit]

Parenthesis are added to the operator table then special-cased in the code. This solution includes the extra credit.

from collections import namedtuple
from pprint import pprint as pp
 
OpInfo = namedtuple('OpInfo', 'prec assoc')
L, R = 'Left Right'.split()
 
ops = {
'^': OpInfo(prec=4, assoc=R),
'*': OpInfo(prec=3, assoc=L),
'/': OpInfo(prec=3, assoc=L),
'+': OpInfo(prec=2, assoc=L),
'-': OpInfo(prec=2, assoc=L),
'(': OpInfo(prec=9, assoc=L),
')': OpInfo(prec=0, assoc=L),
}
 
NUM, LPAREN, RPAREN = 'NUMBER ( )'.split()
 
 
def get_input(inp = None):
'Inputs an expression and returns list of (TOKENTYPE, tokenvalue)'
 
if inp is None:
inp = input('expression: ')
tokens = inp.strip().split()
tokenvals = []
for token in tokens:
if token in ops:
tokenvals.append((token, ops[token]))
#elif token in (LPAREN, RPAREN):
# tokenvals.append((token, token))
else:
tokenvals.append((NUM, token))
return tokenvals
 
def shunting(tokenvals):
outq, stack = [], []
table = ['TOKEN,ACTION,RPN OUTPUT,OP STACK,NOTES'.split(',')]
for token, val in tokenvals:
note = action = ''
if token is NUM:
action = 'Add number to output'
outq.append(val)
table.append( (val, action, ' '.join(outq), ' '.join(s[0] for s in stack), note) )
elif token in ops:
t1, (p1, a1) = token, val
v = t1
note = 'Pop ops from stack to output'
while stack:
t2, (p2, a2) = stack[-1]
if (a1 == L and p1 <= p2) or (a1 == R and p1 < p2):
if t1 != RPAREN:
if t2 != LPAREN:
stack.pop()
action = '(Pop op)'
outq.append(t2)
else:
break
else:
if t2 != LPAREN:
stack.pop()
action = '(Pop op)'
outq.append(t2)
else:
stack.pop()
action = '(Pop & discard "(")'
table.append( (v, action, ' '.join(outq), ' '.join(s[0] for s in stack), note) )
break
table.append( (v, action, ' '.join(outq), ' '.join(s[0] for s in stack), note) )
v = note = ''
else:
note = ''
break
note = ''
note = ''
if t1 != RPAREN:
stack.append((token, val))
action = 'Push op token to stack'
else:
action = 'Discard ")"'
table.append( (v, action, ' '.join(outq), ' '.join(s[0] for s in stack), note) )
note = 'Drain stack to output'
while stack:
v = ''
t2, (p2, a2) = stack[-1]
action = '(Pop op)'
stack.pop()
outq.append(t2)
table.append( (v, action, ' '.join(outq), ' '.join(s[0] for s in stack), note) )
v = note = ''
return table
 
if __name__ == '__main__':
infix = '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3'
print( 'For infix expression: %r\n' % infix )
rp = shunting(get_input(infix))
maxcolwidths = [len(max(x, key=len)) 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 RPN is: %r' % rp[-1][2])
Sample output
For infix expression: '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3'

TOKEN         ACTION                RPN OUTPUT         OP STACK            NOTES            
3     Add number to output   3                                                              
+     Push op token to stack 3                         +                                    
4     Add number to output   3 4                       +                                    
*     Push op token to stack 3 4                       + *                                  
2     Add number to output   3 4 2                     + *                                  
/     (Pop op)               3 4 2 *                   +        Pop ops from stack to output
      Push op token to stack 3 4 2 *                   + /                                  
(     Push op token to stack 3 4 2 *                   + / (                                
1     Add number to output   3 4 2 * 1                 + / (                                
-     Push op token to stack 3 4 2 * 1                 + / ( -                              
5     Add number to output   3 4 2 * 1 5               + / ( -                              
)     (Pop op)               3 4 2 * 1 5 -             + / (    Pop ops from stack to output
      (Pop & discard "(")    3 4 2 * 1 5 -             + /                                  
      Discard ")"            3 4 2 * 1 5 -             + /                                  
^     Push op token to stack 3 4 2 * 1 5 -             + / ^                                
2     Add number to output   3 4 2 * 1 5 - 2           + / ^                                
^     Push op token to stack 3 4 2 * 1 5 - 2           + / ^ ^                              
3     Add number to output   3 4 2 * 1 5 - 2 3         + / ^ ^                              
      (Pop op)               3 4 2 * 1 5 - 2 3 ^       + / ^    Drain stack to output       
      (Pop op)               3 4 2 * 1 5 - 2 3 ^ ^     + /                                  
      (Pop op)               3 4 2 * 1 5 - 2 3 ^ ^ /   +                                    
      (Pop op)               3 4 2 * 1 5 - 2 3 ^ ^ / +                                      

