QT计算器 之 大数运算「建议收藏」

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1、简介：
计算器是我们生活中很常见的东西，它可以由多种语言多种方式来实现，今天我想讲的是基于C++语言，由QT实现的可以计算大数的简单计算器。

2、作品演示：
（1）简单四则运算
（2）大数运算

3、重点原理讲解
（1）四则运算如何实现
（2）大数的加减乘除

4、代码主体框架

1个主函数；
两个类：
一个calculator类，实现了对界面的布局，其实这个布局很简单，就设置了一些按钮以及一个显示框。

类的声明：

class calculator : public QMainWindow
{
    Q_OBJECT

public:
    calculator(QWidget *parent = 0);
    ~calculator();

private:
      QLineEdit *inputLine;//显示框
      QString input="0"; //输入框

      //0-9按钮
      QPushButton *zeroButton;
      QPushButton *oneButton;
      QPushButton *twoButton;
      QPushButton *threeButton;
      QPushButton *fourButton;
      QPushButton *fiveButton;
      QPushButton *sixButton;
      QPushButton *sevenButton;
      QPushButton *eightButton;
      QPushButton *nineButton;


      QPushButton *addButton;
      QPushButton *subButton;
      QPushButton *divButton;
      QPushButton *mulButton;
      QPushButton *equButton;
      QPushButton *timButton; //Time
      QPushButton *decButton;
      QPushButton *botButton;

      QPushButton *CEButton;
      QPushButton *ACButton;
      QPushButton *lefButton;
      QPushButton *rigButton;

private slots:

      void buttonZeroClicked();
      void buttonOneClicked();
      void buttonTwoClicked();
      void buttonThreeClicked();
      void buttonFourClicked();
      void buttonFiveClicked();
      void buttonSixClicked();
      void buttonSevenClicked();
      void buttonEightClicked();
      void buttonNineClicked();


      void buttonAddClicked();//+
      void buttonSubClicked();//-
      void buttonMulClicked();//乘
      void buttonDivClicked();//除
      void buttonTimClicked(); //时间
      void buttonDecClicked();//小数点
      void buttonBotClicked(); //加减号

      void buttonEquClicked();//等于号

      void buttonLefClicked();//左括号
      void buttonRigClicked();//右括号

      void buttonCEClicked();//CE
      void buttonACClicked();//AC
};

界面布局：

calculator::calculator(QWidget *parent) : QMainWindow(parent)
{


       QWidget *widget=new QWidget; //构建一个QWidget布局将设置的布局添加进这个QWidget
       this->setCentralWidget(widget);

       inputLine=new QLineEdit;
       inputLine->setText(input);

       zeroButton=new QPushButton("0");
       oneButton=new QPushButton("1");
       twoButton=new QPushButton("2");
       threeButton=new QPushButton("3");
       fourButton=new QPushButton("4");
       fiveButton=new QPushButton("5");
       sixButton=new QPushButton("6");
       sevenButton=new QPushButton("7");
       eightButton=new QPushButton("8");
       nineButton=new QPushButton("9");
       decButton=new QPushButton(".");

       botButton=new QPushButton("±");
       timButton=new QPushButton("Time");
       addButton=new QPushButton("+");
       subButton=new QPushButton("-");
       mulButton=new QPushButton("*");
       divButton=new QPushButton("/");
       equButton=new QPushButton("=");

       lefButton=new QPushButton("(");
       rigButton=new QPushButton(")");
       CEButton=new QPushButton("CE");
       ACButton=new QPushButton("AC");

       QGridLayout *H=new QGridLayout(this); //声明了一个网格布局

       inputLine->setFixedHeight(50); //调整第一行大小
       CEButton->setFixedHeight(50);
       ACButton->setFixedHeight(50);

       H->addWidget(inputLine,0,0,1,3);
       H->setRowStretch(0,100);
       H->addWidget(CEButton,0,3);
       H->addWidget(ACButton,0,4);

       H->addWidget(oneButton,1,0);
       H->addWidget(twoButton,1,1);
       H->addWidget(threeButton,1,2);
       H->addWidget(botButton,1,3);
       H->addWidget(timButton,1,4);

       H->addWidget(fourButton,2,0);
       H->addWidget(fiveButton,2,1);
       H->addWidget(sixButton,2,2);
       H->addWidget(addButton,2,3);
       H->addWidget(subButton,2,4);

       H->addWidget(sevenButton,3,0);
       H->addWidget(eightButton,3,1);
       H->addWidget(nineButton,3,2);
       H->addWidget(mulButton,3,3);
       H->addWidget(divButton,3,4);

