C Arithmetic Expression Calculator

debugcn Published at Dev

user2976897

I have to implement an expression calculator without using stacks. I'm just really confused as to how to start this. If anyone could explain to me what I'm supposed to do, I would really appreciate it. I realize this isn't the best question, nor is it specific, but I'm just having a really hard time even getting started.

I just don't understand (at all) how I'm supposed to use recursion to implement this calculator. How am I supposed to use the m_exp l_op h_op etc that they defined? I just don't understand at all, sorry for the lack of better words :(

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MBlanc

Given the expression 2.3 * 4 - 7.8 / 9, you want to build a parse tree:

                         "-"
                    ._____|_____.
                    |           |
                   "*"         "/"
                 .__|__.     .__|__.
                 |     |     |     |
                2.3    4    7.8    9

It can be generated by recursively applying the definitions given in the last part of the exercise:

Start:  EXP
Rule 4: EXP L_OP M_EXP
Rule 5: M_EXP "-" M_EXP
Rule 2: M_EXP H_OP M_EXP "-" M_EXP H_OP M_EXP
Rule 6: M_EXP "*" M_EXP "-" M_EXP "/" M_EXP 
Rule 1: 2.3 * 4 - 7.8 / 9

A way of approaching this is making a series of functions that handle each rule:

void m_exp();
void   exp();
etc...

Each of these functions will try to match the next part of the input, and update some global variables accordingly. Wikipedia has a great article about recursive descent parsers, which includes a C example.

How exactly am I supposed to "recurisvely apply the definitions given in the last part of the exercise", the stuff you wrote?

Here is an excerpt from the aforementioned article, slightly modified:

// Implements Rule 1
void num(void) {
    // Reads a number
}

// Implements Rule 2
void m_exp(void) {
    num();
    while (sym == '*' || sym == '/') {
        getsym();
        num();
        // Does more work...
    }
}

// Implements Rule 4
void exp(void) {
    m_exp();
    while (sym == '+' || sym == '-') {
        getsym();
        m_exp();
        // Does more work...
   }
}

Rules 5 and 6 are already built-in. Rule 3 is the entry point.

Here, the [tail recursion] has been replaced by loops. Note how exp calls m_exp many times, and m_exp does the same with num.

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edited at2021-06-26

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