【模板】【數論】高精度
阿新 • • 發佈:2019-02-08
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstdlib>
#include <cstring>
#include <cmath>
#define re register
using namespace std;
const int MAXN = 10003;
const int base = 10000;
struct Bigint{
int num[MAXN];
int len,sign;
Bigint() {memset (num,0,sizeof(num)); len=1; sign=1;}
Bigint operator = (const char *s)
{
int l=strlen(s);
int k=1;
len=1;
for(re int i=1;i<=l;i++)
{
if(k==base) k=1,++len;
num[len]+=(s[l-i]-'0')*k;
k=k*10;
}
return *this;
}
Bigint operator = (const int &x)
{
char s[MAXN];
sprintf(s,"%d",x);
*this=s;
return *this;
}
bool operator < (const Bigint &x) const
{
bool flag=0;
if(sign==-1&&x.sign==1) return true;
if(sign==1 &&x.sign==-1) return false;
if(sign==-1&&x.sign==-1) flag=1;
if(len!=x.len) return len<x.len;
for(re int i=len;i>=1;i--)
if(num[i]!=x.num[i]) return flag?x.num[i]<num[i]:num[i]<x.num[i];
return false;
}
bool operator > (const Bigint &x) const {return x<*this;}
bool operator <= (const Bigint &x) const {return !(*this>x);}
bool operator >= (const Bigint &x) const {return !(*this<x);}
bool operator == (const Bigint &x) const {return !(*this<x)&&!(*this>x);}
bool operator != (const Bigint &x) const {return !(*this==x);}
Bigint operator + (const Bigint &b) const
{
Bigint c;
c.len=max(len,b.len);
for(re int i=1;i<=c.len;i++)
{
c.num[i]+=num[i]+b.num[i];
if(c.num[i]>=base) c.num[i]-=base,++c.num[i+1];
}
if(c.num[c.len+1]) ++c.len;
return c;
}
Bigint operator += (const Bigint &b)
{
return *this=*this+b;
}
Bigint operator + (const int &x)
{
Bigint b;
b=x;
return *this+b;
}
Bigint operator += (const int &b)
{
return *this=*this+b;
}
Bigint operator ++ (int b)
{
return *this+=1;
}
Bigint operator - (const Bigint &x) const//一定要加const!因為有swap操作!
{
Bigint a,b,c;
a=*this;b=x;
c.len=max(a.len,b.len);
if(*this<b) swap(a,b),c.sign=-1;
for(re int i=1;i<=c.len;i++)
{
c.num[i]+=a.num[i]-b.num[i];
if(c.num[i]<0) c.num[i]+=base,--c.num[i+1];
}
while(!c.num[c.len]&&c.len>1) --c.len;
return c;
}
Bigint operator -= (const Bigint &b)
{
return *this=*this-b;
}
Bigint operator - (const int &x)
{
Bigint b;
b=x;
return *this-b;
}
Bigint operator -= (const int &b)
{
return *this=*this-b;
}
Bigint operator -- (int b)
{
return *this-=1;
}
Bigint operator * (const int &b) const
{
Bigint c;
c.len=len+1;
for(re int i=1;i<=len;i++)
{
c.num[i]+=num[i]*b;
c.num[i+1]=c.num[i]/base;
c.num[i]%=base;
}
while(!c.num[c.len]&&c.len>1) --c.len;
return c;
}
Bigint operator * (const Bigint &b) const
{
Bigint c;
if(*this+b==*this||*this+b==b) return c;
c.len=len+b.len;
for(re int i=1;i<=len;i++)
for(re int j=1;j<=b.len;j++)
{
c.num[i+j-1]+=num[i]*b.num[j];
c.num[i+j]+=c.num[i+j-1]/base;
c.num[i+j-1]%=base;
}
while(!c.num[c.len]&&c.len>1) --c.len;
return c;
}
Bigint operator *= (const Bigint &b)
{
return *this=*this*b;
}
Bigint operator / (const int &b) const
{
Bigint c;
c.len=len;
int x=0;
for(re int i=c.len;i>=1;i--)
{
c.num[i]+=(x*base+num[i])/b;
x=(x*base+num[i])%b;
}
while(!c.num[c.len]&&c.len>1) --c.len;
return c;
}
int operator % (const int &b) const
{
int ans=0;
for(re int i=1;i<=len;i++) ans=(ans*10+num[i])%b;
return ans;
}
Bigint operator %= (const int &b)
{
return *this=*this%b;
}
Bigint Copy(const Bigint &a,int x)//從高位開始擷取長度為x的子段
{
Bigint t;
t.len=a.len+x-1;
for(int i=1;i<=a.len;i++) t.num[i+x-1]=a.num[i];
while(!t.num[t.len]&&t.len>1) --t.len;
return t;
}
//模擬豎式 高精除
Bigint Div1(const Bigint &a,const Bigint &b,Bigint &mod)
{
Bigint c;
c.len=a.len-b.len+1;
mod=a;
for(int i=c.len;i>=1;i--)
{
Bigint t;
t=Copy(b,i);
while(mod>=t)
{
c.num[i]++;
mod-=t;
}
}
while(!c.num[c.len]&&c.len>0) --c.len;
return c;
}
//倍增 模擬豎式 高精除
Bigint Div2(const Bigint &a,const Bigint &b,Bigint &mod)
{
Bigint c;
c.len=a.len-b.len+1;
mod=a;
int pw[20]; pw[0]=1;
for(int i=1;i<=15;i++) pw[i]=pw[i-1]<<1;//預處理倍增陣列(2^k)
for(int i=c.len;i>=1;i--)
{
Bigint t;
t=Copy(b,i);
for(int j=15;j>=0;j--)
if(mod>=t*pw[j])
{
c.num[i]+=pw[j];
mod-=t*pw[j];
}
}
while(!c.num[c.len]&&c.len>1) --c.len;
return c;
}
Bigint operator / (const Bigint &b)
{
Bigint c;
if(*this<b) return c;
return Div2(*this,b,c);
}
Bigint operator % (const Bigint &b)
{
if(*this<b) return *this;
Bigint c;
Div2(*this,b,c);
return c;
}
/*
//二分高精除,基於高精乘,高精除單精 O(len^2*loglen)
Bigint operator / (const Bigint &b)
{
Bigint l,r,mid;
if(*this<b) return l;
r=*this;
while(l<r)
{
mid=(l+r)/2;
if(mid*b<*this) l=mid+1;
else r=mid;
}
if(l*b>*this) l--;
return l;
}
Bigint operator % (const Bigint &b)
{
return *this-(*this/b)*b;
}
*/
Bigint operator %= (const Bigint &b)
{
return *this=*this%b;
}
inline void read()
{
char s[MAXN];
scanf("%s",s);
*this=s;
}
inline void write()
{
if(sign==-1) putchar('-');
printf("%d",num[len]);
for(re int i=len-1;i>=1;i--) printf("%04d",num[i]);
putchar('\n');
}
};
Bigint a,b;
int main()
{
a.read();
b.read();
(a+b).write();
(a-b).write();
(a*b).write();
(a/b).write();
(a%b).write();
return 0;
}