       H->addWidget(zeroButton,4,0);
       H->addWidget(decButton,4,1);
       H->addWidget(lefButton,4,2);
       H->addWidget(rigButton,4,3);
       H->addWidget(equButton,4,4);

       widget->setLayout(H); //将布局显示出来

       connect(zeroButton,SIGNAL(clicked()),this,SLOT(buttonZeroClicked()));//信号与槽函数
       connect(oneButton,SIGNAL(clicked()),this,SLOT(buttonOneClicked()));
       connect(twoButton,SIGNAL(clicked()),this,SLOT(buttonTwoClicked()));
       connect(threeButton,SIGNAL(clicked()),this,SLOT(buttonThreeClicked()));
       connect(fourButton,SIGNAL(clicked()),this,SLOT(buttonFourClicked()));
       connect(fiveButton,SIGNAL(clicked()),this,SLOT(buttonFiveClicked()));
       connect(sixButton,SIGNAL(clicked()),this,SLOT(buttonSixClicked()));
       connect(sevenButton,SIGNAL(clicked()),this,SLOT(buttonSevenClicked()));
       connect(eightButton,SIGNAL(clicked()),this,SLOT(buttonEightClicked()));
       connect(nineButton,SIGNAL(clicked()),this,SLOT(buttonNineClicked()));

       connect(addButton,SIGNAL(clicked()),this,SLOT(buttonAddClicked()));
       connect(subButton,SIGNAL(clicked()),this,SLOT(buttonSubClicked()));
       connect(mulButton,SIGNAL(clicked()),this,SLOT(buttonMulClicked()));
       connect(divButton,SIGNAL(clicked()),this,SLOT(buttonDivClicked()));

       connect(botButton,SIGNAL(clicked(bool)),this,SLOT(buttonBotClicked()));//正负号
       connect(timButton,SIGNAL(clicked(bool)),this,SLOT(buttonTimClicked()));//时间
       connect(decButton,SIGNAL(clicked(bool)),this,SLOT(buttonDecClicked()));//点号

       connect(lefButton,SIGNAL(clicked(bool)),this,SLOT(buttonLefClicked()));//左括号
       connect(rigButton,SIGNAL(clicked(bool)),this,SLOT(buttonRigClicked()));//右括号

       connect(CEButton,SIGNAL(clicked()),this,SLOT(buttonCEClicked()));
       connect(ACButton,SIGNAL(clicked()),this,SLOT(buttonACClicked()));

       connect(equButton,SIGNAL(clicked()),this,SLOT(buttonEquClicked())); //等于号*/

}

槽函数实现部分举例说明，其它类似：

void calculator::buttonZeroClicked()  //以下是实现相应的槽函数
{
    if(input=="0")
    input='0';
    else input=input+'0';
    inputLine->setText(input);
}

void calculator::buttonTimClicked() //Time
{
   input=QDateTime::currentDateTime().toString("yyyy-MM-dd hh:mm:ss:zzz"); //格式化输出当前时间
   inputLine->setText(input);
}

点击等于号的时候调用Change函数和Exchange函数，对式子进行运算。

Change 函数，将显示框里面的中缀表达式转化为了后缀表达式，存入OPS字符数组中，数字之间用#分开，保存数组长度，方便后面的运算。

Exchange函数，将后缀表达式进行运算，对每两个数的加法减法乘法或者除法都是采用大数运算，通过CDashu类对 + – * / 的重载，然后在Exchange 函数中建立对象调用，最后将返回值再转化为字符输出到屏幕上。

void calculator::buttonEquClicked()//等于号
{

      std::string str=input.toStdString();
      const char *S=str.c_str();
      cout<<S[strlen(S)];
      char OPS[max1];
      int len;
      double result;
      char* change = new char[max1];
      bool flag;
      Change(S,OPS,len);
      change = EXchange(OPS,len,result,flag);
      //QString::number(result,10,6);
      input=input+"="+change;
      inputLine->setText(input);
}

int Change(const char *S,char OPS[],int &len)
{
    QStack<char> OPE;
    int i = 0 ,j = 0;
    int l = strlen(S);
    for( i ;i < strlen(S);i++)
    {
        switch(S[i])
        {
        case '+':
            if(OPE.isEmpty())
                OPE.push(S[i]);
            else if(OPE.top() == '*' || OPE.top() == '/' || OPE.top() == '-')
            {
                OPS[j++] = OPE.pop();
                i--;//多次判断OPE.top()符号的优先级是否高于'+'
            }
            else
                OPE.push(S[i]);
            break;
        case '-':
            //if('('!=S[i-1]&&0!=i)
            //{
            if(OPE.isEmpty())
                OPE.push(S[i]);
            else if(OPE.top() == '*' || OPE.top() == '/' || OPE.top() == '+')
            {
                OPS[j++] = OPE.pop();
                i--;
            }
            else
                OPE.push(S[i]);
            break;

