大整数四则运算

#include<iostream>
#include<stdlib.h>
#include<string.h>
using namespace std;

#define N 100

int c[2];
int a1[N];
int a2[N];
int a3[N];

int judgebig(char n1[N], char n2[N]);     //判断大小
void sub(char n1[N], char n2[N], int len1, int len2);
char toAdd(char n1[N], char n2[N]);        //加 
char toSub(char n1[N], char n2[N]);        //减 
void toMul(char n1[N], char n2[N]);        //乘 
void toDiv(char n1[N], char n2[N]);        //除
char toSub2(char n1[N], char n2[N]);
 
char Add(char n1[N], char[N]);
char Sub(char n1[N], char[N]);
void Mul(char n1[N], char[N]);
void Div(char n1[N], char[N]);

/*
将n1，n2的长度存入数组k 
返回n1，n2的比较结果 ，若大小相等返回0，n1>n2返回1，n2>n1返回2 
*/
int judgebig(char n1[N], char n2[N])
{
    int k[2];
    
//    统计n1的长度存入k[0],n2存入k[1]
    k[0] = strlen(n1);
    k[1] = strlen(n2); 
    
//    cout<<k[0]<<" "<<k[1]<<endl; 
    
    if(k[0] > k[1])            //n1长度 > n2长度 
    {
        return 1;
    }
    else if(k[0] < k[1])    //n1长度 < n2长度
    {
        return 2;
    }
    else if(k[0] == k[1])      //n1长度 = n2长度 
    {
        //两个数的位数相等，在从头开始判断 
        int k = strcmp(n1, n2);        //比较n1, n2的大小 
        if(k == 0)        //n1 = n2 
        {
            return 0;
        }
        else if(k > 0)     //n1 > n2
        {
            return 1;
        }
        else if(k < 0)    //n2 > n1
        {
            return 2;    
        }
        
    }
    
    return -1;
}

//用于除法的减 
void sub(char n1[N], char n2[N], int len1, int len2)
{
    int i=0;
    int j;
    while(1)
    {
        if(n1[i]==‘0‘)
            i++;
        else
        {
            j=i;
            break;
        }
    }
    
    for(;i<len2;i++)
    {
        n1[i]=n1[i]-n2[i]+‘0‘;
    }
    for(i=len2-1;i>j;i--)    //低位开始检测是否小于0
    {
        if(n1[i]<‘0‘)
        {
            n1[i]+=10;
            n1[i-1]--;
        }
    }
}

//加法2 
char toAdd2(char n1[N], char n2[N]) 
{
    int i,L,z;
    
    L=strlen(n1);
    for (i=0;i<L;i++)    //将n1转换为数字存入数组a1 
    {
        a1[i]=n1[L-1-i]-‘0‘;
    }

    L=strlen(n2);
    for (i=0;i<L;i++) //将n2转换为数字存入数组a2 
    {
        a2[i]=n2[L-1-i]-‘0‘;
    }

    for (i=0;i<N;i++) 
    {
        a3[i]=a1[i]+a2[i];
    }

    for (i=0;i<N;i++) 
    {
        if (a3[i]>=10) 
        {
            a3[i+1]+=a3[i]/10;
            a3[i]=a3[i]%10;
        }
    }

    z=0;
    for (i=N-1;i>=0;i--) 
    {
        if (z==0) 
        {
            if (a3[i]!=0) 
            {
                cout<<a3[i];
                z=1;
            }
        } 
        else 
        {
            cout<<a3[i];
        }
    }
    if (z==0) 
    {
        cout<<"0"<<endl;
    }
    return ‘0‘;
}

//加
char toAdd(char n1[N], char n2[N])
{
    int i,L,z;
    
    L=strlen(n1);
    for (i=0;i<L;i++)    //将n1转换为数字存入数组a1 
    {
        a1[i]=n1[L-1-i]-‘0‘;
    }

    L=strlen(n2);
    for (i=0;i<L;i++) //将n2转换为数字存入数组a2 
    {
        a2[i]=n2[L-1-i]-‘0‘;
    }



    for (i=0;i<N;i++) 
    {
        a3[i]=a1[i]+a2[i];
    }

    for (i=0;i<N;i++) 
    {
        if (a3[i]>=10) 
        {
            a3[i+1]+=a3[i]/10;
            a3[i]=a3[i]%10;
        }
    }
    
