各种模板 长期更新

大数模板

#include <iostream>#include <cstdio>#include <algorithm>#include <string>#include <cmath>#include <stack>#include <cstring>using namespace std;//const int maxn = 1e6;  //大数位数#define MAXN 9999#define MAXSIZE 10#define DLEN 4class BigNum{private:    int a[MAXN];    //可以控制大数的位数    int len;       //大数长度public:    BigNum(){ len = 1;memset(a,0,sizeof(a)); }   //构造函数    BigNum(const int);       //将一个int类型的变量转化为大数    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 BigNum & T) const;    bool   operator==(const BigNum & T) const;    bool   operator>(const int & t)const;      //大数和一个int类型的变量的大小比较    bool   operator<(const int &t) const;    bool   operator==(const int &t) const;    void print();       //输出大数};bool BigNum::operator==(const BigNum & T) const {    return !(*this > T) && !(T > *this);}bool BigNum::operator==(const int &t) const {    BigNum T = BigNum(t);    return *this == T;}bool BigNum::operator<(const BigNum & T) const {    return T > *this;}bool BigNum::operator<(const int &t) const {    return BigNum(t) > *this;}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，大数之间进行赋值运算{    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)   //重载输入运算符{    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--)    {        cout.width(DLEN);        cout.fill('0');        cout << b.a[i];    }    return out;}BigNum BigNum::operator+(const BigNum & T) const   //两个大数之间的相加运算{    BigNum t(*this);    int i,big;      //位数    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[t1.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运算{    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运算{    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 (int i = len-2; i >= 0; --i) {        printf("%04d", a[i]);    }}int main(){    int t, n;    cin >> t;    while(t--)    {        scanf("%d", &n);        BigNum cnt = 1, ans = 0;        for(int i = 1; i <= n; i++)        {            cnt = cnt * i;        };        for(int i = 1; i <= n; i++)        {            ans = ans + cnt/i;;            BigNum tmp = (cnt/i);        }        ans.print();        printf(".0\n");    }    return 0;}