            //}
            /*else
            {
                while ((S[i] >= '0'&&S[i] <= '9' )|| S[i] == '.'||('-'==S[i]&&(S[i-1]<'0'||S[i-1]>'9' || i == 0)))
                {
                    if(S[i] == '-')
                      OPS[j++]='#';
                    OPS[j++] = S[i];
                    i++;
                }
                i--;
                OPS[j++] = '#';  //数字中的间隔符
            }*/

        case '*':
            if(OPE.isEmpty())
            {
                OPE.push(S[i]);
            }
            else if(OPE.top() == '/')
            {
                OPS[j++] = OPE.pop();
                i--;
            }
            else
                OPE.push(S[i]);
            break;
        case '/':
            if(OPE.isEmpty())
            {
                OPE.push(S[i]);
            }
            else if(OPE.top() == '*')
            {
                OPS[j++] = OPE.pop();
                i--;
            }
            else
                OPE.push(S[i]);
            break;
        case'(':
            OPE.push(S[i]);
            break;
        case')':
            while (OPE.top() != '(')
            {
                OPS[j++] = OPE.pop();//遇到右括号，一直弹出操作符知道遇到左括号
            }
            OPE.pop();//直接不放入数组弹出左括号
            break;
        default:
            while (S[i] >= '0'&&S[i] <= '9' || S[i] == '.'||('-'==S[i]&&S[i-1]<'0'&&S[i-1]>'9'))
            {

                OPS[j++] = S[i];
                i++;
            }
            i--;
            OPS[j++] = '#';  //数字中的间隔符
            break;
        }//switch
    }//for
    while (!OPE.isEmpty())
    {
        OPS[j++] = OPE.pop();
    }
    len = j;
    return 0;
}//Change

char* EXchange(char OPS[], int len, double &result,bool &flag)
{

    int tag = 0,t3;
    QStack<char*> SZ;
    char *s = new char[max1];
    char *str1 = new char[max1];
    char *str2 = new char[max1];
    char *str = new char[max1]; 
    char st1[max1][max1];
    CDashu x1;
    CDashu x2;
    CDashu y;
    int i,j,t = 0,temp;
    for(i = 0;i < len;i++)
    {
        switch(OPS[i])
        {
        case '+':
            str1 = SZ.pop();
            str2 = SZ.pop();
            x1.Change(str1);
            x2.Change(str2);
            y = x2 + x1;
            tag = 0;
            temp = 0;
            if(y.a[0])
            {
                s[tag] = y.a[0]+'0';
                tag++;
            }
            else
                temp++;
            for( ;tag <= y.getlength()-temp;tag++)
            {
                s[tag] = y.a[tag + temp]+'0';
            }
            s[tag] = '\0';
            SZ.push(s);
            break;
        case '-':
            str1 = SZ.pop();
            str2 = SZ.pop();
            x1.Change(str1);
            x2.Change(str2);
            y = x2 - x1;
            tag = 0;
            temp = 0;
            if(y.getflag())
            {
                s[tag] = '-';
                tag++;
            }
            if(y.a[0])
            {
                s[tag] = y.a[0]+'0';
                tag++;
            }
            else
                temp++;
            if(s[0] == '-')
            {
                for( ;tag <= y.getlength();tag++)
                {
                    s[tag] = y.a[tag]+'0';
                }
                s[tag] = '\0';
            }
            else
            {
                for( ;tag <= y.getlength()-temp;tag++)
                {
                    s[tag] = y.a[tag + temp]+'0';
                }
                s[tag] = '\0';

            }
            SZ.push(s);
            break;
        case '*':
            int max,min,max2;
            str1 = SZ.pop();
            str2 = SZ.pop();
            x1.Change(str1);
            x2.Change(str2);
            y = x1*x2;
            y.get(max,max2,min);
            j = 0;
            for(t3 = max;t3 >= min;t3--)
            {
                s[j++] = y.a[t3]+'0';
            }
            s[j] = '\0';
            SZ.push(s);
            break;

        case '/':
        {
            str1 = SZ.pop();
            str2 = SZ.pop();
            x1.Change(str1);
            x2.Change(str2);
            y = x2 / x1;
            int x = 0;
            i = 0;
            int num[max1];
            while(y.yushu[0])
            {
                num[x] = y.yushu[0]%10;
                y.yushu[0] = y.yushu[0]/10;
                x++;
            }
            x--;
            while(x > -1)
            {