//    cout<<n1<<"+"<<n2<<"=";
    
    //判断正负号 
    if(c[0] == c[1])     
    {
        if(c[0] == ‘-‘)    //负相同时 
        {
            cout<<‘-‘;
        }
    }
    if(c[0] != c[1])    //一正一负 
    {
        if(c[0] == ‘+‘ & c[1] == ‘-‘)
        {
            int m = judgebig(n1, n2);
            if(m == 1)    //n1》n2    
            {
                return toSub2(n1, n2); 
            }
            else if(m == 2)
            {
                cout<<‘-‘;
                return toSub2(n2, n1);        //注意调换了n1,n2的位置 
            }
        }
        else if(c[0] == ‘-‘ & c[1] == ‘+‘)
        {
            int m = judgebig(n1, n2);
            if(m == 1)
            {
                cout<<‘-‘;
                return toSub2(n1, n2);    
            }
            else if(m == 2)
            {
                return toSub2(n2, n1);
            }
        }
    }


    z=0;
    for (i=N-1;i>=0;i--) 
    {
        if (z==0) 
        {
            if (a3[i]!=0) 
            {
                cout<<a3[i];
                z=1;
            }
        } 
        else 
        {
            cout<<a3[i];
        }
    }
    if (z==0) 
    {
        cout<<"0"<<endl;
    }
    
    return ‘0‘;        
}

//减法2 
char toSub2(char n1[N], char n2[N]) 
{
    int i,j,len1,len2;
    int a[N]={0},b[N]={0};
    len1=strlen(n1);
    len2=strlen(n2);
    
    for(i=len1-1,j=0;i>=0;i--,j++)    //变为数组 
    {
        a[j]=n1[i]-‘0‘;
    }
    for(i=len2-1,j=0;i>=0;i--,j++)
    {
        b[j]=n2[i]-‘0‘;
    }
    
    for(i=0;i<len1;i++)            //低位开始减，若减得结果<0，想高位借一(即加上十)，高位减一(即减去十) 
    {
        a[i]=a[i]-b[i];
        if(a[i]<0)
        {
            a[i]+=10;
            a[i+1]--;
        }
    }
    
    i=len1-1;    
    while(a[i]==0)        //求i为结果的位数 
    {
        i--;
    }
    
    
    for(;i>=0;i--)
    {
        cout<<a[i];
    }
    return ‘0‘;
}

//减
char toSub(char n1[N], char n2[N])
{
    if(c[0] == ‘+‘ & c[1] == ‘+‘)
    {
        int m = judgebig(n1, n2);
        if(m == 2)        //n2 > n1
        {
            cout<<‘-‘;
            return  toSub(n2, n1); 
        }
    }
    else if(c[0] == ‘-‘ & c[1] == ‘-‘)    //这里的递归调用的也不合理，递归会产生循环， 
    {
//        cout<<"#";
        int m = judgebig(n1, n2);
        if(m == 2)    //n2 > n1
        {
//            c[0] = ‘+‘;
//            return toSub(n2, n1);
            return toSub2(n2, n1);         //用toSub2合适，解决递归产生的循环问题 
        }
        else if(m == 1)
        {
            cout<<‘-‘; 
        }
        else if(m == 0)
        {
            cout<<‘0‘;
            return ‘0‘;
        }
    }
    else if(c[0] == ‘+‘ & c[1] == ‘-‘)        //这里从tosub传入在间接传入toadd和直接从toadd传入是不一样的 ， 有错 
    {
        return toAdd2(n1, n2);
    }
    else if(c[0] = ‘-‘ & c[1] == ‘+‘)
    {
        cout<<‘-‘;
        return toAdd(n1, n2);
    }
    int i,j,len1,len2;
    int a[N]={0}, b[N]={0};        //要初始化为0 
    
    len1=strlen(n1);
    len2=strlen(n2);
    for(i = len1-1,j = 0; i >= 0; i--,j++)
    {
        a[j] = n1[i] - ‘0‘;
    }
    for(i = len2-1,j = 0; i >= 0; i--,j++)
    {
        b[j] = n2[i] - ‘0‘;
    }
    for(i = 0; i < len1; i++)
    {
        a[i] = a[i] - b[i];
        if(a[i] < 0)
        {
            a[i] += 10;
            a[i+1]--;
        }
    }
    i = len1 - 1;
    while(a[i] == 0)
    {
        i--;
    }
    
