Infix to Postfix Algorithm in C

Question

I'm solve an exercise in which one of the functions has to translate infix notation to postfix notation. Here follows my whole code

#include<stdio.h>
#define MAX 100
char stack[MAX];
int top;
void compact(char Descomp[], char Compac[]);
void init_stack();
int push(char Elem);
int desempilha(char *Elem);
int priority(char Operator);
int arity(char Exp[], int position);
int translate_pos(char exp[], char exp_pos[]);
int main()
    {
        char Exp[MAX]; /* stores the expression read from stdin */
            char Exp_compact[MAX]; /* stores expression without spaces */
            char Exp_pos[MAX]; /* stores the expression after the translation for postfix*/
            int indicator; /* indicate if an error occurred, 0 for NO ERROR and -1 for ERROR*/
            indicator = 0;
            printf("\nType the expression: ");
            gets(Exp);
            compact(Exp, Exp_compact);
            indicator = translate_pos(Exp_compact, Exp_pos);
            puts(Exp_pos);
            return indicator;
        }
/* compact function delete spaces within the expression read from stdin */
void compact(char Descomp[], char Compac[])
        {
            int i;
            int j;
            i = 0;
            j = 0;
            while(Descomp[j] != '\0')
                {
                    if(Descomp[j] != ' ')
                        {
                            Compac[i] = Descomp[j];
                            i++;
                        }
                    j++;
                }
        }
/* initiate the stack by setting top = -1 */
void init_stack()
        {
            top = -1;
        }
/* puts the element Elem in the stack */
int push(char Elem)
        {
            if(top == MAX - 1) /* Stack is full */
                return -1;
            top++;
            stack[top] = Elem;
            return 0;
        }
/* remove the element in stack[top] and puts it in &Elem*/
int pop(char *Elem)
        {
            if(top == -1) /* stack is empty */
                return -1;
            *Elem = stack[top];
            top--;
            return 0;
        }
/* Return the priority of an operator */
int priority(char Operator)
        {
            switch(Operator)
                {
                    case '+': return 1;
                    case '-': return 1;
                    case '*': return 2;
                    case '/': return 2;
                    case '^': return 3;
                    case '(': return 4;
                    case ')': return 5;
                    default : return 0; 
                }
        }
/* returns the arity of CONSTANTS + - * / and ^, for ( an ) is merely symbolic */
int arity(char Exp[], int position)
        {
            if(priority(Exp[position]) == 1)
                {
                    if( (position == 0) || ( (priority(Exp[position - 1]) >= 1) && (priority(Exp[position - 1]) <= 3) ))
                        return 1;
                    else
                        return 2;
                }
            else if( (priority(Exp[position]) > 1) && (priority(Exp[position]) <= 4))
                return 2;
            else
                return priority(Exp[position]);
        }
/* reads an infix expression and returns postfix expression */ 
int translate_pos(char exp[], char exp_pos[])
        {
            int i;
            int j;
            int ind;
            char trash;
            i = 0;
            j = 0;
            ind = 0;
            trash = ' ';
                    init_stack();
            while(exp[i]!= '\0')
                {
                    if(arity(exp, i) == 0)
                        {
                            exp_pos[j] = exp[i];
                            j++;
                        }
                    if(arity(exp, i) == 1)
                        {
                            switch(exp[i])
                                {
                                    case '-': 
                                        {
                                            exp_pos[j] = exp_pos[i];
                                            j++;
                                        }
                                    case '+': trash = exp_pos[i];
                                }
                        }
                    if(arity(exp, i) == 2)
                        {
                            while((top != -1) && (priority(stack[top]) <= priority(exp[i])))
                                {
                                    ind = pop(&exp_pos[j]);
                                    j++;
                                }
                            ind = push(exp[i]);
                        }
                    if(priority(exp[i]) == 4)
                        {
                            ind = push(exp[i]);
                        }
                    if(priority(exp[i]) == 5)
                        {
                            while( (top != -1) && (stack[top] != '('))
                                {
                                    ind = pop(&exp_pos[j]);
                                    j++;
                                }
                            if(stack[top] == '(')
                                ind = pop(&trash);
                        }
                    i++;
                }
            while(top != -1)
                {
                    ind = pop(&exp_pos[j]);
                    j++;
                }
            return ind;

