hdu5184 给出（和）前半段问后面有多少种加括号方法使合法：类似卡特兰数+逆元模板
题解说的很好呀==
就是拿50和100的买票多少种方案==
1 #include<stdio.h> 2 #include<string.h> 3 #include<algorithm> 4 using namespace std; 5 #define LL long long 6 #define MOD 1000000007 7 LL fac[1000005]; 8 char s[1000005]; 9 LL inv(LL a,LL mod) 10 { 11 LL b=mod,b0=b,t,q,x0=0,x1=1; 12 if (b==1) return 1; 13 while (a>1) 14 { 15 q=a/b; 16 t=b,b=a%b,a=t; 17 t=x0,x0=x1-q*x0,x1=t; 18 } 19 if (x1<0) x1+=b0; 20 return x1; 21 } 22 int main() 23 { 24 LL n,len,a,b,i,judge,p,q,x; 25 fac[0]=1; 26 for (i=1;i<=1000000;i++) fac[i]=fac[i-1]*i%MOD; 27 while (~scanf("%I64d",&n)) 28 { 29 scanf("%s",s); 30 len=strlen(s); 31 a=b=0; judge=1; 32 for (i=0;i<len;i++) 33 { 34 if (s[i]=='(') a++; 35 else b++; 36 if (a<b) judge=0; 37 } 38 if (judge==0||a>n/2||b>n/2||n%2) { 39 printf("0\n"); 40 continue; 41 } 42 p=n/2-b; q=n/2-a; 43 x=(p-q+1)*fac[p+q]%MOD; 44 x=x*inv(p+1,MOD)%MOD; 45 x=x*inv(fac[p],MOD)%MOD; 46 x=x*inv(fac[q],MOD)%MOD; 47 printf("%I64d\n",x); 48 } 49 return 0; 50 }
