題目連接

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

卡特蘭數。。

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

1 #include<algorithm> 2 #include<iostream> 3 #include<cstdlib> 4 #include<cstring> 5 #include<cassert> 6 #include<cstdio> 7 #include<vector> 8 #include<string> 9 #include<map> 10 #include<set> 11 using std::cin; 12 using std::max; 13 using std::cout; 14 using std::endl; 15 using std::string; 16 using std::istream; 17 using std::ostream; 18 #define sz(c) (int)(c).size() 19 #define all(c) (c).begin(), (c).end() 20 #define iter(c) decltype((c).begin()) 21 #define cls(arr,val) memset(arr,val,sizeof(arr)) 22 #define cpresent(c, e) (find(all(c), (e)) != (c).end()) 23 #define rep(i, j, n) for (int i = j; i < (int)(n); i++) 24 #define fork(i, k, n) for (int i = (int)k; i <= (int)n; i++) 25 #define tr(c, i) for (iter(c) i = (c).begin(); i != (c).end(); ++i) 26 #define pb(e) push_back(e) 27 #define mp(a, b) make_pair(a, b) 28 struct BigN { 29 typedef unsigned long long ull; 30 static const int Max_N = 2010; 31 int len, data[Max_N]; 32 BigN() { memset(data, 0, sizeof(data)), len = 0; } 33 BigN(const int num) { 34 memset(data, 0, sizeof(data)); 35 *this = num; 36 } 37 BigN(const char *num) { 38 memset(data, 0, sizeof(data)); 39 *this = num; 40 } 41 void clear() { len = 0, memset(data, 0, sizeof(data)); } 42 BigN& clean(){ while (len > 1 && !data[len - 1]) len--; return *this; } 43 string str() const { 44 string res = ""; 45 for (int i = len - 1; ~i; i--) res += (char)(data[i] + '0'); 46 if (res == "") res = "0"; 47 res.reserve(); 48 return res; 49 } 50 BigN operator = (const int num) { 51 int j = 0, i = num; 52 do data[j++] = i % 10; while (i /= 10); 53 len = j; 54 return *this; 55 } 56 BigN operator = (const char *num) { 57 len = strlen(num); 58 for (int i = 0; i < len; i++) data[i] = num[len - i - 1] - '0'; 59 return *this; 60 } 61 BigN operator + (const BigN &x) const { 62 BigN res; 63 int n = max(len, x.len) + 1; 64 for (int i = 0, g = 0; i < n; i++) { 65 int c = data[i] + x.data[i] + g; 66 res.data[res.len++] = c % 10; 67 g = c / 10; 68 } 69 return res.clean(); 70 } 71 BigN operator * (const BigN &x) const { 72 BigN res; 73 int n = x.len; 74 res.len = n + len; 75 for (int i = 0; i < len; i++) { 76 for (int j = 0, g = 0; j < n; j++) { 77 res.data[i + j] += data[i] * x.data[j]; 78 } 79 } 80 for (int i = 0; i < res.len - 1; i++) { 81 res.data[i + 1] += res.data[i] / 10; 82 res.data[i] %= 10; 83 } 84 return res.clean(); 85 } 86 BigN operator * (const int num) const { 87 BigN res; 88 res.len = len + 1; 89 for (int i = 0, g = 0; i < len; i++) res.data[i] *= num; 90 for (int i = 0; i < res.len - 1; i++) { 91 res.data[i + 1] += res.data[i] / 10; 92 res.data[i] %= 10; 93 } 94 return res.clean(); 95 } 96 BigN operator - (const BigN &x) const { 97 assert(x <= *this); 98 BigN res; 99 for (int i = 0, g = 0; i < len; i++) { 100 int c = data[i] - g; 101 if (i < x.len) c -= x.data[i]; 102 if (c >= 0) g = 0; 103 else g = 1, c += 10; 104 res.data[res.len++] = c; 105 } 106 return res.clean(); 107 } 108 BigN operator / (const BigN &x) const { 109 BigN res, f = 0; 110 for (int i = len - 1; ~i; i--) { 111 f *= 10; 112 f.data[0] = data[i]; 113 while (f >= x) { 114 f -= x; 115 res.data[i]++; 116 } 117 } 118 res.len = len; 119 return res.clean(); 120 } 121 BigN operator % (const BigN &x) { 122 BigN res = *this / x; 123 res = *this - res * x; 124 return res; 125 } 126 BigN operator += (const BigN &x) { return *this = *this + x; } 127 BigN operator *= (const BigN &x) { return *this = *this * x; } 128 BigN operator -= (const BigN &x) { return *this = *this - x; } 129 BigN operator /= (const BigN &x) { return *this = *this / x; } 130 BigN operator %= (const BigN &x) { return *this = *this % x; } 131 bool operator < (const BigN &x) const { 132 if (len != x.len) return len < x.len; 133 for (int i = len - 1; ~i; i--) { 134 if (data[i] != x.data[i]) return data[i] < x.data[i]; 135 } 136 return false; 137 } 138 bool operator >(const BigN &x) const { return x < *this; } 139 bool operator<=(const BigN &x) const { return !(x < *this); } 140 bool operator>=(const BigN &x) const { return !(*this < x); } 141 bool operator!=(const BigN &x) const { return x < *this || *this < x; } 142 bool operator==(const BigN &x) const { return !(x < *this) && !(x > *this); } 143 friend istream& operator >> (istream &in, BigN &x) { 144 string src; 145 in >> src; 146 x = src.c_str(); 147 return in; 148 } 149 friend ostream& operator << (ostream &out, const BigN &x) { 150 out << x.str(); 151 return out; 152 } 153 }A[101], B; 154 inline void init() { 155 A[1] = 1; 156 rep(i, 2, 101) { 157 B = 4 * i - 2; 158 A[i] = A[i - 1] * B / (i + 1); 159 B.clear(); 160 } 161 } 162 int main() { 163 #ifdef LOCAL 164 freopen("in.txt", "r", stdin); 165 freopen("out.txt", "w+", stdout); 166 #endif 167 init(); 168 std::ios::sync_with_stdio(false); 169 int n; 170 while (cin >> n) cout << A[n] << endl; 171 return 0; 172 } View Code

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轉載于:https://www.cnblogs.com/GadyPu/p/4578972.html

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