[HDOJ4828]Grids（组合数，Catalan）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4828

题意：据说是热身赛的原题。

  1 #include <algorithm>
  2 #include <iostream>
  3 #include <iomanip>
  4 #include <cstring>
  5 #include <climits>
  6 #include <complex>
  7 #include <cassert>
  8 #include <cstdio>
  9 #include <bitset>
 10 #include <vector>
 11 #include <deque>
 12 #include <queue>
 13 #include <stack>
 14 #include <ctime>
 15 #include <set>
 16 #include <map>
 17 #include <cmath>
 18 using namespace std;
 19 #define fr first
 20 #define sc second
 21 #define cl clear
 22 #define BUG puts("here!!!")
 23 #define W(a) while(a--)
 24 #define pb(a) push_back(a)
 25 #define Rint(a) scanf("%d", &a)
 26 #define Rll(a) scanf("%I64d", &a)
 27 #define Rs(a) scanf("%s", a)
 28 #define Cin(a) cin >> a
 29 #define FRead() freopen("in", "r", stdin)
 30 #define FWrite() freopen("out", "w", stdout)
 31 #define Rep(i, len) for(int i = 0; i < (len); i++)
 32 #define For(i, a, len) for(int i = (a); i < (len); i++)
 33 #define Cls(a) memset((a), 0, sizeof(a))
 34 #define Clr(a, x) memset((a), (x), sizeof(a))
 35 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
 36 #define lrt rt << 1
 37 #define rrt rt << 1 | 1
 38 #define pi 3.14159265359
 39 #define RT return
 40 #define lowbit(x) x & (-x)
 41 #define onecnt(x) __builtin_popcount(x)
 42 typedef long long LL;
 43 typedef long double LD;
 44 typedef unsigned long long ULL;
 45 typedef pair<int, int> pii;
 46 typedef pair<string, int> psi;
 47 typedef pair<LL, LL> pll;
 48 typedef map<string, int> msi;
 49 typedef vector<int> vi;
 50 typedef vector<LL> vl;
 51 typedef vector<vl> vvl;
 52 typedef vector<bool> vb;
 53
 54 const LL mod =(LL) 1e9+7;
 55 const int maxn = 2100001;
 56 LL f[maxn];
 57 int n;
 58
 59 LL mul(LL x, LL n) {
 60   LL ret = 1;
 61   while(n) {
 62     if(n & 1) ret = (ret * x) % mod;
 63     n >>= 1;
 64     x = (x * x) % mod;
 65   }
 66   return ret;
 67 }
 68
 69 LL exgcd(LL a, LL b, LL &x, LL &y) {
 70   if(b == 0) {
 71     x = 1;
 72     y = 0;
 73     return a;
 74   }
 75   else {
 76     LL ret = exgcd(b, a%b, x, y);
 77     LL tmp = x;
 78     x = y;
 79     y = tmp - a / b * y;
 80     return ret;
 81   }
 82 }
 83 LL inv(LL a) {
 84   LL x, y;
 85   exgcd(a, mod, x, y);
 86   return (x % mod + mod) % mod;
 87 }
 88
 89 LL C(LL x, LL y) {
 90   return f[x] * inv(f[x-y]) % mod * inv(f[y]) % mod;
 91 }
 92
 93 LL Catalan(int n) {
 94   return C(2*n, n) * inv(n+1) % mod;
 95 }
 96
 97 signed main() {
 98   // FRead();
 99   f[0] = 1; f[1] = 1;
100   For(i, 1, 2000001) f[i] = (f[i-1] * i) % mod;
101   int T, _ = 1;
102   Rint(T);
103   W(T) {
104     Rint(n);
105     printf("Case #%d:\n%I64d\n", _++, Catalan(n));
106   }
107   RT 0;
108 }