                s[i] = num[x]+'0';
                x--;
                i++;
            }
            s[i] = '.';
            for(i = i+1,j = 1;j < 50;i++,j++)
            {
                s[i] = y.yushu[j]+'0';
            }
            s[i] = '\0';
            SZ.push(s);
        }
            break;
        default:
            j = 0;

            while (OPS[i] != '#')
            {
                st1[t][j] = OPS[i];

                j++;
                i++;
            }
            st1[t][j] = '\0';
            SZ.push(st1[t]);
            t++;
            break;
        }
    }
    return SZ.top();
}

下面重点介绍一下大数类：

类的声明与部分成员函数的实现

#ifndef CDASHU_H
#define CDASHU_H
#include<cstring>
using namespace std;
#define max1 500
#define MAXN 9999
class CDashu
{
public:
    int a[max1];
    int yushu[max1];
    CDashu() { length = 1; memset(a, 0, sizeof(a)); }   //构造函数
    void Change( char *s); //将字符串转换为大数
    long getlength()
    {
        return length;
    }
    int getflag()
    {
         return flag;
    }
    friend int Compare(CDashu a,CDashu b);
    void get(int &m,int &m2,int &min)
    {
        m = max;
        m2 = max2;
        min = this->min;
    }

    ~CDashu();
    CDashu operator +(CDashu b);//对各类运算的重载
    CDashu operator -(CDashu b);
    CDashu operator *(CDashu b);
    CDashu operator /(CDashu b);
private:

    long length;
    int flag;
    int max,min,max2;
};

#endif // CDASHU_H

大数类的实现：

#include "cdashu.h"

#include "cdashu.h"
#include <iostream>
#include <string.h>
using namespace std;
/*
ostream& operator<<(ostream& out, CDashu& b)   //重载输出运算符
{
    int i;
    out << b.a[b.length - 1];
    for (i = b.length - 2; i >= 0; i--)
    {
        out.width(4);
        out.fill('0');
        out << b.a[i];
    }
    return out;
}*/
void CDashu::Change( char *s)
{
    memset(a, 0, sizeof(a));
    long l = strlen(s);
    length = l;
    for (int i = 1; i <= l; i++)
    {
        a[i] = (int)s[i-1] - '0';
    }
    for (int i = 1; i <= l; i++)
    {
        cout << a[i];
    }
    cout << endl;
}
CDashu CDashu::operator+(CDashu b)
{
    int i = length, j = b.length;
    if (i >= j)
    {
        for (; i > 0 && j > 0; i--, j--)
            a[i] += b.a[j];//逐个相加
        i = length;
        for (i; i >= 0; i--)
        {
            if (a[i] >= 10) //进位运算
            {
                a[i - 1] += a[i] / 10;
                a[i] %= 10;
            }
        }
        return *this;
    }

    else
    {
        for (; i >= 0 && j >= 0; i--, j--)
            b.a[j] += a[i];//逐个相加
        i = b.length;
        for (i; i > 0; i--)
        {
            if (b.a[i] >= 10) //进位运算
            {
                b.a[i - 1] += b.a[i] / 10;
                b.a[i] %= 10;
            }
        }
        return b;
    }

}
CDashu CDashu::operator -(CDashu b)
{
    flag = 0;
    b.flag = 0;
    int i, j;
    if (length == b.length)
    {
        i = 1;j = 1;
        while (a[i] == b.a[i])
        {
            i++;
        }
        if (a[i] < b.a[i])
            b.flag = 1;
    }
    i = length;
    j = b.length;
    if (i < j || b.flag)
    {        
        for (i; i > 0 && j > 0; i--, j--)
            b.a[j] -= a[i];//一一相减
        i = b.length;
        for (i; i > 0; i--)
        {
            if (b.a[i] < 0) //补位运算
            {
                b.a[i] += 10;
                b.a[i - 1] -= 1;
            }
        }
        return b;
    }
    else
    {
        for (i; i >= 0 && j >= 0; i--, j--)
            a[i] -= b.a[j];//一一相减
        i = length;
        for (i; i >= 0; i--)
        {
            if (a[i] < 0) //补位运算
            {
                a[i] += 10;
                a[i - 1] -= 1;
            }
        }
        return *this;
    }
    cout << endl;

