高精度模板

/*
高精度模版
*/

#include <stdio.h>
#include <math.h>
#include <string.h>
#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

const int numlen = 2005; // 需要的位数
const int numbit = 4;   // 数组一位表示的整数
const int addbit = 10000;//进位数
const int maxn = numlen/numbit + 10;   // 数组要开的位数

int max(int a, int b) { return a>b?a:b; }
struct bign {
int len, s[numlen];
bign() {
memset(s, 0, sizeof(s));
len = 1;
}
bign(int num) { *this = num; }
bign(const char *num) { *this = num; }
bign operator = (const int num) {
char s[numlen];
sprintf(s, "%d", num);
*this = s;
return *this;
}
bign operator = (const char *num) {
int clen = strlen(num);
while(clen > 1 && num[0] == '0') num++, clen--;
len = 0;
for(int i = clen-1;i >= 0;i -= numbit) {
int top = min(numbit, i+1), mul = 1;
s[len] = 0;
for(int j = 0;j < top; j++) {
s[len] += (num[i-j]-'0')*mul;
mul *= 10;
}
len++;
}
deal();
return *this;
}

void deal() {
while(len > 1 && !s[len-1]) len--;
}

bign operator + (const bign &a) const {
bign ret;
ret.len = 0;
int top = max(len, a.len) , add = 0;
for(int i = 0;add || i < top; i++) {
int now = add;
if(i < len) now += s[i];
if(i < a.len)   now += a.s[i];
ret.s[ret.len++] = now%addbit;
add = now/addbit;
}
return ret;
}
bign operator - (const bign &a) const {
bign ret;
ret.len = 0;
int cal = 0;
for(int i = 0;i < len; i++) {
int now = s[i] - cal;
if(i < a.len)   now -= a.s[i];
if(now >= 0)    cal = 0;
else {
cal = 1; now += addbit;
}
ret.s[ret.len++] = now;
}
ret.deal();
return ret;
}
bign operator * (const bign &a) const {
bign ret;
ret.len = len + a.len;
for(int i = 0;i < len; i++) {
int pre = 0;
for(int j = 0;j < a.len; j++) {
int now = s[i]*a.s[j] + pre;
pre = 0;
ret.s[i+j] += now;
if(ret.s[i+j] >= addbit) {
pre = ret.s[i+j]/addbit;
ret.s[i+j] -= pre*addbit;
}
}
if(pre) ret.s[i+a.len] = pre;
}
ret.deal();
return ret;
}

//乘以小数，直接乘快点  ***********注意计算过程可能会爆int
bign operator * (const int num) {
bign ret;
ret.len = 0;
int bb = 0;
for(int i = 0;i < len; i++) {
int now = bb + s[i]*num;
ret.s[ret.len++] = now%addbit;
bb = now/addbit;
}
while(bb) {
ret.s[ret.len++] = bb % addbit;
bb /= addbit;
}
ret.deal();
return ret;
}
// 除以一个小整数     ***********注意计算过程可能会爆int
bign operator / (const int a) const {
bign ret;
ret.len = len;
int pre = 0;
for(int i = len-1;i >= 0; i--) {
ret.s[i] = (s[i] + pre*addbit)/a;
pre = s[i] + pre*addbit - a*ret.s[i];
}
ret.deal();
return ret;
}

bign operator % (const int a) const {
bign b = *this / a;
return *this - b*a;
}

bign operator += (const bign &a) { *this = *this + a; return *this; }
bign operator -= (const bign &a) { *this = *this - a; return *this; }
bign operator *= (const bign &a) { *this = *this * a; return *this; }
bign operator /= (const int a) { *this = *this / a; return *this; }
bign operator %= (const int a) { *this = *this % a; return *this; }

bool operator < (const bign &a) const {
if(len != a.len)    return len < a.len;
for(int i = len-1;i >= 0; i--) if(s[i] != a.s[i])
return s[i] < a.s[i];
return false;
}
bool operator > (const bign &a) const  { return a < *this; }
bool operator <= (const bign &a) const { return !(*this > a); }
bool operator >= (const bign &a) const { return !(*this < a); }
bool operator == (const bign &a) const { return !(*this > a || *this < a); }
bool operator != (const bign &a) const { return *this > a || *this < a; }