 The final output RPN is: '3 4 2 * 1 5 - 2 3 ^ ^ / +'

Racket[edit]

 
#lang racket
;print column of width w
(define (display-col w s)
(let* ([n-spaces (- w (string-length s))]
[spaces (make-string n-spaces #\space)])
(display (string-append s spaces))))
;print columns given widths (idea borrowed from PicoLisp)
(define (tab ws . ss) (for-each display-col ws ss) (newline))
 
(define input "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3")
 
(define (paren? s) (or (string=? s "(") (string=? s ")")))
(define-values (prec lasso? rasso? op?)
(let ([table '(["^" 4 r]
["*" 3 l]
["/" 3 l]
["+" 2 l]
["-" 2 l])])
(define (asso x) (caddr (assoc x table)))
(values (λ (x) (cadr (assoc x table)))
(λ (x) (symbol=? (asso x) 'l))
(λ (x) (symbol=? (asso x) 'r))
(λ (x) (member x (map car table))))))
 
(define (shunt s)
(define widths (list 8 (string-length input) (string-length input) 20))
(tab widths "TOKEN" "OUT" "STACK" "ACTION")
(let shunt ([out '()] [ops '()] [in (string-split s)] [action ""])
(match in
['() (if (memf paren? ops)
(error "unmatched parens")
(reverse (append (reverse ops) out)))]
[(cons x in)
(tab widths x (string-join (reverse out) " ") (string-append* ops) action)
(match x
[(? string->number n) (shunt (cons n out) ops in (format "out ~a" n))]
["(" (shunt out (cons "(" ops) in "push (")]
[")" (let-values ([(l r) (splitf-at ops (λ (y) (not (string=? y "("))))])
(match r
['() (error "unmatched parens")]
[(cons _ r) (shunt (append (reverse l) out) r in "clear til )")]))]
[else (let-values ([(l r) (splitf-at ops (λ (y) (and (op? y)
((if (lasso? x) <= <) (prec x) (prec y)))))])
(shunt (append (reverse l) out) (cons x r) in (format "out ~a, push ~a" l x)))])])))
 
Output:
> (shunt input)
TOKEN   OUT                          STACK                        ACTION              
3                                                                                     
+       3                                                         out 3               
4       3                            +                            out (), push +      
*       3 4                          +                            out 4               
2       3 4                          *+                           out (), push *      
/       3 4 2                        *+                           out 2               
(       3 4 2 *                      /+                           out (*), push /     
1       3 4 2 *                      (/+                          push (              
-       3 4 2 * 1                    (/+                          out 1               
5       3 4 2 * 1                    -(/+                         out (), push -      
)       3 4 2 * 1 5                  -(/+                         out 5               
^       3 4 2 * 1 5 -                /+                           clear til )         
2       3 4 2 * 1 5 -                ^/+                          out (), push ^      
^       3 4 2 * 1 5 - 2              ^/+                          out 2               
3       3 4 2 * 1 5 - 2              ^^/+                         out (), push ^      
'("3" "4" "2" "*" "1" "5" "-" "2" "3" "^" "^" "/" "+")

REXX[edit]

These REXX versions below allow multi-character tokens   (both operands and operators).

assume expression is correct[edit]

/*REXX pgm converts infix arith. expressions to Reverse Polish notation (shunting─yard).*/
parse arg x /*obtain optional argument from the CL.*/
if x='' then x= '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3' /*Not specified? Then use the default.*/
ox=x
x='(' space(x) ") " /*force stacking for the expression. */
#=words(x) /*get number of tokens in expression. */
do i=1 for #; @.i=word(x, i) /*assign the input tokens to an array. */
end /*i*/
tell=1 /*set to 0 if working steps not wanted.*/
L=max( 20, length(x) ) /*use twenty for the minimum show width*/
 
