【Qt】14 计算器核心解析算法(下)

一、后缀表达式中的数字与运算符

后缀表达式的数字和运算符

当前元素为数字：进栈
当前元素的运算符
1.从栈中弹出右操作符
2.从栈中弹出右操作符
3.根据符号进行运算
4.将运算结果压入栈中

遍历结束

栈中的唯一数字为运算结果。

while(!exp.isEmpty)
{
     if(当前元素为数字)
     {
      入栈；
     }
     else if(当前元素为运算符)
     {
        1.从栈中弹出右操作符
        2.从栈中弹出右操作符
        3.根据符号进行运算
        4.将运算结果压入栈中
     }
     else
     {
            表达式错误。
     }
}

二、编程实验
QCalculatorDec.cpp

#include "QCalculatorDec.h"

QCalculatorDec::QCalculatorDec()
{
    m_exp = "";
    m_result = "";
}

QCalculatorDec::~QCalculatorDec()
{

}

bool QCalculatorDec::isDigitOrDot(QChar c)
{
    return (('0' <= c) && (c <= '9')) || (c == '.');
}

bool QCalculatorDec::isSymbol(QChar c)
{
    return isOperator(c) || (c == '(') || (c == ')');
}

bool QCalculatorDec::isSign(QChar c)
{
    return (c == '+') || (c == '-');
}

bool QCalculatorDec::isNumber(QString s)
{
    bool ret = false;

    s.toDouble(&ret);

    return ret;
}

bool QCalculatorDec::isOperator(QString s)
{
    return (s == "+") || (s == "-") || (s == "*") || (s == "/");
}

bool QCalculatorDec::isLeft(QString s)
{
    return (s == "(");
}

bool QCalculatorDec::isRight(QString s)
{
    return (s == ")");
}

int QCalculatorDec::priority(QString s)
{
    int ret = 0;

    if( (s == "+") || (s == "-") )
    {
        ret = 1;
    }

    if( (s == "*") || (s == "/") )
    {
        ret = 2;
    }

    return ret;
}

bool QCalculatorDec::expression(const QString& exp)
{
    bool ret = false;
    QQueue<QString> spExp = split(exp);
    QQueue<QString> postExp;

    m_exp = exp;

    if( transform(spExp, postExp) )
    {
        m_result = calculate(postExp);

        ret = (m_result != "Error");
    }
    else
    {
        m_result = "Error";
    }


    return ret;
}

QString QCalculatorDec::result()
{
    return m_result;
}

QQueue<QString> QCalculatorDec::split(const QString& exp)
{
    QQueue<QString> ret;
    QString num = "";
    QString pre = "";

    for(int i=0; i<exp.length(); i++)
    {
        if( isDigitOrDot(exp[i]) )
        {
            num += exp[i];
            pre = exp[i];
        }
        else if( isSymbol(exp[i]) )
        {
            if( !num.isEmpty() )
            {
                ret.enqueue(num);

                num.clear();
            }

            if( isSign(exp[i]) && ((pre == "") || (pre == "(") || isOperator(pre)) )
            {
                num += exp[i];
            }
            else
            {
                ret.enqueue(exp[i]);
            }

            pre = exp[i];
        }
    }

    if( !num.isEmpty() )
    {
        ret.enqueue(num);
    }

    return ret;
}

bool QCalculatorDec::match(QQueue<QString>& exp)
{
    bool ret = true;
    int len = exp.length();
    QStack<QString> stack;

    for(int i=0; i<len; i++)
    {
        if( isLeft(exp[i]) )
        {
            stack.push(exp[i]);
        }
        else if( isRight(exp[i]) )
        {
            if( !stack.isEmpty() && isLeft(stack.top()) )
            {
                stack.pop();
            }
            else
            {
                ret = false;
                break;
            }
        }
    }

    return ret && stack.isEmpty();
}

bool QCalculatorDec::transform(QQueue<QString>& exp, QQueue<QString>& output)
{
    bool ret = match(exp);
    QStack<QString> stack;

    output.clear();

    while( ret && !exp.isEmpty() )
    {
        QString e = exp.dequeue();

        if( isNumber(e) )
        {
            output.enqueue(e);
        }
        else if( isOperator(e) )
        {
            while( !stack.isEmpty() && (priority(e) <= priority(stack.top())) )
            {
                output.enqueue(stack.pop());
            }

            stack.push(e);
        }
        else if( isLeft(e) )
        {
            stack.push(e);
        }
        else if( isRight(e) )
        {
            while( !stack.isEmpty() && !isLeft(stack.top()) )
            {
                output.enqueue(stack.pop());
            }

            if( !stack.isEmpty() )
            {
                stack.pop();
            }
        }
        else
        {
            ret = false;
        }
    }

    while( !stack.isEmpty() )
    {
        output.enqueue(stack.pop());
    }

    if( !ret )
    {
        output.clear();
    }

    return ret;
}

QString QCalculatorDec::calculate(QString l, QString op, QString r)
{
    QString ret = "Error";

    if( isNumber(l) && isNumber(r) ) //检测左右操作数必须是数字
    {
        double lp = l.toDouble(); //将字符串转换为数字运算
        double rp = r.toDouble();

        if( op == "+" )
        {
            ret.sprintf("%f", lp + rp);
        }
        else if( op == "-" )
        {
            ret.sprintf("%f", lp - rp);
        }
        else if( op == "*" )
        {
            ret.sprintf("%f", lp * rp);
        }
        else if( op == "/" )
        {
            const double P = 0.000000000000001;

            if( (-P < rp) && (rp < P) )
            {
                ret = "Error";
            }
            else
            {
                ret.sprintf("%f", lp / rp);
            }

        }
        else
        {
            ret = "Error";
        }
    }

    return ret;
}

QString QCalculatorDec::calculate(QQueue<QString>& exp)
{
    QString ret = "Error";
    QStack<QString> stack;

    while( !exp.isEmpty() )
    {
        QString e = exp.dequeue();

        if( isNumber(e) )
        {
            stack.push(e);
        }
        else if( isOperator(e) )
        {
            QString rp = !stack.isEmpty() ? stack.pop() : "";
            QString lp = !stack.isEmpty() ? stack.pop() : "";
            QString result = calculate(lp, e, rp);

            if( result != "Error" )
            {
                stack.push(result);
            }
            else
            {
                break;
            }
        }
        else
        {
            break;
        }
    }

    if( exp.isEmpty() && (stack.size() == 1) && isNumber(stack.top()) )
    {
        ret = stack.pop();
    }

    return ret;
}

QCalculatorDec.h

#ifndef _CALCULATORCORE_H_
#define _CALCULATORCORE_H_

#include <QString>
#include <QStack>
#include <QQueue>

class QCalculatorDec
{
protected:
    QString m_exp;
    QString m_result;

    bool isDigitOrDot(QChar c);
    bool isSymbol(QChar c);
    bool isSign(QChar c);
    bool isNumber(QString s);
    bool isOperator(QString s);
    bool isLeft(QString s);
    bool isRight(QString s);
    int priority(QString s);
    bool match(QQueue<QString>& exp);
    QString calculate(QQueue<QString>& exp);
    QString calculate(QString l, QString op, QString r);
    bool transform(QQueue<QString>& exp, QQueue<QString>& output);
    QQueue<QString> split(const QString& exp);
public:
    QCalculatorDec();
    ~QCalculatorDec();
    bool expression(const QString& exp);
    QString expression();
    QString result();
};

#endif

二、小结

Qt项目在整体上采用面向对象分析与设计
局部的算法设计依旧采用面向过程的方法完成
Qt开发是各种开发技术的综合运用