void print() {
printf("%d", s[len-1]);
for(int i = len-2;i >= 0; i--) {
printf("%04d", s[i]);
}
puts("");
}

string str() const {
string ret = "";
for(int i = 0;i < len; i++) ret = char(s[i] + '0') + ret;
return ret;
}
};
istream& operator >> (istream &in, bign &x) {
string s;
in >> s;
x = s.c_str();
return in;
}
ostream& operator << (ostream &out, const bign &x) {
printf("%d", x.s[x.len-1]);
for(int i = x.len-2;i >= 0; i--)    printf("%04d", x.s[i]);
return out;
}

/*
* 完全大数模板 By Kuangbin
* 输出cin>>a
* 输出a.print();
* 注意：这个输入不能自动去掉前导0的，
*		先读入到char数组，去掉前导0，再用构造函数。
*/
#define MAXN 9999
#define MAXSIZE 1010
#define DLEN 4

class BigNum
{
private:
int a[500];  //可以控制大数的位数
int len;
public:
BigNum(){len=1;memset(a,0,sizeof(a));}  //构造函数
BigNum(const int);     //将一个int类型的变量转化成大数
BigNum(const char*);   //将一个字符串类型的变量转化为大数
BigNum(const BigNum &); //拷贝构造函数
BigNum &operator=(const BigNum &); //重载赋值运算符，大数之间进行赋值运算
friend istream& operator>>(istream&,BigNum&); //重载输入运算符
friend ostream& operator<<(ostream&,BigNum&); //重载输出运算符

BigNum operator+(const BigNum &)const;  //重载加法运算符，两个大数之间的相加运算
BigNum operator-(const BigNum &)const;  //重载减法运算符，两个大数之间的相减运算
BigNum operator*(const BigNum &)const;  //重载乘法运算符，两个大数之间的相乘运算
BigNum operator/(const int &)const;     //重载除法运算符，大数对一个整数进行相除
运算

BigNum operator^(const int &)const;     //大数的n次方运算
int operator%(const int &)const;        //大数对一个int类型的变量进行取模运算
bool operator>(const BigNum &T)const;   //大数和另一个大数的大小比较
bool operator>(const int &t)const;      //大数和一个int类型的变量的大小比较