say 'token' center("input" , L, '─') center("stack" , L%2, '─'),
center("output", L, '─') center("action", L, '─')
op= ")(-+/*^"; Rop=substr(op,3); p.=; n=length(op); RPN= /*some handy-dandy vars.*/
s.=
do i=1 for n; _=substr(op,i,1); s._=(i+1)%2; p._=s._+(i==n); end /*i*/
$= /* [↑] assign the operator priorities.*/
do k=1 for #;  ?=@.k /*process each token from the @. list.*/
select /*@.k is: (, operator, ), operand*/
when ?=='(' then do; $="(" $; call show 'moving'  ? "──► stack"; end
when isOp(?) then do;  !=word($, 1) /*get token from stack*/
do while ! \==')' & s.!>=p.?
RPN=RPN ! /*add token to RPN.*/
$=subword($, 2) /*del token from stack*/
call show 'unstacking:'  !
 !=word($, 1) /*get token from stack*/
end /*while*/
$=? $ /*add token to stack*/
call show 'moving'  ? "──► stack"
end
when ?==')' then do;  !=word($, 1) /*get token from stack*/
do while  !\=='('; RPN=RPN ! /*add token to RPN. */
$=subword($, 2) /*del token from stack*/
 != word($, 1) /*get token from stack*/
call show 'moving stack' ! "──► RPN"
end /*while*/
$=subword($, 2) /*del token from stack*/
call show 'deleting ( from the stack'
end
otherwise RPN=RPN ? /*add operand to RPN. */
call show 'moving'  ? "──► RPN"
end /*select*/
end /*k*/
say
RPN=space(RPN $) /*elide any superfluous blanks in RPN. */
say ' input:' ox; say " RPN──►" RPN /*display the input and the RPN. */
parse source upper . y . /*invoked via the C.L. or REXX pgm? */
if y=='COMMAND' then exit /*stick a fork in it, we're all done. */
else return RPN /*return RPN to invoker (the RESULT). */
/*──────────────────────────────────────────────────────────────────────────────────────────*/
isOp: return pos(arg(1),rOp) \== 0 /*is the first argument a "real" operator? */
show: if tell then say center(?,5) left(subword(x,k),L) left($,L%2) left(RPN,L) arg(1); return

output   when using the default input:

token ──────────────input─────────────── ──────stack────── ──────────────output────────────── ──────────────action──────────────
  (   ( 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 )  (                                                    moving ( ──► stack
  3   3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 )    (                 3                                  moving 3 ──► RPN
  +   + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 )      + (               3                                  moving + ──► stack
  4   4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 )        + (               3 4                                moving 4 ──► RPN
  *   * 2 / ( 1 - 5 ) ^ 2 ^ 3 )          * + (             3 4                                moving * ──► stack
  2   2 / ( 1 - 5 ) ^ 2 ^ 3 )            * + (             3 4 2                              moving 2 ──► RPN
  /   / ( 1 - 5 ) ^ 2 ^ 3 )              + (               3 4 2 *                            unstacking: *
  /   / ( 1 - 5 ) ^ 2 ^ 3 )              / + (             3 4 2 *                            moving / ──► stack
  (   ( 1 - 5 ) ^ 2 ^ 3 )                ( / + (           3 4 2 *                            moving ( ──► stack
  1   1 - 5 ) ^ 2 ^ 3 )                  ( / + (           3 4 2 * 1                          moving 1 ──► RPN
  -   - 5 ) ^ 2 ^ 3 )                    - ( / + (         3 4 2 * 1                          moving - ──► stack
  5   5 ) ^ 2 ^ 3 )                      - ( / + (         3 4 2 * 1 5                        moving 5 ──► RPN
  )   ) ^ 2 ^ 3 )                        ( / + (           3 4 2 * 1 5 -                      moving stack ( ──► RPN
  )   ) ^ 2 ^ 3 )                        / + (             3 4 2 * 1 5 -                      deleting ( from the stack
  ^   ^ 2 ^ 3 )                          ^ / + (           3 4 2 * 1 5 -                      moving ^ ──► stack
  2   2 ^ 3 )                            ^ / + (           3 4 2 * 1 5 - 2                    moving 2 ──► RPN
  ^   ^ 3 )                              ^ ^ / + (         3 4 2 * 1 5 - 2                    moving ^ ──► stack
  3   3 )                                ^ ^ / + (         3 4 2 * 1 5 - 2 3                  moving 3 ──► RPN
  )   )                                  ^ / + (           3 4 2 * 1 5 - 2 3 ^                moving stack ^ ──► RPN
  )   )                                  / + (             3 4 2 * 1 5 - 2 3 ^ ^              moving stack / ──► RPN
  )   )                                  + (               3 4 2 * 1 5 - 2 3 ^ ^ /            moving stack + ──► RPN
  )   )                                  (                 3 4 2 * 1 5 - 2 3 ^ ^ / +          moving stack ( ──► RPN
  )   )                                                    3 4 2 * 1 5 - 2 3 ^ ^ / +          deleting ( from the stack

input: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
RPN──► 3 4 2 * 1 5 - 2 3 ^ ^ / +

checks expression for balanced ()[edit]

Since these REXX versions of infix to RPN conversion affixes a leading   (   and trailing   )   to the expression, an
invalid expression such as   )  (   would be made legal by the aforemention affixing:     )   (  
gets transformed into     (   )   (   )  

Therefore, code was added to check for this condition, and also checks for mismatched parenthesis.

