2822. [AHOI2012]树屋阶梯【卡特兰数】

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cmath>
 4 using namespace std;
 5 
 6 int n,a[5009],cnt[1009];
 7 
 8 void Divide(int x,int opt)
 9 {
10     for (int i=2; i<=sqrt(x); ++i)
11         while (x%i==0) x/=i,cnt[i]+=opt;
12     if (x>1) cnt[x]+=opt;
13 }
14 
15 void Mul(int *a,int b)
16 {
17     int g=0;
18     for (int i=1; i<=a[0]; ++i)
19         a[i]=a[i]*b+g,g=a[i]/10,a[i]%=10;
20     while (g) a[0]++,a[a[0]]=g%10,g/=10;
21 }
22 
23 int main()
24 {
25     scanf("%d",&n);
26     for (int i=n+1; i<=2*n; ++i) Divide(i,1);
27     for (int i=2; i<=n+1; ++i) Divide(i,-1);
28     a[0]=a[1]=1;
29     for (int i=2; i<=1000; ++i)
30         while (cnt[i]>=1) 
31             Mul(a,i),cnt[i]--;
32     for (int i=a[0]; i>=1; --i)
33         printf("%d",a[i]);
34 }