luogu 1375 小猫 （卡特兰数）

 1 #include<cstdio>
 2 #include<cstdlib>
 3 long long c[100010]={1,1,2};
 4 int main(){
 5     int n,i,j;
 6     scanf("%d",&n);
 7     for(i=3;i<=n;i++){
 8         j=0;
 9         while(j<=i-1){
10             c[i]+=c[j]*c[i-1-j];
11             while(c[i]>=1000000007) c[i]%=1000000007;
12             j++;
13         }
14     }
15     printf("%lld",c[n]);
16 }

 1 int jc(int a) {
 2     if (a == 1) return 1 ;
 3     else return 1ll * a * jc(a - 1) % MOD ;
 4 }
 5 
 6 int power(int a, int b) {
 7     int res = 1 ;
 8     for (; b >>= 1; a = 1ll * a * a % MOD) if (b & 1) res = 1ll * res * a % MOD ;
 9     return res ;
10 }
11 
12 int C(int a, int b){
13     return 1ll * jc(a) * power(jc(b), MOD - 2) % MOD * power(jc(a - b), MOD - 2) % MOD;
14 }
15 
16 int n ;
17 
18 int main(){
19     scanf("%d", &n) ;
20     printf("%lld\n", 1ll * C(2 * n, n) * power(n + 1, MOD - 2) % MOD) ;
21 }

 1 #include <map>
 2 #include <set>
 3 #include <cmath>
 4 #include <ctime>
 5 #include <queue>
 6 #include <stack>
 7 #include <vector>
 8 #include <bitset>
 9 #include <cstdio>
10 #include <cctype>
11 #include <string>
12 #include <cstring>
13 #include <cassert>
14 #include <climits>
15 #include <cstdlib>
16 #include <iostream>
17 #include <algorithm>
18 #include <functional>
19 using namespace std ;
20 #define int long long
21 #define rep(i, a, b) for (int (i)=(a);(i)<=(b);(i)++)
22 #define Rep(i, a, b) for (int (i)=(a)-1;(i)<(b);(i)++)
23 #define REP(i, a, b) for (int (i)=(a);(i)>=(b);(i)--)
24 #define reg(i, x) for (int (i)=head[x];(i);i=e[i].next)
25 #define clr(a) memset(a,0,sizeof(a))
26 #define Sort(a, len) sort(a + 1, a + len + 1)
27 #define Sort2(a, len, cmp) sort(a + 1, a + len + 1, cmp)
28 #define ass(a, sum) memset(a, sum, sizeof(a))
29 
30 #define ull unsigned long long
31 #define ll long long
32 #define ls ((rt) << 1)
33 #define rs ((rt) << 1 | 1)
34 #define mp make_pair
35 #define pb push_back
36 #define fi first
37 #define se second
38 #define endl ‘\n‘
39 #define Pii pair<int, int>
40 
41 const int N = 100010 ;
42 const int iinf = INT_MAX/2 ;
43 const ll linf = LLONG_MAX/2 ;
44 const int MOD = 1e9 + 7 ;
45 
46 inline int read(){
47     int X = 0,w = 0 ;
48     char ch = 0;
49     while(!isdigit(ch)) {w |= ch == ‘-‘;ch = getchar();}
50     while(isdigit(ch)) X = (X<<3) + (X<<1) + (ch ^ 48),ch = getchar();
51     return w ? -X : X;
52 }
53 
54 void write(int x){
55      if(x < 0) putchar(‘-‘),x = -x;
56      if(x > 9) write(x / 10);
57      putchar(x%10 + ‘0‘);
58 }
59 
60 int jc(int a) {
61     if (a == 1) return 1 ;
62     else return 1ll * a * jc(a - 1) % MOD ;
63 }
64 
65 int power(int a, int b) {
66     int res = 1 ;
67     for (; b; b >>= 1, a = 1ll * a * a % MOD) if (b & 1) res = 1ll * res * a % MOD ;
68     return res ;
69 }
70 
71 int C(int a, int b){
72     return 1ll * jc(a) * power(jc(b), MOD - 2) % MOD * power(jc(a - b), MOD - 2) % MOD;
73 }
74 
75 int n ;
76 
77 signed main(){
78     scanf("%lld", &n) ;
79     printf("%lld\n", 1ll * C(2 * n, n) * power(n + 1, MOD - 2) % MOD) ;
80 }
81 
82 /*
83 写代码时请注意：
84     1.是否要开Long Long？数组边界处理好了么？
85     2.特殊情况处理好了么？
86     3.做一些总比不做好。
87     4.最大值和最小值问题可不可以用二分答案？
88     5.有没有贪心策略？否则能不能dp？
89     6.实数精度有没有处理？
90 */