The   select   group could've been modified to check for mismatched parenthesis, but it would be harder to peruse the source.

/*REXX pgm converts infix arith. expressions to Reverse Polish notation (shunting─yard).*/
parse arg x /*obtain optional argument from the CL.*/
if x='' then x= '3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3' /*Not specified? Then use the default.*/
g=0 /* G is a counter of ( and ) */
do p=1 for words(x); _=word(x,p) /*catches unbalanced ( ) and ) ( */
if _=='(' then g=g+1
else if _==')' then do; g=g-1; if g<0 then g=-1e8; end
end /*p*/
ox=x
x='(' space(x) ") " /*force stacking for the expression. */
#=words(x) /*get number of tokens in expression. */
good= (g==0) /*indicate expression is good or bad.*/
do i=1 for #; @.i=word(x, i) /*assign the input tokens to an array. */
end /*i*/
tell=1 /*set to 0 if working steps not wanted.*/
L=max( 20, length(x) ) /*use twenty for the minimum show width*/
if good then say 'token' center("input" , L, '─') center("stack" , L%2, '─'),
center("output", L, '─') center("action", L, '─')
op= ")(-+/*^"; Rop=substr(op,3); p.=; n=length(op); RPN= /*some handy-dandy vars.*/
s.=
do i=1 for n; _=substr(op,i,1); s._=(i+1)%2; p._=s._+(i==n); end /*i*/
$= /* [↑] assign the operator priorities.*/
do k=1 for #*good;  ?=@.k /*process each token from the @. list.*/
select /*@.k is: ( operator ) operand.*/
when ?=='(' then do; $="(" $; call show 'moving'  ? "──► stack"; end
when isOp(?) then do;  !=word($, 1) /*get token from stack*/
do while ! \==')' & s.!>=p.?
RPN=RPN ! /*add token to RPN.*/
$=subword($, 2) /*del token from stack*/
call show 'unstacking:'  !
 !=word($, 1) /*get token from stack*/
end /*while*/
$=? $ /*add token to stack*/
call show 'moving'  ? "──► stack"
end
when ?==')' then do;  !=word($, 1) /*get token from stack*/
do while  !\=='('; RPN=RPN ! /*add token to RPN.*/
$=subword($, 2) /*del token from stack*/
 != word($, 1) /*get token from stack*/
call show 'moving stack' ! "──► RPN"
end /*while*/
$=subword($, 2) /*del token from stack*/
call show 'deleting ( from the stack'
end
otherwise RPN=RPN ? /*add operand to RPN.*/
call show 'moving'  ? "──► RPN"
end /*select*/
end /*k*/
say
RPN=space(RPN $); if \good then RPN= '─────── error in expression ───────' /*error? */
say ' input:' ox; say " RPN──►" RPN /*display the input and the RPN. */
parse source upper . y . /*invoked via the C.L. or REXX pgm? */
if y=='COMMAND' then exit /*stick a fork in it, we're all done. */
else return RPN /*return RPN to invoker (the RESULT). */
/*──────────────────────────────────────────────────────────────────────────────────────────*/
isOp: return pos(arg(1), Rop) \== 0 /*is the first argument a "real" operator? */
show: if tell then say center(?,5) left(subword(x,k),L) left($,L%2) left(RPN,L) arg(1); return

output   when using the input: )   (

 input: ) (
 RPN──► ─────── error in expression ───────

Ruby[edit]

See Parsing/RPN/Ruby

rpn = RPNExpression.from_infix("3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3")

