大数高精度运算（模板）

Posted 2020-06-14

前言：高精度运算。是指參与运算的数(加数。减数，因子……）范围大大超出了标准数据类型（整型，实型）能表示的范围的运算。

模板：包含大数加减乘除。大数与int数的乘法，模板能够不断扩充。

代码：

/*
所有亲測可用，可是不能用于负数的运算，仅仅能对正数进行大数运算
*/
const int ten[4]= {1,10,100,1000};
const int maxl = 300;
struct BigNumber
{
    int d[maxl];
    char s[maxl];
    BigNumber(const char s[])
    {
        int len=strlen(s);
        d[0]=(len-1)/4+1;
        int i,j,k;
        for(int i=1; i<maxl; i++)
            d[i]=0;
        for(int i=len-1; i>=0; i--)
        {
            j=(len-i-1)/4+1;
            k=(len-i-1)%4;
            d[j]+=ten[k]*(s[i]-'0');
        }
        while(d[0]>1&&d[d[0]]==0)
            d[0]--;
    }
    BigNumber()
    {
        *this=BigNumber("0");
    }
    BigNumber(int x)
    {
        for (int i=0; i<maxl; i++) d[i]=0;
        if (!x) d[0]=1;
        while(x)
        {
            d[++d[0]]=x%10000;
            x/=10000;
        }
    }
    BigNumber(long long x)
    {
        for (int i=0; i<maxl; i++) d[i]=0;
        if (!x) d[0]=1;
        while(x)
        {
            d[++d[0]]=x%10000;
            x/=10000;
        }
    }
    void print()
    {
        int len=d[0];
        printf("%d",d[d[0]]);
        for(int i=len-1; i>=1; i--)
        {
            if(d[i]>=1000)
                printf("%d",d[i]);
            else if(d[i]>=100)
                printf("0%d",d[i]);
            else if(d[i]>=10)
                printf("00%d",d[i]);
            else printf("000%d",d[i]);
        }

        printf("\n");
    }
    void toString()
    {
        int top=0;
        int i,j,temp;
        for(i=3; i>=1; i--)
            if(d[d[0]]>=ten[i])
                break;
        temp=d[d[0]];
        for(j=i; j>=0; j--)
        {
            s[top++]=(char)(temp/ten[j]+'0');
            temp%=ten[j];
        }
        for(i=d[0]-1; i>0; i--)
        {
            temp=d[i];
            for(j=3; j>=0; j--)
            {
                s[top++]=(char)(temp/ten[j]+'0');
                temp%=ten[j];
            }
        }
    }
} zero=BigNumber(),d,temp,mid1[15],a[3005];
bool operator < (const BigNumber &a,const BigNumber &b)
{
    if(a.d[0]!=b.d[0])
        return a.d[0]<b.d[0];
    int i;
    for(i=a.d[0]; i>0; i--)
        if(a.d[i]!=b.d[i])
            return a.d[i]<b.d[i];
    return false;
}
bool operator > (const BigNumber &a,const BigNumber &b)
{
    if(b.d[0]!=a.d[0])
        return b.d[0]<a.d[0];
    int i;
    for(i=b.d[0]; i>0; i--)
        if(a.d[i]!=b.d[i])
            return b.d[i]<a.d[i];
    return false;
}
bool operator ==(const BigNumber &a,const BigNumber &b)
{
    int i;
    if(a.d[0]!=b.d[0])
        return false;
    for(i=1; i<=a.d[0]; i++)
        if(a.d[i]!=b.d[i])
            return false;
    return true;
}
bool operator <= (const BigNumber &a,const BigNumber &b)
{
    return a<b||a==b;
}
bool operator >= (const BigNumber &a,const BigNumber &b)
{
    return a>b||a==b;
}
BigNumber operator +(const BigNumber &a,const BigNumber &b)
{
    BigNumber c;
    c.d[0]=max(a.d[0],b.d[0]);
    int i,x=0;
    for(i=1; i<=c.d[0]; i++)
    {
        x=a.d[i]+b.d[i]+x;
        c.d[i]=x%10000;
        x/=10000;
    }
    while(x!=0)
    {
        c.d[++c.d[0]]=x%10000;
        x/=10000;
    }
    return c;
}
BigNumber operator -(const BigNumber &a,const BigNumber &b)
{
    BigNumber c;
    c.d[0]=a.d[0];
    int i,x=0;
    for(i=1; i<=c.d[0]; i++)
    {
        x=10000+a.d[i]-b.d[i]+x;
        c.d[i]=x%10000;
        x=x/10000-1;
    }
    while((c.d[0]>1)&&(c.d[c.d[0]]==0))
        c.d[0]--;
    return c;
}
BigNumber operator *(const BigNumber &a,const BigNumber &b)
{
    BigNumber c;
    c.d[0]=a.d[0]+b.d[0];
    int i,j,x;
    for(i=1; i<=a.d[0]; i++)
    {
        x=0;
        for(int j=1; j<=b.d[0]; j++)
        {
            x=a.d[i]*b.d[j]+x+c.d[i+j-1];
            c.d[i+j-1]=x%10000;
            x/=10000;
        }
        c.d[i+b.d[0]]=x;
    }
    while((c.d[0]>1)&&(c.d[c.d[0]]==0))
        --c.d[0];
    return c;
}
bool smaller(const BigNumber &a,const BigNumber &b,int delta)
{
    if(a.d[0]+delta!=b.d[0])
        return a.d[0]+delta<b.d[0];
    int i;
    for(i=a.d[0]; i>0; i--)
        if(a.d[i]!=b.d[i+delta])
            return a.d[i]<b.d[i+delta];
    return true;
}
void Minus (BigNumber &a,const BigNumber &b,int delta)
{
    int i,x=0;
    for(i=1; i<=a.d[0]-delta; i++)
    {
        x=10000+a.d[i+delta]-b.d[i]+x;
        a.d[i+delta]=x%10000;
        x=x/10000-1;
    }
    while((a.d[0]>1)&&(a.d[a.d[0]]==0))
        a.d[0]--;
}
BigNumber operator *(const BigNumber &a,const int &k)
{
    BigNumber c;
    c.d[0]=a.d[0];
    int i,x=0;
    for(i=1; i<=a.d[0]; i++)
    {
        x=a.d[i]*k+x;
        c.d[i]=x%10000;
        x/=10000;
    }
    while(x>0)
    {
        c.d[++c.d[0]]=x%10000;
        x/=10000;
    }
    while((c.d[0]>1)&&(c.d[c.d[0]]==0))
        c.d[0]--;
    return c;
}
BigNumber operator /(const BigNumber &a,const BigNumber &b)
{
    BigNumber c;
    d=a;
    int i,j,temp;
    mid1[0]=b;
    for(int i=1; i<=13; i++)
        mid1[i]=mid1[i-1]*2;
    for(i=a.d[0]-b.d[0]; i>=0; i--)
    {
        temp=8192;
        for(j=13; j>=0; j--)
        {
            if(smaller(mid1[j],d,i))
            {
                Minus(d,mid1[j],i);
                c.d[i+1]+=temp;
            }
            temp/=2;
        }
    }
    c.d[0]=max(1,a.d[0]-b.d[0]+1);
    while((c.d[0]>1)&&(c.d[c.d[0]]==0))
        c.d[0]--;
    return c;
}
BigNumber operator %(const BigNumber &a,const BigNumber &b)
{
    BigNumber c=a/b;
    return a-b*c;
}