//    cout<<n1<<‘-‘<<n2<<"=";
    
    //判断正负号 
    if(c[0] == c[1])
    {
        if(c[0] == ‘+‘)        //正相同 
        {
            int m = judgebig(n1, n2);
//            cout<<m<<endl;
            if(m == 2)        //n2>n1 
            {
                cout<<"-";
            }
        }
        else if(c[0] == ‘-‘)    //负相同,将n1-n2变成，n2-n1; 
        {
            return toSub(n2, n1);
        }
    } 
    if(c[0] != c[1])
    {
        //进入加运算 
        if(c[0] == ‘-‘)
        {
            int m = judgebig(n1, n2);
            if(m == 1)
            {
                cout<<‘-‘;
            }
        }
    }
    
    for(;i >= 0; i--)
    {
        cout<<a[i];
    }
    return ‘0‘;
}

//乘
void toMul(char n1[N], char n2[N])
{
    char temp[N];
    int a[N],b[N],k[N] = {0};    //注意这里数组k是存储结果,不要顺手用全局数组c 
    int i,j,h;
    int len1,len2;
    if( strlen(n1)<strlen(n2) )
    {
        strcpy(temp,n1);
        strcpy(n1,n2);
        strcpy(n2,temp);
    }
    
    len1=strlen(n1);
    len2=strlen(n2);
//    memset(c,0,sizeof(c)); //将数组c全换成0
    
    for(i=len1-1,j=0;i>=0;i--,j++)    //存储n1为整型数组a 
    {
        a[j]=n1[i]-‘0‘;
    }
    for(i=len2-1,j=0;i>=0;i--,j++)    //存储n2为整型数组b 
    {
        b[j]=n2[i]-‘0‘;
    }
    
    /*
    从第一个数开始，依次乘以第二个数的每一位，超过10进位 
    */ 
    for(i=0;i<len2;i++)
    {
        for(j=0;j<len1;j++)
        {
            k[i+j]=a[j]*b[i]+k[i+j];
        }
    }
    for(i=0;i<2*len1;i++)    
    {
        if(k[i]>=10)    //超过10进位 
        {
            k[i+1]=k[i+1]+k[i]/10;
            k[i]=k[i]%10;
        }
    }
    
    
    i=2*len1;
    while(k[i]==0)
    {
        i--;
    }
    
    //判断正负号
    if(c[0] != c[1])
    {
        cout<<‘-‘;
    }
     
    if(i<0)
    {
        cout<<"0"<<endl;
    }
    else
    {
        for(;i>=0;i--)
               cout<<k[i];
    } 
}

//除
void toDiv(char n1[N], char n2[N])
{
    int i,p;
    int len1,len2;
    int result[N];

    len1=strlen(n1);
    len2=strlen(n2);
    if(len1<len2||(len1==len2&&strncmp(n1,n2,len2)<0))   //如果n1<n2,除法运算直接输出0
    {
        cout<<"0"<<endl; 
    }
    p=0;
    while(1)
    {
        result[p]=0;
        //要比较两数的大小 
        while(strncmp(n1,n2,len2)>=0)       //一直进行减法，直到不能减为止
         {
            sub(n1, n2, len1, len2);
            result[p]++;
        }
        p++;
        if(len1==len2)
            break;
        for(i=len2-1;i>=0;i--)             //在n2前面补0，以便进行减法运算
         {
            n2[i+1]=n2[i];
        }
        n2[0]=‘0‘;
        len2++;
        n2[len2]=‘\0‘;
    }
    i=0;
    while(1)
    {
        if(result[i]==0)
            i++;
        else
            break;
    }
    