outputs

for Infix expression: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
Term	Action	Output	Stack
3	PUSH V	["3"]	[]
+	PUSH OP	["3"]	["+"]
4	PUSH V	["3", "4"]	["+"]
*	PUSH OP	["3", "4"]	["+", "*"]
2	PUSH V	["3", "4", "2"]	["+", "*"]
/	MUL	["3", "4", "2", "*"]	["+"]	* has higher precedence than /
/	PUSH OP	["3", "4", "2", "*"]	["+", "/"]
(	OPEN_P	["3", "4", "2", "*"]	["+", "/", "("]
1	PUSH V	["3", "4", "2", "*", "1"]	["+", "/", "("]
-	PUSH OP	["3", "4", "2", "*", "1"]	["+", "/", "(", "-"]
5	PUSH V	["3", "4", "2", "*", "1", "5"]	["+", "/", "(", "-"]
)	SUB	["3", "4", "2", "*", "1", "5", "-"]	["+", "/", "("]	unwinding parenthesis
)	CLOSE_P	["3", "4", "2", "*", "1", "5", "-"]	["+", "/"]
^	PUSH OP	["3", "4", "2", "*", "1", "5", "-"]	["+", "/", "^"]
2	PUSH V	["3", "4", "2", "*", "1", "5", "-", "2"]	["+", "/", "^"]
^	PUSH OP	["3", "4", "2", "*", "1", "5", "-", "2"]	["+", "/", "^", "^"]
3	PUSH V	["3", "4", "2", "*", "1", "5", "-", "2", "3"]	["+", "/", "^", "^"]
RPN = 3 4 2 * 1 5 - 2 3 ^ ^ / +

Sidef[edit]

Translation of: Perl 6
var prec = Hash(
'^' => 4,
'*' => 3,
'/' => 3,
'+' => 2,
'-' => 2,
'(' => 1,
);
 
var assoc = Hash(
'^' => 'right',
'*' => 'left',
'/' => 'left',
'+' => 'left',
'-' => 'left',
);
 
func shunting_yard(prog) {
var inp = prog.words;
var ops = [];
var res = [];
 
func report (op) { printf("%25s  %-7s %10s %s\n", res.join(' '), ops.join(' '), op, inp.join(' ')) }
func shift (t) { report( "shift #{t}"); ops << t }
func reduce (t) { report("reduce #{t}"); res << t }
 
while (inp) {
given(var t = inp.shift) {
when (/\d/) { reduce(t) }
when ('(') { shift(t) }
when (')') { var x; while (ops && (x = ops.pop) && (x != '(')) { reduce(x) } }
default {
var newprec = prec{t};
while (ops) {
var oldprec = prec{ops[-1]};
 
break if (newprec > oldprec)
break if ((newprec == oldprec) && (assoc{t} == 'right'))
 
reduce(ops.pop);
}
shift(t);
}
}
}
while (ops) { reduce(ops.pop) }
return res
}
 
say shunting_yard('3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3').join(' ');
Output:
                                       reduce 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                        3               shift + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                        3    +         reduce 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
                      3 4    +          shift * 2 / ( 1 - 5 ) ^ 2 ^ 3
                      3 4    + *       reduce 2 / ( 1 - 5 ) ^ 2 ^ 3
                    3 4 2    +         reduce * ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    +          shift / ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    + /        shift ( 1 - 5 ) ^ 2 ^ 3
                  3 4 2 *    + / (     reduce 1 - 5 ) ^ 2 ^ 3
                3 4 2 * 1    + / (      shift - 5 ) ^ 2 ^ 3
                3 4 2 * 1    + / ( -   reduce 5 ) ^ 2 ^ 3
              3 4 2 * 1 5    + / (     reduce - ^ 2 ^ 3
            3 4 2 * 1 5 -    + /        shift ^ 2 ^ 3
            3 4 2 * 1 5 -    + / ^     reduce 2 ^ 3
          3 4 2 * 1 5 - 2    + / ^      shift ^ 3
          3 4 2 * 1 5 - 2    + / ^ ^   reduce 3 
        3 4 2 * 1 5 - 2 3    + / ^     reduce ^ 
      3 4 2 * 1 5 - 2 3 ^    + /       reduce ^ 
    3 4 2 * 1 5 - 2 3 ^ ^    +         reduce / 
  3 4 2 * 1 5 - 2 3 ^ ^ /              reduce + 
3 4 2 * 1 5 - 2 3 ^ ^ / +

Swift[edit]

import Foundation
 
// Using arrays for both stack and queue
struct Stack<T> {
private(set) var elements = [T]()
var isEmpty: Bool { return elements.isEmpty }
 
mutating func push(newElement: T) {
elements.append(newElement)
}
 
mutating func pop() -> T {
return elements.removeLast()
}
 
func top() -> T? {
return elements.last
}
}
 
struct Queue<T> {
private(set) var elements = [T]()
var isEmpty: Bool { return elements.isEmpty }
 
mutating func enqueue(newElement: T) {
elements.append(newElement)
}
 
mutating func dequeue() -> T {
return elements.removeFirst()
}
}
 
enum Associativity { case Left, Right }
 
// Define abstract interface, which can be used to restrict Set extension
protocol OperatorType: Comparable, Hashable {
var name: String { get }
var precedence: Int { get }
var associativity: Associativity { get }
}
 
