表达式计算器（LL1文法）

LL(1)文法求算数表达式的值
递归子程序法

分析过程：

表达式文法G[E]:
E->E+T|E-T|T
T->T*F|T/F|T%F|F
F->N^F|N
N->(E)|NUM|+NUM|-NUM

消除左递归、左公共因子
E ->TE'
E'->+TE'|-TE'|ε
T ->FT'
T'->*FT'|/FT'|%FT'|ε
F ->NF'
F'->^F|ε
N->(E)|NUM|+NUM|-NUM

FIRST集和FOLLOW集

LL(1)分析表

(应该没错吧……表示昨天刚考完试……)

（嗯。。我承认我抄。。咳咳。。借鉴了这份代码http://ideone.com/o2Ag4。。还是炮姐写的好。。）

#include <cstdio>
#include <cmath>

/**
 * LL(1)文法求算数表达式的值
 * 递归子程序法
**/

enum SYM_KIND {     // 符号类型
    SYM_NUM,        // num
    SYM_ADD,        // +
    SYM_SUB,        // -
    SYM_MUL,        // *
    SYM_DIV,        // /
    SYM_MOD,        // %
    SYM_POW,        // ^
    SYM_LBR,        // (
    SYM_RBR,        // )
    SYM_END,        // '\0'
    SYM_ERR         // 其他不合法符号
};

enum ERR_KIND {     // 状态
    ERR_OK,
    ERR_INVALID_CHAR,
    ERR_NO_OPERATOR,
    ERR_BR_NOT_MATCH,
    ERR_NO_NUM,
    ERR_END
};

char expr[];    // 表达式
int pos;            // 读取到表达式的位置
double val;
ERR_KIND err;

void F();
void E();

void NUM()
{
    val = ;
    while (expr[pos] <= '' && expr[pos] >= '')
    {
        val = val *  + expr[pos] - '';
        pos++;
    }
    if (expr[pos] == '.')
    {
        pos++;
        double eo = 0.1;
        while (expr[pos] <= '' && expr[pos] >= '')
        {
            val += (expr[pos] - '') * eo;
            eo *= 0.1;
            pos++;
        }
    }
}

SYM_KIND get_sym()   // 读取一个单词
{
    char ch = expr[pos++];
    while (ch == ' ' || ch == '\t') // 忽略空格
        ch = expr[pos++];
    if (ch <= '' && ch >= '')
    {
        pos--;
        NUM();
        return SYM_NUM;
    }
    else if (ch == '+') return SYM_ADD;
    else if (ch == '-') return SYM_SUB;
    else if (ch == '*') return SYM_MUL;
    else if (ch == '/') return SYM_DIV;
    else if (ch == '%') return SYM_MOD;
    else if (ch == '^') return SYM_POW;
    else if (ch == '(') return SYM_LBR;
    else if (ch == ')') return SYM_RBR;
    else if (ch == '\0')
    {
        err = ERR_END;
        return SYM_END;
    }
    err = ERR_INVALID_CHAR;
    return SYM_ERR;
}

void N()  // N->(E)|NUM|+NUM|-NUM
{
    if (err != ERR_OK) return ;
    SYM_KIND kind = get_sym();
    if (kind == SYM_LBR)
    {
        E();
        if (err == ERR_END)
        {
            err = ERR_BR_NOT_MATCH;
        }
        else if (err == ERR_OK)
        {
            kind = get_sym();
            if (kind != SYM_RBR)
                err = ERR_BR_NOT_MATCH;
        }
    }
    else if (kind == SYM_ADD)
    {
        kind = get_sym();
        if (kind != SYM_NUM)
        {
            err = ERR_NO_NUM;
        }
    }
    else if (kind == SYM_SUB)
    {
        kind = get_sym();
        if (kind != SYM_NUM)
        {
            err = ERR_NO_NUM;
        }
        val = -val;
    }
    else if (kind != SYM_NUM)
    {
        err = ERR_NO_NUM;
    }
}

void F_() // F'->^F|ε
{
    if (err != ERR_OK) return ;
    SYM_KIND kind = get_sym();
    double tmp = val;
    if (kind == SYM_POW)
    {
        F();
        val = pow(tmp, val);
    }
    else if (kind == SYM_ADD || kind == SYM_SUB || kind == SYM_MUL || kind == SYM_DIV
            || kind == SYM_MOD || kind == SYM_END || kind == SYM_RBR)
    {
        pos--;
    }
    else if (kind != SYM_ERR)
        err = ERR_NO_OPERATOR;
}

void F()  // F ->NF'
{
    if (err != ERR_OK) return ;
    N();
    F_();
}

void T_() // T'->*FT'|/FT'|%FT'|ε
{
    if (err != ERR_OK) return ;
    SYM_KIND kind = get_sym();
    double tmp = val;
    if (kind == SYM_MUL)
    {
        F();
        val *= tmp;
        T_();
    }
    else if (kind == SYM_DIV)
    {
        F();
        val = tmp / val;
        T_();
    }
    else if (kind == SYM_MOD)
    {
        F();
        val = fmod(tmp, val);
        T_();
    }
    else if (kind == SYM_ADD || kind == SYM_SUB || kind == SYM_RBR || kind == SYM_END)
    {
        pos--;
    }
    else if (kind != SYM_ERR)
    {
        err = ERR_NO_OPERATOR;
    }
}

void T()   // T ->FT'
{
    if (err != ERR_OK) return ;
    F();
    T_();
}

void E_()  // E'->+TE'|-TE'|ε
{
    if (err != ERR_OK) return ;
    SYM_KIND kind = get_sym();
    double tmp = val;
    if (kind == SYM_ADD)
    {
        T();
        val = tmp + val;
        E_();
    }
    else if (kind == SYM_SUB)
    {
        T();
        val = tmp - val;
        E_();
    }
    else if (kind == SYM_END || kind == SYM_RBR)
    {
        pos--;
    }
    else if (kind != SYM_ERR)
    {
        err = ERR_NO_OPERATOR;
    }
}

void E()   // E ->TE'
{
    if (err != ERR_OK) return ;
    T();
    E_();
}

void output_err()
{
    if (err == ERR_OK)
    {
        err = ERR_BR_NOT_MATCH;
        pos++;
    }
    printf("%*s ^", pos, "");
    if (err == ERR_BR_NOT_MATCH) printf("括号不匹配\n");
    else if (err == ERR_NO_NUM) printf("缺少一个数字\n");
    else if (err == ERR_NO_OPERATOR) printf("缺少一份运算符\n");
    else if (err == ERR_INVALID_CHAR) printf("不合法字符\n");
}

int main()
{
    printf(">>");
    while (gets(expr) != NULL)
    {
        pos = ;
        err = ERR_OK;
        E();
        if (err == ERR_END) printf("%g\n", val);
        else output_err();
        printf(">>");
    }
    return ;
}

运行结果：
>>3+4^2.2
24.1121
>>2-7/8
1.125
>>(8+0
           ^括号不匹配
>>7%5
2
>>7+9.9+
              ^缺少一个数字

加个界面……