    }

The algorithm I used to translate the expression is

while there is token to be read;
read the token;
if token is a constant
    push it to Exp_Postfix;
if token is '('
    push it to stack
if token is ')'
    pop from the stack all symbols until '(' be find and remove '(' from the stack
if token is an operator and its arity is 2
    pop all operators with less or equal priority than the token and store then in the Exp_Postfix;
    push token to the stack;
if token is an operator and its arity is 1
    if token is '-'
          push it to Exp_postfix;
    if token is '+'
          pass to the next token;
pop all remaining symbols in the stack and push then, in order, to the Exp_Postfix;

I compiled the .c archive using

gcc -Wall archive.c -o archive

and executed it. I give the expression

5+(6*9^14)

It the returned expression was

I do not now if the error is in my code or in solution to the problem.

This doesn't bear directly on the problem you're reporting, but your compact function doesn't ensure that the \0 terminator is included at the end of Compac[]. — lurker
– lurker, Commented Sep 24, 2013 at 13:58
@Paulo I don't think it will fix your problem, but it should be corrected to prevent a potential memory overrun. Also, on the debugger, of course it might indicate "exit normally" but you should set breakpoints to determine if the code goes where you expect it, and to examine data to see if it's what you might expect to help resolve the problem. — lurker
– lurker, Commented Sep 24, 2013 at 14:15
@PauloHenrique: I meant stepping through the code while observing the state of the program at every step, to see where what actually happens diverges from what you expect to happen. — NPE
– NPE, Commented Sep 24, 2013 at 14:15

Crowman · Accepted Answer · 2013-09-27 22:20:52Z

There are an awful lot of problems, here, for instance:

compact() and translate_pos() leave Exp_compact and Exp_pos, respectively, without a terminating \0, so you're getting garbage printed out.
your arity() function is returning 2 for an opening parenthesis.
in the first switch statement of translate_pos(), you're missing break statements.
Your priority comparison in translate_pos() when arity is 2 is back to front.
When you're comparing operator precedence, you should treat an opening parenthesis specially, since it should have the lowest precedence when on the top of the stack.
You should have a lot more else keywords in translate_pos().
You're using gets(), which was always bad, and now has actually been removed from C.

I haven't exhaustively tested it, but here's a correct version that seems to work for all the test inputs I tried:

#include <stdio.h>
#include <ctype.h>
#include <assert.h>


/*  Function prototypes  */

void compact(char Descomp[], char Compac[]);
void init_stack();
int push(char Elem);
int desempilha(char *Elem);
int priority(char Operator);
int arity(char Exp[], int position);
int translate_pos(char exp[], char exp_pos[]);


/*  Stack variables  */

#define MAX 100
char stack[MAX];
int top;


int main(void) {
    char Exp[MAX];
    char Exp_compact[MAX] = {0};
    char Exp_pos[MAX] = {0};
    int indicator = 0;

    printf("\nType the expression: ");
    fgets(Exp, MAX, stdin);
    compact(Exp, Exp_compact);

    indicator = translate_pos(Exp_compact, Exp_pos);
    puts(Exp_pos);
    return indicator;
}


/* compact function delete spaces within the expression read from stdin */

void compact(char Descomp[], char Compac[]) {
    int i = 0;
    int j = 0;

    while ( Descomp[j] ) {
        if ( !isspace(Descomp[j]) ) {
            Compac[i++] = Descomp[j];
        }
        j++;
    }
}


/* initiate the stack by setting top = -1 */

void init_stack() {
    top = -1;
}


/* puts the element Elem in the stack */

int push(char Elem) {
    if (top == MAX - 1)         /* Stack is full */
        return -1;
    stack[++top] = Elem;
    return 0;
}


