hdu 1023 Train Problem II

题目连接

http://acm.hdu.edu.cn/showproblem.php?pid=1212

Train Problem II

Description

As we all know the Train Problem I, the boss of the Ignatius Train Station want to know if all the trains come in strict-increasing order, how many orders that all the trains can get out of the railway.

Input

The input contains several test cases. Each test cases consists of a number N(1<=N<=100). The input is terminated by the end of file.

Output

For each test case, you should output how many ways that all the trains can get out of the railway.

SampleInput

1
2
3
10

SampleOutput

1
2
5
16796

卡特兰数。。

$ f(n) = f(n-1)*(n*4-2)/(n-1)$

#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cassert>
#include<cstdio>
#include<vector>
#include<string>
#include<map>
#include<set>
using std::cin;
using std::max;
using std::cout;
using std::endl;
using std::string;
using std::istream;
using std::ostream;
#define sz(c) (int)(c).size()
#define all(c) (c).begin(), (c).end()
#define iter(c) decltype((c).begin())
#define cls(arr,val) memset(arr,val,sizeof(arr))
#define cpresent(c, e) (find(all(c), (e)) != (c).end())
#define rep(i, j, n) for (int i = j; i < (int)(n); i++)
#define fork(i, k, n) for (int i = (int)k; i <= (int)n; i++)
#define tr(c, i) for (iter(c) i = (c).begin(); i != (c).end(); ++i)
#define pb(e) push_back(e)
#define mp(a, b) make_pair(a, b)
struct BigN {
    typedef unsigned long long ull;
    static const int Max_N = 2010;
    int len, data[Max_N];
    BigN() { memset(data, 0, sizeof(data)), len = 0; }
    BigN(const int num) {
        memset(data, 0, sizeof(data));
        *this = num;
    }
    BigN(const char *num) {
        memset(data, 0, sizeof(data));
        *this = num;
    }
    void clear() { len = 0, memset(data, 0, sizeof(data)); }
    BigN& clean(){ while (len > 1 && !data[len - 1]) len--;  return *this; }
    string str() const {
        string res = "";
        for (int i = len - 1; ~i; i--) res += (char)(data[i] + '0');
        if (res == "") res = "0";
        res.reserve();
        return res;
    }
    BigN operator = (const int num) {
        int j = 0, i = num;
        do data[j++] = i % 10; while (i /= 10);
        len = j;
        return *this;
    }
    BigN operator = (const char *num) {
        len = strlen(num);
        for (int i = 0; i < len; i++) data[i] = num[len - i - 1] - '0';
        return *this;
    }
    BigN operator + (const BigN &x) const {
        BigN res;
        int n = max(len, x.len) + 1;
        for (int i = 0, g = 0; i < n; i++) {
            int c = data[i] + x.data[i] + g;
            res.data[res.len++] = c % 10;
            g = c / 10;
        }
        return res.clean();
    }
    BigN operator * (const BigN &x) const {
        BigN res;
        int n = x.len;
        res.len = n + len;
        for (int i = 0; i < len; i++) {
            for (int j = 0, g = 0; j < n; j++) {
                res.data[i + j] += data[i] * x.data[j];
            }
        }
        for (int i = 0; i < res.len - 1; i++) {
            res.data[i + 1] += res.data[i] / 10;
            res.data[i] %= 10;
        }
        return res.clean();
    }
    BigN operator * (const int num) const {
        BigN res;
        res.len = len + 1;
        for (int i = 0, g = 0; i < len; i++) res.data[i] *= num;
        for (int i = 0; i < res.len - 1; i++) {
            res.data[i + 1] += res.data[i] / 10;
            res.data[i] %= 10;
        }
        return res.clean();
    }
    BigN operator - (const BigN &x) const {
        assert(x <= *this);
        BigN res;
        for (int i = 0, g = 0; i < len; i++) {
            int c = data[i] - g;
            if (i < x.len) c -= x.data[i];
            if (c >= 0) g = 0;
            else g = 1, c += 10;
            res.data[res.len++] = c;
        }
        return res.clean();
    }
    BigN operator / (const BigN &x) const {
        BigN res, f = 0;
        for (int i = len - 1; ~i; i--) {
            f *= 10;
            f.data[0] = data[i];
            while (f >= x) {
                f -= x;
                res.data[i]++;
            }
        }
        res.len = len;
        return res.clean();
    }
    BigN operator % (const BigN &x) {
        BigN res = *this / x;
        res = *this - res * x;
        return res;
    }
    BigN operator += (const BigN &x) { return *this = *this + x; }
    BigN operator *= (const BigN &x) { return *this = *this * x; }
    BigN operator -= (const BigN &x) { return *this = *this - x; }
    BigN operator /= (const BigN &x) { return *this = *this / x; }
    BigN operator %= (const BigN &x) { return *this = *this % x; }
    bool operator <  (const BigN &x) const {
        if (len != x.len) return len < x.len;
        for (int i = len - 1; ~i; i--) {
            if (data[i] != x.data[i]) return data[i] < x.data[i];
        }
        return false;
    }
    bool operator >(const BigN &x) const { return x < *this; }
    bool operator<=(const BigN &x) const { return !(x < *this); }
    bool operator>=(const BigN &x) const { return !(*this < x); }
    bool operator!=(const BigN &x) const { return x < *this || *this < x; }
    bool operator==(const BigN &x) const { return !(x < *this) && !(x > *this); }
    friend istream& operator >> (istream &in, BigN &x) {
        string src;
        in >> src;
        x = src.c_str();
        return in;
    }
    friend ostream& operator << (ostream &out, const BigN &x) {
        out << x.str();
        return out;
    }
}A[101], B;
inline void init() {
    A[1] = 1;
    rep(i, 2, 101) {
        B = 4 * i - 2;
        A[i] = A[i - 1] * B / (i + 1);
        B.clear();
    }
}
int main() {
#ifdef LOCAL
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w+", stdout);
#endif
    init();
    std::ios::sync_with_stdio(false);
    int n;
    while (cin >> n) cout << A[n] << endl;
    return 0;
}