UVA10288 - Coupons （概率+递推）

公式E（x）=n Σ 1/i

因为当已经拿到k张不同的时候 拿到不同牌的期望是 （n-k）/n    ,1除于这个概率就是  n/(n-k) 然后从1到n加

#include<iostream>
#include<cstring>
#include<string>
#include<algorithm>
#include<cstdio>
#include<cassert>

using namespace std;

typedef long long ll;

ll gcd(ll a,ll b)
{
    return b==0?a:gcd(b,a%b);
}

struct Fraction
{
    long long num;
    long long den;
    Fraction(long long num=0,long long den=1)
    {
        if(den<0)
        {
            num=-num;
            den=-den;
        }
        long long g=gcd(abs(num),den);
        this->num=num/g;
        this->den=den/g;
    }
    Fraction operator +(const Fraction &o)const
    {
        return Fraction(num*o.den+den*o.num,den*o.den);
    }
    Fraction operator -(const Fraction &o)const
    {
        return Fraction(num*o.den-den*o.num,den*o.den);
    }
    Fraction operator *(const Fraction &o)const
    {
        return Fraction(num*o.num,den*o.den);
    }
    Fraction operator /(const Fraction &o)const
    {
        return Fraction(num*o.den,den*o.num);
    }
    bool operator <(const Fraction &o)const
    {
        return num*o.den<den*o.num;
    }
    bool operator ==(const Fraction &o)const
    {
        return num*o.den==den*o.num;
    }
};
int n;
int main()
{
    while(cin>>n)
    {
        Fraction ans(n,1);
        Fraction tmp(0,1);
        for(int i=1;i<=n;i++)
            tmp=tmp+Fraction(1,i);
        ans=ans*tmp;
        long long a,b,c;
        a=ans.num;
        b=ans.den;
        if(a/b!=0)
        {
            long long gd=gcd(a,b);
            a/=gd;
            b/=gd;
            c=a/b;
            a=a-c*b;
        }
        else
            c=0;
        if(a==0)
            printf("%lld\n",c);
        else
        {
            int l1,l2,l3;
            long long t1=c,t2=a,t3=b;
            l1=0;
            while(t1)
            {
                t1/=10;
                l1++;
            }
            l2=0;
            while(t2)
            {
                t2/=10;
                l2++;
            }
            l3=0;
            while(t3)
            {
                t3/=10;
                l3++;
            }
            if(l1!=0)
            {
                for(int i=0;i<=l1;i++) printf(" ");
                printf("%lld\n",a);
                printf("%lld ",c);
                int len=max(l2,l3);
                for(int i=0;i<len;i++) printf("-");
                printf("\n");
                for(int i=0;i<=l1;i++) printf(" ");
                printf("%lld\n",b);
            }
            else
            {
                printf("%I64d\n",a);
                int len=max(l2,l3);
                for(int i=0;i<len;i++)
                    printf("-");
                printf("\n");
                printf("%I64d\n",b);

            }
        }
    }
    return 0;
}