/* remove the element in stack[top] and puts it in &Elem*/

int pop(char *Elem) {
    if (top == -1)              /* stack is empty */
        return -1;
    *Elem = stack[top--];
    return 0;
}


/* Return the priority of an operator */

int priority(char Operator) {
    switch (Operator) {
        case '+':
            return 1;
        case '-':
            return 1;
        case '*':
            return 2;
        case '/':
            return 2;
        case '^':
            return 3;
        case '(':
            return 4;
        case ')':
            return 5;
        default:
            return 0;
    }
}


/* returns the arity of OPERATORS + - * / and ^,
 * for ( an ) is merely symbolic */

int arity(char Exp[], int position) {
    if ( priority(Exp[position]) == 1 ) {
        if ( (position == 0) ||
             ((priority(Exp[position - 1]) >= 1) &&
              (priority(Exp[position - 1]) <= 3)) ) {
            return 1;
        } else {
            return 2;
        }
    } else if ( (priority(Exp[position]) > 1) &&
                (priority(Exp[position]) <= 3) ) {
        return 2;
    } else {
        return priority(Exp[position]);
    }
}


/* reads an infix expression and returns postfix expression */

int translate_pos(char exp[], char exp_pos[]) {
    int i = 0, j = 0, ind = 0;
    char trash = ' ';

    init_stack();

    while ( exp[i] ) {
        if ( arity(exp, i) == 0 ) {
            exp_pos[j++] = exp[i];
        } else if ( arity(exp, i) == 1 ) {
            switch (exp[i]) {
                case '-':
                    exp_pos[j++] = exp[i];
                    break;
                case '+':
                    trash = exp_pos[i];
                    break;
                default:
                    assert(0);
            }
        } else if (arity(exp, i) == 2) {
            while ( (top != -1) &&
                    (priority(stack[top]) >= priority(exp[i])) &&
                    stack[top] != '(' ) {
                ind = pop(&exp_pos[j++]);
            }
            ind = push(exp[i]);
        } else if ( priority(exp[i]) == 4 ) {
            ind = push(exp[i]);
        } else if ( priority(exp[i]) == 5 ) {
            while ( (top != -1) && (stack[top] != '(') ) {
                ind = pop(&exp_pos[j++]);
            }
            if ( (top != - 1) && stack[top] == '(') {
                ind = pop(&trash);
            }
        }
        i++;
    }

    while (top != -1) {
        ind = pop(&exp_pos[j++]);
    }

    return ind;
}

Gives the following output for various test cases:

paul@local:~/src/c/postfix$ ./postfix

Type the expression: 1+2
12+
paul@local:~/src/c/postfix$ ./postfix

Type the expression: (1+2)
12+
paul@local:~/src/c/postfix$ ./postfix

Type the expression: 1+2*3
123*+
paul@local:~/src/c/postfix$ ./postfix

Type the expression: (1+2)*3
12+3*
paul@local:~/src/c/postfix$ ./postfix

Type the expression: (3+4)*4/2
34+4*2/
paul@local:~/src/c/postfix$ ./postfix

Type the expression: 5+(6*9^14)
56914^*+
paul@local:~/src/c/postfix$

I'd suggest comparing my code to yours and trying to understand the individual differences to see where you were going wrong.

when I type operators with arity 1, it returns anything, e.g -a+b+c, the output is empty. Can the problem with compact function be solved without the function isspace?
1. OK - have you tried to fix it? 2. You can, sure, but there's no reason to, this is exactly the kind of thing isspace() is for.
@PauloHenrique: I fixed the issue, there was a line in translate_pos() in my solution which was exp_pos[j++] = exp_pos[i];, and should have been exp_pos[j++] = exp[i];, my bad.
I did fix too, I used an another (distint from +, -, *, ` and ^` and used the arity function while performing the calculation) symbol to indicate the change in the signal of a constant. Thank you very much.

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