Buy the Ticket{HDU1133}

Buy the Ticket
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 6517 Accepted Submission(s): 2720

Problem Description
The "Harry Potter and the Goblet of Fire" will be on show in the next few days. As a crazy fan of Harry Potter, you will go to the cinema and have the first sight, won’t you?

Suppose the cinema only has one ticket-office and the price for per-ticket is 50 dollars. The queue for buying the tickets is consisted of m + n persons (m persons each only has the 50-dollar bill and n persons each only has the 100-dollar bill).

Now the problem for you is to calculate the number of different ways of the queue that the buying process won't be stopped from the first person till the last person.
Note: initially the ticket-office has no money.

The buying process will be stopped on the occasion that the ticket-office has no 50-dollar bill but the first person of the queue only has the 100-dollar bill.

 

Input
The input file contains several test cases. Each test case is made up of two integer numbers: m and n. It is terminated by m = n = 0. Otherwise, m, n <=100.

 

Output
For each test case, first print the test number (counting from 1) in one line, then output the number of different ways in another line.

 

Sample Input
3 0
3 1
3 3
0 0

Sample Output
Test #1:
6
Test #2:
18
Test #3:
180

f[i][j]表示有i个50j个100的方法数。当i<j时，f[i][j]=0。当i=j时，f[i][j]=f[i][j-1]。当i>j时，f[i][j]=f[i-1][j]+f[i][j-1]。