}

CDashu CDashu::operator *(CDashu b)
{
    CDashu t;
    int i, j;
    t.max = t.min = t.max2 = 1;
    for (i = length; i > 0; i--)
    {
        for (j = b.length; j > 0; j--)
        {
            t.a[length+b.length+1 -(i + j)] += a[i] * b.a[j];//t.a[]初始化为0
            t.min = min<(length+b.length+1 -(i + j))?t.min:(length+b.length+1 -(i + j));
            t.max = max>(length+b.length+1 -(i + j))?t.max:(length+b.length+1 -(i + j));
        }
    }
    for (i = t.min; i <= t.max; i++)
    {
        if (t.a[i] >= 10)
        {
            t.a[i + 1] += t.a[i] / 10;
            t.a[i] = t.a[i] % 10;
            t.max2 = i+1;
        }
    }
    t.max = t.max > t.max2 ? t.max:t.max2;
    return t;
}

CDashu CDashu::operator /(CDashu b)
{
    int i,j,flag = 1,count = 0,tag = 0,mm=0;
    min = 1;
    flag = Compare(*this,b);
    max = length;
    if (length < b.length || flag == 0)
        count = 0;
    else
    {

        while (flag == 1 || flag == 2)
        {

            if(min == length && a[min] == 0)
            {
                break;
            }
            else
            {
                i = length;
                j = b.length;
                count++;
                for ( ; i >= min && j > 0; i--, j--)
                    a[i] -= b.a[j];//一一相减
                i = length;
                for (i; i >= min; i--)
                {
                    if (a[i] < 0) //补位运算
                    {
                        a[i] += 10;
                        a[i - 1] -= 1;
                    }
                }
                i = min;
                if (a[i] == 0 && i != length)
                {
                    while (a[i] == 0)
                    {
                        i++;
                    }
                    min = i;

                }//如果有减到前面为0,最小下标右移到不为0的位置
                flag = Compare(*this,b);//比较两个数的大小
            }
            cout<<count<<endl;
        }//while

    }//else
    cout << count << '.';
    yushu[0] = count;
    tag = 0;
    for(i = 1;i <= length;i++)
    {
        if(a[i] != 0)
        {
            tag = 1;
            break;
        }
    }
    if(!tag)
    {
        for(i = 1;i < 50;i++)
        {
            yushu[i] = 0;
        }
    }
    else
    {
        int jingdu = 1;
        while(jingdu < 50)
        {
            count = 0;
            /*if(min == length && a[min] == 0)
            {
                for( ;jingdu < 30;jingdu++)
                {
                    yushu[jingdu] = 0;
                }
                break;
            }*/
            length++;
            a[length] = 0;
            flag = Compare(*this,b);//比较两个数的大小

            if(flag == 2)
            {
                yushu[jingdu] = 1;
                jingdu++;
                for( ; jingdu < 50;jingdu++)
                {
                    yushu[jingdu] = 0;
                }
            }
            else
            {
                if (flag == 0)
                {
                    yushu[jingdu] = 0;
                    jingdu++;
                }
                else
                {
                    while (flag == 1 || flag==2)
                    {
                        if(min == length && a[min] == 0)
                        {
                            mm = 1;
                            yushu[jingdu] = count;
                            for( jingdu = jingdu+1;jingdu < 50;jingdu++)
                            {
                                yushu[jingdu] = 0;
                            }
                            break;
                        }
                        count++;
                        i = length,j = b.length;
                        for(;i >= min && j > 0;i--,j--)
                        {
                            a[i] -= b.a[j];
                        }
                        i = length;
                        for (i; i >= min; i--)
                        {
                            if (a[i] < 0) //补位运算
                            {
                                a[i] += 10;
                                a[i - 1] -= 1;
                            }
                        }
                        i = min;
                        if (a[i] == 0 && i != length)
                        {
                            while(a[i] == 0)
                            {
                                i++;
                            }
                        }
                        min = i;//如果有减到前面为0,最小下标右移到不为0的位置
                        flag = Compare(*this,b);//比较两个数的大小
                    }
                    yushu[jingdu] = count;
                    jingdu++;
                }
            }
            if(mm)
                break;
        }
    }
    return *this;
}
int Compare(CDashu a,CDashu b)
{
    int i = a.min, j = 1,flag = 1;
    if(a.length-a.min + 1 < b.length)
        flag = 0;
    else if(a.length-a.min+1 > b.length)
        flag = 1;
    else
    {
        while (a.a[i] == b.a[j] && i <= a.length && j <= b.length)
        {
            i++;
            j++;
        }
        if (a.a[i] < b.a[j])
            flag = 0;
        if(a.a[i] == b.a[i])
        {
            flag = 2;
        }
    }
    return flag;
}

CDashu::~CDashu()
{

}