struct Operator: OperatorType {
let name: String
let precedence: Int
let associativity: Associativity
// same operator names are not allowed
var hashValue: Int { return "\(name)".hashValue }
 
init(_ name: String, _ precedence: Int, _ associativity: Associativity) {
self.name = name; self.precedence = precedence; self.associativity = associativity
}
}
 
func ==(x: Operator, y: Operator) -> Bool {
// same operator names are not allowed
return x.name == y.name
}
 
func <(x: Operator, y: Operator) -> Bool {
// compare operators by their precedence and associavity
return (x.associativity == .Left && x.precedence == y.precedence) || x.precedence < y.precedence
}
 
extension Set where Element: OperatorType {
func contains(op: String?) -> Bool {
guard let operatorName = op else { return false }
return contains { $0.name == operatorName }
}
 
subscript (operatorName: String) -> Element? {
get {
return filter { $0.name == operatorName }.first
}
}
}
 
// Convenience
extension String {
var isNumber: Bool { return Double(self) != nil }
}
 
struct ShuntingYard {
enum Error: ErrorType {
case MismatchedParenthesis(String)
case UnrecognizedToken(String)
}
 
static func parse(input: String, operators: Set<Operator>) throws -> String {
var stack = Stack<String>()
var output = Queue<String>()
let tokens = input.componentsSeparatedByString(" ")
 
for token in tokens {
// Wikipedia: if token is a number add it to the output queue
if token.isNumber {
output.enqueue(token)
}
// Wikipedia: else if token is a operator:
else if operators.contains(token) {
// Wikipedia: while there is a operator on top of the stack and has lower precedence than current operator (token)
while operators.contains(stack.top()) && hasLowerPrecedence(token, stack.top()!, operators) {
// Wikipedia: pop it off to the output queue
output.enqueue(stack.pop())
}
// Wikipedia: push current operator (token) onto the operator stack
stack.push(token)
}
// Wikipedia: If the token is a left parenthesis, then push it onto the stack.
else if token == "(" {
stack.push(token)
}
// Wikipedia: If the token is a right parenthesis:
else if token == ")" {
// Wikipedia: Until the token at the top of the stack is a left parenthesis
while !stack.isEmpty && stack.top() != "(" {
// Wikipedia: pop operators off the stack onto the output queue.
output.enqueue(stack.pop())
}
 
// If the stack runs out, than there are mismatched parentheses.
if stack.isEmpty {
throw Error.MismatchedParenthesis(input)
}
 
// Wikipedia: Pop the left parenthesis from the stack, but not onto the output queue.
stack.pop()
}
// if token is not number, operator or a parenthesis, then is not recognized
else {
throw Error.UnrecognizedToken(token)
}
}
 
// Wikipedia: When there are no more tokens to read:
 
// Wikipedia: While there are still operator tokens in the stack:
while operators.contains(stack.top()) {
// Wikipedia: Pop the operator onto the output queue.
output.enqueue(stack.pop())
}
 
// Wikipedia: If the operator token on the top of the stack is a parenthesis, then there are mismatched parentheses
// Note: Assume that all operators has been poped onto the output queue.
if stack.isEmpty == false {
throw Error.MismatchedParenthesis(input)
}
 
return output.elements.joinWithSeparator(" ")
}
 
static private func containsOperator(stack: Stack<String>, _ operators: [String: NSDictionary]) -> Bool {
guard stack.isEmpty == false else { return false }
// Is there a matching operator in the operators set?
return operators[stack.top()!] != nil ? true : false
}
 
static private func hasLowerPrecedence(x: String, _ y: String, _ operators: Set<Operator>) -> Bool {
guard let first = operators[x], let second = operators[y] else { return false }
return first < second
}
}
 
let input = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
let operators: Set<Operator> = [
Operator("^", 4, .Right),
Operator("*", 3, .Left),
Operator("/", 3, .Left),
Operator("+", 2, .Left),
Operator("-", 2, .Left)
]
let output = try! ShuntingYard.parse(input, operators: operators)
 
print("input: \(input)")
print("output: \(output)")
 
Output:
input: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
output: 3 4 2 * 1 5 - 2 3 ^ ^ / +

