UVA 10288 Coupons---概率 && 分数类模板

题目链接：

https://cn.vjudge.net/problem/UVA-10288

题目大意：

一种刮刮卡一共有n种图案，每张可刮出一个图案，收集n种就有奖，问平均情况下买多少张才能中奖？用最简的分数形式表示答案。n<=33。

解题思路：

假设现在已刮到k个图案了，刮到新图案的概率是(n-k)/n，即若要再收集一个新图案平均要刮s=n/(n-k)次。所以只需要穷举k=1 to n，累加s的和就行了。注意式子可以将分子n提取出来。

先附上分数类模板

 struct Fraction//分数类
 {
     ll num, den;//num为分子，den为分母
     Fraction(ll num = , ll den =  )
     {
         if(den < )
         {
             num = -num;
             den = -den;
         }
         assert(den != );//den=0程序终止
         ll 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;
     }
 };

注意输出格式（很伤）

 #include<bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 struct Fraction//分数类
 {
     ll num, den;//num为分子，den为分母
     Fraction(ll num = , ll den =  )
     {
         if(den < )
         {
             num = -num;
             den = -den;
         }
         assert(den != );//den=0程序终止
         ll 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 main()
 {
     ll n, k, ans, cases = ;
     while(cin >> n)
     {
         Fraction ans;
         for(int i = ; i <= n; i++)
         {
             ans = ans + Fraction(n, i);
         }
         ll t = ans.num / ans.den;
         ans.num -= t * ans.den;
         if(ans.num == )
         {
             cout<<t<<endl;
         }
         else
         {
             string s;
             stringstream ss, ss1;
             ss << t;
             ss >> s;
             int kongge = s.size();
             for(int i = ; i <= kongge; i++)cout<<" ";
             cout<<ans.num<<"\n";

             ss1 << ans.den;
             ss1 >> s;
             int duanxian = s.size();
             cout<<t<<" ";
             for(int i = ; i < duanxian; i++)cout<<"-";
             cout<<"\n";
             for(int i = ; i <= kongge; i++)cout<<" ";
             cout<<ans.den<<"\n";
         }
     }
     return ;
 }