How to evaluate arithmetic expression using stack c?

问题

by now I just finish the expression turning to postfix expression, and I try to evaluate but something goes wrong and confusing me long time, and I just know how to fix it.

This is my code turn to postfix expression:

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

    #define STACK_INIT_SIZE 20
    #define STACKINCREMENT  10
    #define MAXBUFFER       10
    #define OK              1
    #define ERROR           0

    typedef char ElemType;
    typedef int Status;

    typedef struct {
        ElemType *base;
        ElemType *top;
        int stackSize;
    }sqStack;

    Status InitStack(sqStack *s) {
        s->base = (ElemType *)malloc(STACK_INIT_SIZE * sizeof(ElemType));

        if ( !s->base ) {
            exit(0);
        }

        s->top = s->base;
        s->stackSize = STACK_INIT_SIZE;

        return OK;
    }

    Status Push(sqStack *s, ElemType e) {
        //if the stack is full
        if ( s->top - s->base >= s->stackSize ) {
            s->base = (ElemType *)realloc(s->base, (s->stackSize + STACKINCREMENT) * sizeof(ElemType));

            if ( !s->base ) {
                exit(0);
            }

            s->top = s->base + s->stackSize;
            s->stackSize += STACKINCREMENT;
        }
        //store data
        *(s->top) = e;
        s->top++;

        return OK;
    }

    Status Pop(sqStack *s, ElemType *e) {
        if ( s->top == s->base ) {
            return ERROR;
        }

        *e = *--(s->top);

        return OK;
    }

    int StackLen(sqStack s) {
        return (s.top - s.base);
    }

    int main() {
        sqStack s;
        char c;
        char e;

        InitStack(&s);

        printf("Please input your calculate expression(# to quit):\n");
        scanf("%c", &c);

        while ( c != '#' ) {
            while ( c >= '0' && c <= '9' ) {
                printf("%c", c);
                scanf("%c", &c);

                if ( c < '0' || c > '9' ) {
                    printf(" ");
                }
            }

            if ( ')' == c ) {
                Pop(&s, &e);

                while ( '(' != e ) {
                    printf("%c ", e);
                    Pop(&s, &e);
                }
            } else if ( '+' == c || '-' == c ) {
                if ( !StackLen(s) ) {
                    Push(&s, c);
                } else {
                    do {
                        Pop(&s, &e);
                        if ( '(' == e ) {
                            Push(&s, e);
                        } else {
                            printf("%c", e);
                        }
                    }while ( StackLen(s) && '(' != e );

                    Push(&s, c);
                } 
            } else if ( '*' == c || '/' == c || '(' == c ) {
                Push(&s, c);
            } else if ( '#' == c ) {
                break;
            } else {
                printf("\nInput format error!\n");
                return -1;
            }

            scanf("%c", &c);
        }

        while ( StackLen(s) ) {
            Pop(&s, &e);
            printf("%c ", e);
        }

        return 0;

    }

When I put 3*(7-2)# it returns 3 7 2 -

Things go right, but I don't know how to do evaluate it next, I just turn it to postfix expression and I want to evaluate it using stack.

回答1:

You have not taken care of operator precedence at all while converting to polish notation. Its difficult to give full code but this is how i did it assuming we build a string along strBuild.

Converting to RPN

               if (token is integer)
                {
                    strBuild.Append(token);  
                    strBuild.Append(" ");
                }
                else if (token is Operator)
                {
                    while (isOperator(Stack.Peek()))
                    {
                        if (GetExprPrecedence(token) <= GetExprPrecedence(Stack.Peek()))
                        {
                            strBuild.Append(Stack.Pop());
                            strBuild.Append(" ");
                        }
                        else
                            break;
                    }
                    Stack.Push(token);
                }
                else if (token == '(')
                {
                    Stack.Push(token);
                }
                else if (token == ')')
                {
                    while (Stack.Peek() != '(')
                    {
                        if (Stack.Count > 0)
                        {
                            strBuild.Append(Stack.Pop());
                            strBuild.Append(" ");
                        }
                        else
                        {
                            Show("Syntax Error while Parsing");
                            break;
                        }
                    }
                    Stack.Pop();
                }

        while (Stack.Count > 0 && isOperator(Stack.Peek()))
        {
            if (Stack.Peek() == '(' || Stack.Peek() == ')')
            {
                MessageBox.Show("All Tokens Read - Syntax Error");
                break;
            }
            Stack.Pop();
        }
        return strBuild;

strBuild should be the RPN string. Now to evaluate.

Evaluate

        for (int i = 0; i < StrPostFix.Length; i++)
        {
            token = StrPostFix[i];
            if (isOperator(token))
            {
                switch (token)
                {
                    case "/":
                        op2 = Stack.Pop();
                        op1 = Stack.Pop();
                        val = op1 / op2;
                        break;
                    case "*":
                        op2 = Stack.Pop();
                        op1 = Stack.Pop();
                        val = op1 * op2;
                        break;
                    case "+":
                        op2 = Stack.Pop();
                        op1 = Stack.Pop();
                        val = op1 + op2;
                        break;
                    case "-":
                        op2 = Stack.Pop();
                        op1 = Stack.Pop();
                        val = op1 - op2;
                        break;
                }
                Stack.Push(val);
            }
            else
                Stack.Push(token);
        }
        return Stack.Pop();

return Stack.Pop(); pops the evaluated value and returns. Now for your main doubt which i did not answer since you have not taken care of it, this is how you can handle precedence issue:

enum OperatorPrecedence { Add, Minus, Mult, Div, Brackets };

    int GetExprPrecedence(string op)
    {
        int p = 0;
        switch (op)
        {
            case "(":
                p = (int)OperatorPrecedence .Brackets;
                break;
            case "/":
                p = (int)OperatorPrecedence .Div;
                break;
            case "*":
                p = (int)OperatorPrecedence .Mult;
                break;
            case "-":
                p = (int)OperatorPrecedence .Minus;
                break;
            case "+":
                p = (int)OperatorPrecedence .Add;
                break;
        }
        return p;
    }

Note the pseudo-code resembles C-Sharp since that is what i work on. I have tried my best to make it look algorithmic and also not vague so that you can relate to your code. Result by my Algorithm:

Note i use Box Brackets [ instead of Round (for my expressions. Final Answer was 15.

来源：https://stackoverflow.com/questions/19443251/how-to-evaluate-arithmetic-expression-using-stack-c