Tcl[edit]

package require Tcl 8.5
 
# Helpers
proc tokenize {str} {
regexp -all -inline {[\d.]+|[-*^+/()]} $str
}
proc precedence op {
dict get {^ 4 * 3 / 3 + 2 - 2} $op
}
proc associativity op {
if {$op eq "^"} {return "right"} else {return "left"}
}
 
proc shunting {expression} {
set stack {}
foreach token [tokenize $expression] {
if {[string is double $token]} {
puts "add to output: $token"
lappend output $token
} elseif {$token eq "("} {
puts "push parenthesis"
lappend stack $token
} elseif {$token eq ")"} {
puts "popping to parenthesis"
while {[lindex $stack end] ne "("} {
lappend output [lindex $stack end]
set stack [lreplace $stack end end]
puts "...popped [lindex $output end] to output"
}
set stack [lreplace $stack end end]
puts "...found parenthesis"
} else {
puts "adding operator: $token"
set p [precedence $token]
set a [associativity $token]
while {[llength $stack]} {
set o2 [lindex $stack end]
if {
$o2 ne "(" &&
(($a eq "left" && $p <= [precedence $o2]) ||
($a eq "right" && $p < [precedence $o2]))
} then {
puts "...popped operator $o2 to output"
lappend output $o2
set stack [lreplace $stack end end]
} else {
break
}
}
lappend stack $token
}
puts "\t\tOutput:\t$output\n\t\tStack:\t$stack"
}
puts "transferring tokens from stack to output"
lappend output {*}[lreverse $stack]
}
 
puts [shunting "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"]

Output:

add to output: 3
		Output:	3
		Stack:	
adding operator: +
		Output:	3
		Stack:	+
add to output: 4
		Output:	3 4
		Stack:	+
adding operator: *
		Output:	3 4
		Stack:	+ *
add to output: 2
		Output:	3 4 2
		Stack:	+ *
adding operator: /
...popped operator * to output
		Output:	3 4 2 *
		Stack:	+ /
push parenthesis
		Output:	3 4 2 *
		Stack:	+ / (
add to output: 1
		Output:	3 4 2 * 1
		Stack:	+ / (
adding operator: -
		Output:	3 4 2 * 1
		Stack:	+ / ( -
add to output: 5
		Output:	3 4 2 * 1 5
		Stack:	+ / ( -
popping to parenthesis
...popped - to output
...found parenthesis
		Output:	3 4 2 * 1 5 -
		Stack:	+ /
adding operator: ^
		Output:	3 4 2 * 1 5 -
		Stack:	+ / ^
add to output: 2
		Output:	3 4 2 * 1 5 - 2
		Stack:	+ / ^
adding operator: ^
		Output:	3 4 2 * 1 5 - 2
		Stack:	+ / ^ ^
add to output: 3
		Output:	3 4 2 * 1 5 - 2 3
		Stack:	+ / ^ ^
transferring tokens from stack to output
3 4 2 * 1 5 - 2 3 ^ ^ / +


VBA[edit]

Translation of: Liberty BASIC
Option Explicit
Option Base 1
 
Function ShuntingYard(strInfix As String) As String
Dim i As Long, j As Long, token As String, tokenArray() As String
Dim stack() As Variant, queue() As Variant, discard As String
Dim op1 As String, op2 As String
 
Debug.Print strInfix
 
' Get tokens
tokenArray = Split(strInfix)
 
' Initialize array (removed later)
ReDim stack(1)
ReDim queue(1)
 
' Loop over tokens
Do While 1
i = i + 1
If i - 1 > UBound(tokenArray) Then
Exit Do
Else
token = tokenArray(i - 1) 'i-1 due to Split returning a Base 0
End If
If token = "" Then: Exit Do
 
' Print
Debug.Print i, token, Join(stack, ","), Join(queue, ",")
' If-loop over tokens (either brackets, operators, or numbers)
If token = "(" Then
stack = push(token, stack)
ElseIf token = ")" Then
While Peek(stack) <> "("
queue = push(pop(stack), queue)
Wend
discard = pop(stack) 'discard "("
ElseIf isOperator(token) Then
op1 = token
Do While (isOperator(Peek(stack)))
' Debug.Print Peek(stack)
op2 = Peek(stack)
If op2 <> "^" And precedence(op1) = precedence(op2) Then
'"^" is the only right-associative operator
queue = push(pop(stack), queue)
ElseIf precedence(op1$) < precedence(op2$) Then
queue = push(pop(stack), queue)
Else
Exit Do
End If
Loop
stack = push(op1, stack)
Else 'number
'actually, wrong operator could end up here, like say %
'If the token is a number, then add it to the output queue.
queue = push(CStr(token), queue)
End If
Loop
 
While stack(1) <> ""
If Peek(stack) = "(" Then Debug.Print "no matching ')'": End
queue = push(pop(stack), queue)
Wend
 
