Buy the Ticket

Posted 2022-07-20 cadcadcad

Buy the Ticket
参考：Buy the Ticket

上面博客中好像 n 和 m 的意思写反了，不过问题不大，反着输入就好了，题目中说 n 是 50 的人数，m 是 100 的人数，这里反了一下。另外还需要用到高精度。

公式（m 是 50 的人数，n 是 100 的人数）：
\\[ (\\binom m+nn-\\binom m+nm+1)*m!*n! \\]
化简得：
\\[ \\frac(m+n)!*(m-n+1)m+1 \\]
代码：

// Created by CAD on 2019/8/17.
#include <bits/stdc++.h>
using namespace std;
#define MAXN 9999
#define MAXSIZE 10000
#define DLEN 4
class BigNum

public:
    int a[MAXSIZE];
    int len;
public:
    BigNum()len = 1;memset(a,0,sizeof(a));
    BigNum(const int);
    BigNum &operator=(const BigNum &);
    friend ostream& operator<<(ostream&,  BigNum&);
    BigNum operator*(const BigNum &) const;
    BigNum operator/(const int  &) const;
;
ostream& operator<<(ostream& out,  BigNum& b)

    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(const int b)

    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::operator=(const BigNum & n)

    len = n.len;
    memset(a,0,sizeof(a));
    for (int i = 0 ; i < len ; i++)
        a[i] = n.a[i];
    return *this;

BigNum BigNum::operator*(const BigNum & T) const

    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

    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 jc[205];
int main()

    ios::sync_with_stdio(false);
    cin.tie(0);
    jc[0]=jc[1]=BigNum(1);
    for(int i=2;i<=200;++i)
        jc[i]=jc[i-1]*BigNum(i);
    int n=1,m=1,t=0;
    while(cin>>m>>n&&(n+m))
    
        BigNum ans(1);
        if(m<n) ans=BigNum(0);
        else
            ans=jc[m+n]*BigNum(m+1-n)/(m+1);
        cout<<"Test #"<<++t<<":"<<endl<<ans<<endl;
    
    return 0;