最后分别再乘上n和m的阶乘。

#include <iostream>
#include <string>
using namespace std;
#ifndef BIGNUM
#define BIGNUM
class BigNum {
#define MAXSIZEOFBIGNUM 500
#define BASE 10
#define DLEN 1
public:
    int Len;
    int d[MAXSIZEOFBIGNUM];
public:
    BigNum(void);
    BigNum(const int);
    BigNum(const char *);
    BigNum(const BigNum &);
    BigNum & operator = (const BigNum &);
    void clear(void);
    friend istream& operator>>(istream&, BigNum&);
    friend ostream& operator<<(ostream&, BigNum&);
    bool operator == (const BigNum &) const;
    bool operator > (const BigNum &) const;
    bool operator < (const BigNum &) const;
    bool operator >= (const BigNum &) const;
    bool operator <= (const BigNum &) const;
    BigNum operator + (const BigNum &) const;
    BigNum operator - (const BigNum &) const;
    BigNum operator * (const BigNum &) const;
    BigNum operator / (const BigNum &) const;
    BigNum operator % (const BigNum &) const;
    void operator ++ (void);
    void operator -- (void);
    BigNum operator + (const int &) const;
    BigNum operator - (const int &) const;
    BigNum operator * (const int &) const;
    BigNum operator / (const int &) const;
    int operator % (const int &) const;
    BigNum operator ^ (const int &) const;
    ~BigNum() {}
};
BigNum::BigNum() {
    Len = 0;
    memset(d, 0, sizeof(d));
}
BigNum::BigNum(const int ops) {
    int x = ops;
    Len = 0;
    memset(d, 0, sizeof(d));
    while(x) {
        Len++;
        d[Len] = x % BASE;
        x /= BASE;
    }
}
BigNum::BigNum(const char * ops) {
    int L = strlen(ops) - 1, b = 0;
    memset(d, 0, sizeof(d));
    while(ops[b] == '0') {
        b++;
    }
    Len = 0;
    while(L - b + 1 >= DLEN) {
        int x = 0;
        for(int i = L - DLEN + 1; i <= L; i++) {
            x = x * 10 + ops[i] - '0';
        }
        Len++;
        d[Len] = x;
        L -= DLEN;
    }
    int x = 0;
    for(int i = b; i <= L; i++) {
        x = x * 10 + ops[i] - '0';
    }
    Len++;
    d[Len] = x;
}
BigNum::BigNum(const BigNum &ops) : Len(ops.Len) {
    memset(d, 0, sizeof(d));
    for(int i = 1; i <= Len; i++) {
        d[i] = ops.d[i];
    }
}
BigNum & BigNum::operator = (const BigNum &ops) {
    memset(d, 0, sizeof(d));
    Len = ops.Len;
    for(int i = 1; i <= Len; i++) {
        d[i] = ops.d[i];
    }
    return *this;
}
void BigNum::clear(void) {
    for(int i = 1; i <= MAXSIZEOFBIGNUM - 2; i++) {
        if(d[i] < 0) {
            d[i] += BASE;
            d[i + 1]--;
        }
        if(d[i] >= BASE) {
            d[i] -= BASE;
            d[i + 1]++;
        }
    }
    for(int i = MAXSIZEOFBIGNUM - 1; i >= 1; i--)
        if(d[i] > 0) {
            Len = i;
            return;
        }
    Len = 0;
}
istream& operator>>(istream &in, BigNum &ops) {
    char str[MAXSIZEOFBIGNUM + 100];
    in >> str;
    int L = strlen(str), b = 0;
    while(str[b] == '0') {
        b++;
    }
    ops.Len = 0;
    for(int i = L - 1; i >= b; i--) {
        ops.Len++;
        ops.d[ops.Len] = str[i] - '0';
    }
    return in;
}
ostream& operator<<(ostream& out, BigNum& ops) {
    for(int i = ops.Len; i >= 1; i--) {
        out << ops.d[i];
    }
    if(ops.Len == 0) {
        out << "0";
    }
    return out;
}
bool BigNum::operator == (const BigNum &ops) const {
    if(Len != ops.Len) {
        return false;
    }
    for(int i = Len; i >= 1; i--)
        if(d[i] != ops.d[i]) {
            return false;
        }
    return true;
}
bool BigNum::operator > (const BigNum &ops) const {
    if(Len < ops.Len) {
        return false;
    } else if(Len > ops.Len) {
        return true;
    } else {
        for(int i = Len; i >= 1; i--)
            if(d[i] < ops.d[i]) {
                return false;
            } else if(d[i] > ops.d[i]) {
                return true;
            }
    }
    return false;
}
bool BigNum::operator < (const BigNum &ops) const {
    if(Len < ops.Len) {
        return true;
    } else if(Len > ops.Len) {
        return false;
    } else {
        for(int i = Len; i >= 1; i--)
            if(d[i] < ops.d[i]) {
                return true;
            } else if(d[i] > ops.d[i]) {
                return false;
            }
    }
    return false;
}
bool BigNum::operator >= (const BigNum &ops) const {
    if(Len < ops.Len) {
        return false;
    } else if(Len > ops.Len) {
        return true;
    } else {
        for(int i = Len; i >= 1; i--)
            if(d[i] < ops.d[i]) {
                return false;
            } else if(d[i] > ops.d[i]) {
                return true;
            }
    }
    return true;
}
bool BigNum::operator <= (const BigNum &ops) const {
    if(Len < ops.Len) {
        return true;
    } else if(Len > ops.Len) {
        return false;
    } else {
        for(int i = Len; i >= 1; i--)
            if(d[i] < ops.d[i]) {
                return true;
            } else if(d[i] > ops.d[i]) {