' Print final output
ShuntingYard = Join(queue, " ")
Debug.Print "Output:"
Debug.Print ShuntingYard
End Function
 
'------------------------------------------
Function isOperator(op As String) As Boolean
isOperator = InStr("+-*/^", op) <> 0 And Len(op$) = 1
End Function
 
Function precedence(op As String) As Integer
If isOperator(op$) Then
precedence = 1 _
- (InStr("+-*/^", op$) <> 0) _
- (InStr("*/^", op$) <> 0) _
- (InStr("^", op$) <> 0)
End If
End Function
 
'------------------------------------------
Function push(str, stack) As Variant
Dim out() As Variant, i As Long
If Not IsEmpty(stack(1)) Then
out = stack
ReDim Preserve out(1 To UBound(stack) + 1)
out(UBound(out)) = str
Else
ReDim out(1 To 1)
out(1) = str
End If
push = out
End Function
 
Function pop(stack)
pop = stack(UBound(stack))
If UBound(stack) > 1 Then
ReDim Preserve stack(1 To UBound(stack) - 1)
Else
stack(1) = ""
End If
End Function
 
Function Peek(stack)
Peek = stack(UBound(stack))
End Function
Output:
?ShuntingYard("3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3")
3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
 1            3                           
 2            +                           3
 3            4             +             3
 4            *             +             3,4
 5            2             +,*           3,4
 6            /             +,*           3,4,2
 7            (             +,/           3,4,2,*
 8            1             +,/,(         3,4,2,*
 9            -             +,/,(         3,4,2,*,1
 10           5             +,/,(,-       3,4,2,*,1
 11           )             +,/,(,-       3,4,2,*,1,5
 12           ^             +,/           3,4,2,*,1,5,-
 13           2             +,/,^         3,4,2,*,1,5,-
 14           ^             +,/,^         3,4,2,*,1,5,-,2
 15           3             +,/,^,^       3,4,2,*,1,5,-,2
Output:
3 4 2 * 1 5 - 2 3 ^ ^ / +

zkl[edit]

Translation of: Go
var input = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3";
 
var opa = D("^",T(4,True), "*",T(3,False), // op:(prec,rAssoc)
"/",T(3,False), "+",T(2,False), "-",T(2,False),
);
 
"infix: ".println(input);
"postfix:".println(parseInfix(input));
 
fcn parseInfix(e){
stack := List(); // holds operators and left parenthesis
rpn:="";
foreach tok in (e.split(" ")){
switch(tok){
case("("){ stack.append(tok) } // push "(" to stack
case(")"){
while(True){ // pop item ("(" or operator) from stack
op:=stack.pop();
if(op == "(") break; // discard "("
rpn += " " + op; // add operator to result
}
}
else{ // default
o1 := opa.find(tok); // op or Void
if(o1){ // token is an operator
while(stack){
// consider top item on stack
op := stack[-1]; o2 := opa.find(op);
if(not o2 or o1[0] > o2[0] or
(o1[0] == o2[0] and o1[1])) break;
// top item is an operator that needs to come off
stack.pop();
rpn += " " + op; // add it to result
}
// push operator (the new one) to stack
stack.append(tok);
}else // token is an operand
rpn += (rpn and " " or "") + tok; // add operand to result
}
} // switch
display(tok,rpn,stack);
} // foreach
// drain stack to result
rpn + stack.reverse().concat(" ");
}
fcn display(tok,rpn,stack){
"Token|".println(tok);
"Stack|".println(stack.concat());
"Queue|".println(rpn);
println();
}
Output:
infix:  3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
Token|3
Stack|
Queue|3

Token|+
Stack|+
Queue|3

Token|4
Stack|+
Queue|3 4

Token|*
Stack|+*
Queue|3 4

Token|2
Stack|+*
Queue|3 4 2

Token|/
Stack|+/
Queue|3 4 2 *

Token|(
Stack|+/(
Queue|3 4 2 *

Token|1
Stack|+/(
Queue|3 4 2 * 1

Token|-
Stack|+/(-
Queue|3 4 2 * 1

Token|5
Stack|+/(-
Queue|3 4 2 * 1 5

Token|)
Stack|+/
Queue|3 4 2 * 1 5 -

Token|^
Stack|+/^
Queue|3 4 2 * 1 5 -

Token|2
Stack|+/^
Queue|3 4 2 * 1 5 - 2

Token|^
Stack|+/^^
Queue|3 4 2 * 1 5 - 2

Token|3
Stack|+/^^
Queue|3 4 2 * 1 5 - 2 3

postfix:3 4 2 * 1 5 - 2 3^ ^ / +