    //判断正负号 
    if(c[0] != c[1])
    {
        cout<<‘-‘;
    }
    
    for(;i<p;i++)
        cout<<result[i];
}


//加等于 
char Add(char n1[N], char n2[N])
{
    return toAdd(n1, n2);
}

//减等于 
char Sub(char n1[N], char n2[N])
{
    return toSub(n1, n2);
}

//乘等于 
void Mul(char n1[N], char n2[N])
{
    toMul(n1, n2);
}

//除等于 
void Div(char n1[N], char n2[N])        //有问题，除等于情况输出为零 
{
    toDiv(n1, n2);
}

int main(void)
{
    while(1)
    {
        char num1[N], num2[N], result[N], i = 0, j;
        char n1[N], n2[N];                        
        cout<<"请输入第一个运算数："<<endl;
        cin>>num1;
        
        cout<<"请输入第二个运算数："<<endl;
        cin>>num2; 
        
        //去掉正负号存入n1 
        if(num1[0] == ‘-‘)
        {
            i++;
            c[0] = num1[0];
            while(i<N)
            {
                n1[i-1] = num1[i];
                i++;
            }
        }
        else
        {
            c[0] = ‘+‘;
            while(i<N)
            {
                n1[i] = num1[i];
                i++;
            }
        }
        
        //去掉正负号存入n2 
        if(num2[0] == ‘-‘)
        {
            i = 1;
            c[1] = num2[0];
            while(i<N)
            {
                n2[i-1] = num2[i];
                i++;
            }
        }
        else
        {
            i = 0;
            c[1] = ‘+‘;
            while(i<N)
            {
                n2[i] = num2[i];
                i++;
            } 
        }
//        cout<<n1<<‘ ‘<<n2<<endl;
        
        cout<<"请输入数字：1.+ 2.- 3.* 4./ 5.+= 6.-= 7.*= 8./="<<endl; 
        int q;
        cin>>q;
        switch(q)
        {
            case 1:
                cout<<"加运算："<<endl;
                toAdd(n1, n2);
                break;
                
            case 2:
                cout<<endl;
                cout<<"减运算："<<endl;
                toSub(n1, n2);
                break;
                
            case 3:
                cout<<endl; 
                cout<<"乘运算："<<endl;
                toMul(n1, n2);
                break;
                
            case 4:
                cout<<endl;
                cout<<"除运算："<<endl;
                toDiv(n1, n2);
                break;
                
            case 5:    
                cout<<endl;
                cout<<"加等于运算："<<endl;
                Add(n1, n2);cout<<endl; 
                break;
                
            case 6:    
                cout<<"减等于运算："<<endl;
                Sub(n1, n2);cout<<endl;
                break; 
            case 7:    
                cout<<"乘等于运算："<<endl;             
                Mul(n1, n2);cout<<endl; 
                break;
            case 8:    
                cout<<"除等于运算："<<endl;
                Div(n1, n2);cout<<endl; 
                break;
//            case 9:
//                cout<<"加运算："<<endl;
//                toAdd(n1, n2);
//                cout<<endl;
//                cout<<"减运算："<<endl;
//                toSub(n1, n2);
//                cout<<endl; 
//                cout<<"乘运算："<<endl;
//                toMul(n1, n2);
//                cout<<endl;
//                cout<<"除运算："<<endl;
//                toDiv(n1, n2);
//                cout<<endl;
//                cout<<"加等于运算："<<endl;
//                Add(n1, n2);cout<<endl; 
//                cout<<"减等于运算："<<endl;
//                Sub(n1, n2);cout<<endl;
//                cout<<"乘等于运算："<<endl;            //有问题 
//                Mul(n1, n2);cout<<endl; 
//                cout<<"除等于运算："<<endl;
//                Div(n1, n2);cout<<endl; 
//                break;
            default: 
                cout<<"输入出错！请重新输入："<<endl;
                break;
        }
        cout<<endl<<endl;
    }

    return 0;
}


/*
int a[100];
整数数组不能用cout<<a输出，char a[100]可以那样输出 

要考虑到数组的范围，今天定义了1000大小的数组，反应很慢，误认为是程序出错，定义成100 就好了 
*/