                return false;
            }
    }
    return true;
}
BigNum BigNum::operator + (const BigNum &ops) const {
    BigNum ret(*this);
    for(int i = 1; i <= ops.Len; i++) {
        ret.d[i] += ops.d[i];
    }
    ret.clear();
    return ret;
}
BigNum BigNum::operator - (const BigNum &ops) const {
    BigNum ret(*this);
    for(int i = ops.Len; i >= 1; i--) {
        ret.d[i] -= ops.d[i];
    }
    ret.clear();
    return ret;
}
BigNum BigNum::operator * (const BigNum &ops) const {
    BigNum ret, now(*this);
    for(int i = 1; i <= now.Len; i++)
        for(int j = 1; j <= ops.Len; j++) {
            ret.d[i + j - 1] += now.d[i] * ops.d[j];
        }
    for(int i = 1; i <= MAXSIZEOFBIGNUM - 2; i++)
        if(ret.d[i] >= BASE) {
            ret.d[i + 1] += ret.d[i] / BASE;
            ret.d[i] %= BASE;
        }
    for(int i = MAXSIZEOFBIGNUM - 1; i >= 1; i--)
        if(ret.d[i] > 0) {
            ret.Len = i;
            break;
        }
    return ret;
}
BigNum BigNum::operator / (const BigNum &ops) const {
    BigNum now = (*this), div, mod;
    div.Len = now.Len;
    mod.Len = 0;
    for(int j = now.Len; j >= 1; j--) {
        mod.Len++;
        for(int p = mod.Len; p >= 2; p--) {
            mod.d[p] = mod.d[p - 1];
        }
        mod.d[1] = now.d[j];
        while(mod >= ops) {
            div.d[j]++;
            mod = mod - ops;
        }
        if(mod.Len == 1 && mod.d[1] == 0) {
            mod.Len--;
        }
    }
    div.clear();
    mod.clear();
    return div;
}
BigNum BigNum::operator % (const BigNum &ops) const {
    BigNum now = (*this), div, mod;
    div.Len = now.Len;
    mod.Len = 0;
    for(int j = now.Len; j >= 1; j--) {
        mod.Len++;
        for(int p = mod.Len; p >= 2; p--) {
            mod.d[p] = mod.d[p - 1];
        }
        mod.d[1] = now.d[j];
        while(mod >= ops) {
            div.d[j]++;
            mod = mod - ops;
        }
        if(mod.Len == 1 && mod.d[1] == 0) {
            mod.Len--;
        }
    }
    div.clear();
    mod.clear();
    return mod;
}
void BigNum::operator ++ (void) {
    d[1]++;
    for(int i = 1; i <= MAXSIZEOFBIGNUM - 2; i++)
        if(d[i] >= BASE) {
            d[i] -= BASE;
            d[i + 1]++;
        } else {
            break;
        }
    if(d[Len + 1] > 0) {
        Len++;
    }
}
void BigNum::operator -- (void) {
    d[1]--;
    for(int i = 1; i <= MAXSIZEOFBIGNUM - 2; i++)
        if(d[i] < 0) {
            d[i] += BASE;
            d[i + 1]--;
        } else {
            break;
        }
    if(d[Len] == 0) {
        Len--;
    }
}
BigNum BigNum::operator + (const int & ops) const {
    BigNum ret = (*this);
    ret.d[1] += ops;
    ret.clear();
    return ret;
}
BigNum BigNum::operator - (const int & ops) const {
    BigNum ret = (*this);
    ret.d[1] -= ops;
    ret.clear();
    return ret;
}
BigNum BigNum::operator * (const int & ops) const {
    BigNum ret(*this);
    for(int i = 1; i <= ret.Len; i++) {
        ret.d[i] *= ops;
    }
    for(int i = 1; i <= MAXSIZEOFBIGNUM - 2; i++)
        if(ret.d[i] >= BASE) {
            ret.d[i + 1] += ret.d[i] / BASE;
            ret.d[i] %= BASE;
        }
    for(int i = MAXSIZEOFBIGNUM - 1; i >= 1; i--)
        if(ret.d[i] > 0) {
            ret.Len = i;
            return ret;
        }
    ret.Len = 0;
    return ret;
}
BigNum BigNum::operator / (const int & ops) const {
    BigNum ret;
    int down = 0;
    for(int i = Len; i >= 1; i--) {
        ret.d[i] = (d[i] + down * BASE) / ops;
        down = d[i] + down * BASE - ret.d[i] * ops;
    }
    ret.Len = Len;
    while(ret.d[ret.Len] == 0 && ret.Len > 1) {
        ret.Len--;
    }
    return ret;
}
int BigNum::operator % (const int &ops) const {
    int mod = 0;
    for(int i = Len; i >= 1; i--) {
        mod = ((mod * BASE) % ops + d[i]) % ops;
    }
    return mod;
}
BigNum BigNum::operator ^ (const int &ops) const {
    BigNum t, ret(1);
    if(ops == 0) {
        return ret;
    }
    if(ops == 1) {
        return *this;
    }
    int m = ops, i;
    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;
}
#endif
BigNum f[105][105];
int main() {
    f[0][0] = 1;
    for(int i = 1; i <= 100; i++) {
        for(int j = 0; j <= i; j++) {
            if(j == 0) {
                f[i][j] = 1;
                continue;
            }
            if(i == j) {
                f[i][j] = f[i][j - 1];
            } else {
                f[i][j] = f[i][j - 1] + f[i - 1][j];
            }
        }
    }
    int n, m,t=0;
    BigNum x;
    while(scanf("%d%d", &n, &m) != EOF) {
        t++;
        if(n + m == 0) {
            break;
        }
        x = f[n][m];
        for(int i = 1; i <= n; i++) {
            x = x * i;
        }
        for(int i = 1; i <= m; i++) {
            x = x * i;
        }
        cout << "Test #" << t << ":" << endl;
        cout << x << endl;;
    }
    return 0;
}