Cut the Cake

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 821    Accepted Submission(s): 396


Problem Description MMM got a big big big cake, and invited all her M friends to eat the cake together. Surprisingly one of her friends HZ took some (N) strawberries which MMM likes very much to decorate the cake (of course they also eat strawberries, not just for decoration). HZ is in charge of the decoration, and he thinks that it's not a big deal that he put the strawberries on the cake randomly one by one. After that, MMM would cut the cake into M pieces of sector with equal size and shape (the last one came to the party will have no cake to eat), and choose one piece first. MMM wants to know the probability that she can get all N strawberries, can you help her? As the cake is so big, all strawberries on it could be treat as points.

Input First line is the integer T, which means there are T cases.
For each case, two integers M, N indicate the number of her friends and the number of strawberry.
(2 < M, N <= 20, T <= 400)

Output As the probability could be very small, you should output the probability in the form of a fraction in lowest terms. For each case, output the probability in a single line. Please see the sample for more details.

Sample Input 2 3 3 3 4
Sample Output 1/3 4/27

概率為 n/(m^(n-1))，

要用高精度 。

#include<iostream>
#include<vector>
#include<string.h>
#include<map>
#include<string>
#include<algorithm>
#include<cstdio>
using namespace std;
#define sz(v) (int)(v.size())
#define rep(i,a,n) for(int i=a;i<n;++i)
#define per(i,a,n) for(int i=n-1;i>=a;--i)
#define mem(a,t) memset(a,t,sizeof(a))
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define N 25

#define MAXN 9999
#define MAXSIZE 1010
#define DLEN 4

class BigNum
{
private:
    int a[500];  //可以控制大數的位數
    int len;
public:
    BigNum(){len=1;memset(a,0,sizeof(a));}  //建構函式
    BigNum(const int);     //將一個int型別的變數轉化成大數
    BigNum(const __int64);  //將一個__int64型別的變數轉化成大數
    BigNum(const char*);   //將一個字串型別的變數轉化為大數
    BigNum(const BigNum &); //拷貝建構函式
    BigNum &operator=(const BigNum &); //過載賦值運算子，大數之間進行賦值運算
    friend istream& operator>>(istream&,BigNum&); //過載輸入運算子
    friend ostream& operator<<(ostream&,BigNum&); //過載輸出運算子

    BigNum operator+(const BigNum &)const;  //過載加法運算子，兩個大數之間的相加運算
    BigNum operator-(const BigNum &)const;  //過載減法運算子，兩個大數之間的相減運算
    BigNum operator*(const BigNum &)const;  //過載乘法運算子，兩個大數之間的相乘運算
    BigNum operator/(const int &)const;     //過載除法運算子，大數對一個整數進行相除運算
    BigNum operator/(const __int64 &)const;     //過載除法運算子，大數對一個64位整數進行相除運算
    BigNum operator^(const int &)const;     //大數的n次方運算
    int operator%(const int &)const;        //大數對一個int型別的變數進行取模運算

    __int64 operator%(const __int64 &)const;    //大數對一個__int64型別的變數進行取模運算
    bool operator>(const BigNum &T)const;   //大數和另一個大數的大小比較
    bool operator>(const int &t)const;      //大數和一個int型別的變數的大小比較

    bool operator>(const __int64 &t)const;   //大數和一個__int64型別的變數的大小比較
    void print();        //輸出大數
};
BigNum::BigNum(const int b)   //將一個int型別的變數轉化為大數
{
    int c,d=b;
    len=0;
    memset(a,0,sizeof(a));
    while(d>MAXN)  //每位存四位數字，MAXN=9999；
    {
        c=d-(d/(MAXN+1))*(MAXN+1);
        d=d/(MAXN+1);
        a[len++]=c;
    }
    a[len++]=d;
}
BigNum::BigNum(const __int64 b)   //將一個int型別的變數轉化為大數
{
    __int64 c,d=b;
    len=0;
    memset(a,0,sizeof(a));
    while(d>MAXN)  //每位存四位數字，MAXN=9999；
    {
        c=d-(d/(MAXN+1))*(MAXN+1);
        d=d/(MAXN+1);
        a[len++]=c;
    }
    a[len++]=d;
}
BigNum::BigNum(const char *s)  //將一個字串型別的變數轉化為大數
{
    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)  //拷貝建構函式
{
    int i;
    memset(a,0,sizeof(a));
    for(i=0;i<len;i++)
        a[i]=T.a[i];
}
BigNum & BigNum::operator=(const BigNum &n)  //過載賦值運算子，大數之間賦值運算
{
    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)  //過載輸出運算子
{
    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   //兩個大數之間的相加運算
{
    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  //兩個大數之間的相減運算
{
    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  //兩個大數之間的相乘
{
    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  //大數對一個整數進行相除運算
{
    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;
}
BigNum BigNum::operator/(const __int64 &b)const  //大數對一個整數進行相除運算
{
    BigNum ret;
    __int64 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   //大數對一個 int型別的變數進行取模
{
    int i,d=0;
    for(i=len-1;i>=0;i--)
        d=((d*(MAXN+1))%b+a[i])%b;
    return d;
}
__int64 BigNum::operator%(const __int64 &b)const   //大數對一個 64位整數型別的變數進行取模
{
    __int64 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  //大數的n次方運算
{
    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    //大數和另一個大數的大小比較
{
    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  //大數和一個int型別的變數的大小比較
{
    BigNum b(t);
    return *this>b;
}
void BigNum::print()   //輸出大數
{
    int i;
    printf("%d",a[len-1]);
    for(i=len-2;i>=0;i--)
      printf("%04d",a[i]);
    printf("\n");
}

int main()
{
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    int m,n;
    int T;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d",&m,&n);
        BigNum tt = 1;
        //cin>>t;                //大整數讀入
        for(int i = 1;i < n;i++)
            tt = tt*m;
        int tmp = n;
        for(int i = 2;i <= n;i++)
        {
            while( tmp%i == 0 && (tt%i == 0) )
            {
                tmp /= i;
                tt = tt/i;
            }
        }
        printf("%d/",tmp);
        tt.print();           //大整數輸出
    }
    return 0;
}