codeforces gym 100357 H (DP 高精度）

题目大意

　　有r*s张扑克牌，数字从1到 r，每种数字有s种颜色。

　　询问对于所有随机的d张牌，能选出c张组成顺子的概率和组成同花的概率。

解题分析

　　对于组成顺子的概率，令dp[i][j][k]表示一共选出了i张牌，数字从1~j，最后有k张牌是顺子。对于每个数字进行考虑，有0~s种选法。要保证连续c张牌的顺子。

　　对于组成同花的概率，令dp[i][j]表示一共选出了i张牌，颜色从1~j，。对于每种颜色进行考虑，有0~r种选法。要保证没有c张牌是相同颜色的。

　　最后用高精度来输出答案。

参考程序

 #include <bits/stdc++.h>
 using namespace std;

 const int N=;

 class bign
 {
     public:
     enum {MAXN = };
     int len, s[MAXN];
     void clean()
     {
         while(len >  && !s[len-]) len--;
     }
     bign ()
     {
         memset(s, , sizeof(s));
         len = ;
     }
     bign (int num) { *this = num; }
     bign (long long num) { *this = num; }
     bign (const char *num) { *this = num; }
     bign operator = (const long long num)
     {
         char s[MAXN];
         sprintf(s, "%I64d", num);
         *this = s;
         return *this;
     }
     bign operator = (const int num)
     {
         char s[MAXN];
         sprintf(s, "%d", num);
         *this = s;
         return *this;
     }
     bign operator = (const char *num)
     {
         for(int i = ; num[i] == '' && num[]!='\0'; num++) ;  //去前导0
         len = strlen(num);
         for(int i = ; i < len; i++) s[i] = num[len-i-] - '';
         return *this;
     }
     bign operator + (const bign &b) const //+
     {
         bign c;
         c.len = ;
         for(int i = , g = ; g || i < max(len, b.len); i++)
         {
             int x = g;
             if(i < len) x += s[i];
             if(i < b.len) x += b.s[i];
             c.s[c.len++] = x % ;
             g = x / ;
         }
         return c;
     }
     bign operator += (const bign &b)
     {
         *this = *this + b;
         return *this;
     }
     bign operator * (const int x)
     {
         bign c;
         int j=; for (int y=x;y;y/=,j++);
         c.len = len + j;
         for(int i = ; i < len; i++)
             c.s[i]  = s[i] * x;

         for(int i = ; i < c.len; i++)
         {
             c.s[i+] += c.s[i]/;
             c.s[i] %= ;
         }
         c.clean();
         return c;
     }
     bign operator * (const bign &b) //*
     {
         bign c;
         c.len = len + b.len;
         for(int i = ; i < len; i++)
         {
             for(int j = ; j < b.len; j++)
             {
                 c.s[i+j] += s[i] * b.s[j];
             }
         }
         for(int i = ; i < c.len; i++)
         {
             c.s[i+] += c.s[i]/;
             c.s[i] %= ;
         }
         c.clean();
         return c;
     }
     bign operator *= (const bign &b)
     {
         *this = *this * b;
         return *this;
     }
     bign operator *= (const int x)
     {
         *this = *this * x;
         return *this;
     }
     bign operator - (const bign &b)
     {
         bign c;
         c.len = ;
         for(int i = , g = ; i < len; i++)
         {
             int x = s[i] - g;
             if(i < b.len) x -= b.s[i];
             if(x >= ) g = ;
             else
             {
                 g = ;
                 x += ;
             }
             c.s[c.len++] = x;
         }
         c.clean();
         return c;
     }
     bign operator -= (const bign &b)
     {
         *this = *this - b;
         return *this;
     }
     bign operator / (const bign &b)
     {
         bign c, f = ;
         for(int i = len-; i >= ; i--)
         {
             f = f*;
             f.s[] = s[i];
             while(f >= b)
             {
                 f -= b;
                 c.s[i]++;
             }
         }
         c.len = len;
         c.clean();
         return c;
     }
     bign operator /= (const bign &b)
     {
         *this  = *this / b;
         return *this;
     }
     bign operator % (const bign &b)
     {
         bign r = *this / b;
         r = *this - r*b;
         return r;
     }
     bign operator %= (const bign &b)
     {
         *this = *this % b;
         return *this;
     }
     bool operator < (const bign &b)
     {
         if(len != b.len) return len < b.len;
         for(int i = len-; i >= ; i--)
         {
             if(s[i] != b.s[i]) return s[i] < b.s[i];
         }
         return false;
     }
     bool operator > (const bign &b)
     {
         if(len != b.len) return len > b.len;
         for(int i = len-; i >= ; i--)
         {
             if(s[i] != b.s[i]) return s[i] > b.s[i];
         }
         return false;
     }
     bool operator == (const bign &b)
     {
         return !(*this > b) && !(*this < b);
     }
     bool operator != (const bign &b)
     {
         return !(*this == b);
     }
     bool operator <= (const bign &b)
     {
         return *this < b || *this == b;
     }
     bool operator >= (const bign &b)
     {
         return *this > b || *this == b;
     }
     operator string() const
     {
         string res = "";
         for(int i = ; i < len; i++) res = char(s[i]+'') + res;
         return res;
     }
     friend istream& operator >> (istream &in, bign &x)
     {
         string s;
         in >> s;
         x = s.c_str();
         return in;
     }
     friend ostream& operator << (ostream &out, const bign &x)
     {
         out << string(x);
         return out;
     }
 };

 int r,s,d,c;
 int C[N][N];
 bign dp[N][N];
 bign f[N][N][N];

 bign calc_1(int n,int k)
 {
     bign tmp=;
     for (int i=;i<=k;i++)
     {
         tmp=tmp*(n-(i-));
         tmp=tmp/i;
     }
     return tmp;
 }

 bign gcd(bign x,bign y)
 {
     //return y>0?gcd(y,x % y):x;
     bign tmp;
     if (y>) tmp=gcd(y,x % y); else tmp=x;
     return tmp;
 }

 int main()
 {
     freopen("poker.in","r",stdin);
     freopen("poker.out","w",stdout);

     for (int i=;i<N;i++) C[i][]=;
     for (int i=;i<N;i++)
         for (int j=;j<=i;j++)
             C[i][j]=C[i-][j]+C[i-][j-];

     cin.sync_with_stdio();
     while (cin>>r>>s>>d>>c)
     {
         if (!r && !s && !d && !c) break;

         memset(f,,sizeof(f));
         for (int j=;j<=r;j++) f[][j][]=;
         for (int i=;i<=d;i++)
             for (int j=;j<=r;j++)
             {
                 for (int k=;k<=min(i,c-);k++)
                     f[i][j][]+=f[i][j-][k];
                 for (int k=;k<=min(j,c-);k++)
                     for (int l=;l<=min(i,s);l++)
                         f[i][j][k]+=f[i-l][j-][k-]*C[s][l];
             }
         bign ans=;
         for (int k=;k<=c-;k++) ans+=f[d][r][k];
         bign a=calc_1(r*s,d),b=a-ans;
         cout<<b/gcd(a,b)<<"/"<<a/gcd(a,b)<<endl;

         memset(dp,,sizeof(dp));
         for (int j=;j<=s;j++) dp[][j]=;
         for (int i=;i<=d;i++)
             for (int j=;j<=s;j++)
                 for (int k=;k<=min(i,c-);k++)
                     dp[i][j]+=dp[i-k][j-]*C[r][k];
         a=calc_1(r*s,d),b=a-dp[d][s];
         cout<<b/gcd(a,b)<<"/"<<a/gcd(a,b)<<endl<<endl;
     }
 }