void print();        //输出大数
};
BigNum::BigNum(const int b)   //将一个int类型的变量转化为大数
{
int c,d=b;
len=0;
memset(a,0,sizeof(a));
while(d>MAXN)
{
c=d-(d/(MAXN+1))*(MAXN+1);
d=d/(MAXN+1);
a[len++]=c;
}
a[len++]=d;
}
BigNum::BigNum(const char *s)  //将一个字符串类型的变量转化为大数
{
int t,k,index,L,i;
memset(a,0,sizeof(a));
L=strlen(s);
len=L/DLEN;
if(L%DLEN)len++;
index=0;
for(i=L-1;i>=0;i-=DLEN)
{
t=0;
k=i-DLEN+1;
if(k<0)k=0;
for(int j=k;j<=i;j++)
t=t*10+s[j]-'0';
a[index++]=t;
}
}
BigNum::BigNum(const BigNum &T):len(T.len)  //拷贝构造函数
{
int i;
memset(a,0,sizeof(a));
for(i=0;i<len;i++)
a[i]=T.a[i];
}
BigNum & BigNum::operator=(const BigNum &n)  //重载赋值运算符，大数之间赋值运算
{
int i;
len=n.len;
memset(a,0,sizeof(a));
for(i=0;i<len;i++)
a[i]=n.a[i];
return *this;
}
istream& operator>>(istream &in,BigNum &b)
{
char ch[MAXSIZE*4];
int i=-1;
in>>ch;
int L=strlen(ch);
int count=0,sum=0;
for(i=L-1;i>=0;)
{
sum=0;
int t=1;
for(int j=0;j<4&&i>=0;j++,i--,t*=10)
{
sum+=(ch[i]-'0')*t;
}
b.a[count]=sum;
count++;
}
b.len=count++;
return in;
}
ostream& operator<<(ostream& out,BigNum& b)  //重载输出运算符
{
int i;
cout<<b.a[b.len-1];
for(i=b.len-2;i>=0;i--)
{
printf("%04d",b.a[i]);
}
return out;
}
BigNum BigNum::operator+(const BigNum &T)const   //两个大数之间的相加运
{
BigNum t(*this);
int i,big;
big=T.len>len?T.len:len;
for(i=0;i<big;i++)
{
t.a[i]+=T.a[i];
if(t.a[i]>MAXN)
{
t.a[i+1]++;
t.a[i]-=MAXN+1;
}
}
if(t.a[big]!=0)
t.len=big+1;
else t.len=big;
return t;
}
BigNum BigNum::operator-(const BigNum &T)const  //两个大数之间的相减运算
{
int i,j,big;
bool flag;
BigNum t1,t2;
if(*this>T)
{
t1=*this;
t2=T;
flag=0;
}
else
{
t1=T;
t2=*this;
flag=1;
}
big=t1.len;
for(i=0;i<big;i++)
{
if(t1.a[i]<t2.a[i])
{
j=i+1;
while(t1.a[j]==0)
j++;
t1.a[j--]--;
while(j>i)
t1.a[j--]+=MAXN;
t1.a[i]+=MAXN+1-t2.a[i];
}
else t1.a[i]-=t2.a[i];
}
t1.len=big;
while(t1.a[len-1]==0 && t1.len>1)
{
t1.len--;
big--;
}
if(flag)
t1.a[big-1]=0-t1.a[big-1];
return t1;
}
BigNum BigNum::operator*(const BigNum &T)const  //两个大数之间的相乘
{
BigNum ret;
int i,j,up;
int temp,temp1;
for(i=0;i<len;i++)
{
up=0;
for(j=0;j<T.len;j++)
{
temp=a[i]*T.a[j]+ret.a[i+j]+up;
if(temp>MAXN)
{
temp1=temp-temp/(MAXN+1)*(MAXN+1);
up=temp/(MAXN+1);
ret.a[i+j]=temp1;
}
else
{
up=0;
ret.a[i+j]=temp;
}
}
if(up!=0)
ret.a[i+j]=up;
}
ret.len=i+j;
while(ret.a[ret.len-1]==0 && ret.len>1)ret.len--;
return ret;
}
BigNum BigNum::operator/(const int &b)const  //大数对一个整数进行相除运算
{
BigNum ret;
int i,down=0;
for(i=len-1;i>=0;i--)
{
ret.a[i]=(a[i]+down*(MAXN+1))/b;
down=a[i]+down*(MAXN+1)-ret.a[i]*b;
}
ret.len=len;
while(ret.a[ret.len-1]==0 && ret.len>1)
ret.len--;
return ret;
}
int BigNum::operator%(const int &b)const   //大数对一个 int类型的变量进行取模
{
int i,d=0;
for(i=len-1;i>=0;i--)
d=((d*(MAXN+1))%b+a[i])%b;
return d;
}
BigNum BigNum::operator^(const int &n)const  //大数的n次方运算
{
BigNum t,ret(1);
int i;
if(n<0)exit(-1);
if(n==0)return 1;
if(n==1)return *this;
int m=n;
while(m>1)
{
t=*this;
for(i=1;(i<<1)<=m;i<<=1)
t=t*t;
m-=i;
ret=ret*t;
if(m==1)ret=ret*(*this);
}
return ret;
}
bool BigNum::operator>(const BigNum &T)const    //大数和另一个大数的大小比较
{
int ln;
if(len>T.len)return true;
else if(len==T.len)
{
ln=len-1;
while(a[ln]==T.a[ln]&&ln>=0)
ln--;
if(ln>=0 && a[ln]>T.a[ln])
return true;
else
return false;
}
else
return false;
}

bool BigNum::operator>(const int &t)const  //大数和一个int类型的变量的大小比较
{
BigNum b(t);
return *this>b;
}
void BigNum::print()   //输出大数
{
int i;
printf("%d",a[len-1]);
for(i=len-2;i>=0;i--)
printf("%04d",a[i]);
printf("\n");
}