Bell Number
新學的一個東西,也是類似卡特蘭數能解特定的問題
//
// GGGGGGGGGGGGG CCCCCCCCCCCCC AAA
// GGG::::::::::::G CCC::::::::::::C A:::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::::A
// G:::::G GGGGGG C:::::C CCCCCC A:::::::::A
//G:::::G C:::::C A:::::A:::::A
//G:::::G C:::::C A:::::A A:::::A
//G:::::G GGGGGGGGGGC:::::C A:::::A A:::::A
//G:::::G G::::::::GC:::::C A:::::A A:::::A
//G:::::G GGGGG::::GC:::::C A:::::AAAAAAAAA:::::A
//G:::::G G::::GC:::::C A:::::::::::::::::::::A
// G:::::G G::::G C:::::C CCCCCC A:::::AAAAAAAAAAAAA:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::A A:::::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A A:::::A
// GGG::::::GGG:::G CCC::::::::::::C A:::::A A:::::A
// GGGGGG GGGG CCCCCCCCCCCCCAAAAAAA AAAAAAA
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <cctype>
#include <utility>
#include <ctime>
using namespace std;
#ifdef DEBUG
#define VAR(a,b) decltype(b) a=(b)
#define debug(...) printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)
#define gettime() end\_time=clock();printf("now running time is %.7f\\n",(float)(end\_time - start\_time)/CLOCKS\_PER\_SEC);
#else
#define VAR(a,b) \_\_typeof(b) a=(b)
#define debug(...)
#define gettime()
#endif
typedef unsigned int uint;
typedef long long int Int;
typedef unsigned long long int UInt;
#define Set(a,s) memset(a,s,sizeof(a))
#define Write(w) freopen(w,"w",stdout)
#define Read(r) freopen(r,"r",stdin)
#define Pln() printf("\\n")
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()
#define De(x)printf(#x"%d\\n",x)
#define For(i,x)for(int i=0;i<x;i++)
#define CON(x,y) x##y
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\
printf("%d ",dp\[htx\]\[hty\]);}Pln();}
#define M 920
#define PII pair<int,int\>
#define PB push\_back
#define oo INT\_MAX
#define Set\_oo 0x3f
#define FOR(a,b) for(VAR(a,(b).begin());a!=(b).end();++a)
#define eps 1e-6
#define X first
#define Y second
clock\_t start\_time = clock(), end\_time;
bool xdy(double x, double y) {
return x > y + eps;
}
bool xddy(double x, double y) {
return x > y - eps;
}
bool xcy(double x, double y) {
return x < y - eps;
}
bool xcdy(double x, double y) {
return x < y + eps;
}
int min3(int x, int y, int z) {
int tmp = min(x, y);
return min(tmp, z);
}
int max3(int x, int y, int z) {
int tmp = max(x, y);
return max(tmp, z);
}
struct bignum {
Int n\[252\];
static const int maxn = 120;
static const Int base = 1000000000000000 ;
bignum() {
Set(n, 0);
}
bignum(Int x) {
Set(n, 0);
n\[0\] = x;
}
bignum operator\=(int a) {
int i = 0;
while (a) {
n\[i\] = a % base;
a /= base;
}
return \*this;
}
bignum operator+(int a) const {
bignum ans;
Int c = 0;
for (int i = 0; i < maxn; i++) {
ans.n\[i\] = n\[i\] + a + c;
c = ans.n\[i\] / base;
ans.n\[i\] %= base;
a = 0;
}
return ans;
}
bignum operator+(bignum &d) const {
bignum ans;
Int c = 0;
for (int i = 0; i < maxn; i++) {
Int tmp = n\[i\] + d.n\[i\] + c;
ans.n\[i\] = tmp % base;
c = tmp / base;
}
return ans;
}
void print() {
int i = maxn - 1;
for (; i > 0; i--)
if (n\[i\])
break;
printf("%lld", n\[i--\]);
for (; i >= 0; i--)
printf("%015lld", n\[i\]);
Pln();
}
};
int n;
bignum bell\[M\],ans\[M\],tmp\[M\];
void pre() {
bell\[0\]=1;
ans\[1\]=1;
for(int i=2;i<M;i++){
tmp\[0\]=bell\[i-2\];
ans\[i\]=bell\[i-2\];
// ans\[i\].print();
for(int j=1;j<i;j++){
tmp\[j\]=tmp\[j-1\]+bell\[j-1\];
// tmp\[j\].print();
}//Pln();
for(int j=0;j<i;j++)bell\[j\]=tmp\[j\];
}
}
int main() {
ios\_base::sync\_with\_stdio(0);
pre();
while (~scanf("%d", &n)&&n) {
printf("%d, ",n);
ans\[n+1\].print();
}
}