void main()
{
char a[50];
int l,i,num,den=1,b[26],t;
char temp;
//clrscr();
scanf("%s",a);
l=strlen(a);
for(i=0;i<26;i++)
b[i]=0;
i=0;
while(i<l)
{
t=a[i]-97;
b[t]++;
i++;
}
for(i=0;i<26;i++)
{
if(b[i]!=0)
{
den=den*fac(b[i]);
}
}
num=fac(l);
printf("%d",num/den);
}
main()
{
int n,r;
p("enter number of objects: ");
scanf("%d",&n);
p("enter number of objects taken: ");
scanf("%d",&r);
int fr=fac(r);
int a=fac(n);
int b=fac(n-r);
int P=a/b;
int op;
int C=a/(fr*b);
p("press 1 to display permutations or press 2 for combinations (1/2):");
scanf("%d",&op);
if(op==1)
p("no. of permutations P(%d,%d) = %d\n",n,r,P);
if(op==2)
p("number of combinations: %d\n",C);
printf("the factorial of %d is %d\n",r,fr);
}
int main()
{
int i,j,k,n,m,num[11];
while(scanf("%d %d",&n,&m)!=EOF)
{
memset(c1,0,sizeof(c1));
memset(c1,0,sizeof(c2));
for(i=1;i<=n;i++)
{
scanf("%d",&num[i]);
}
for(i=0;i<=num[1];i++)//ÇмÇҪȡµ½0
{
c1[i]=1.0/fac(i);
}
for(i=2;i<=n;i++)
{
for(j=0;j<=m;j++)
{
for(k=0;k+j<=m && k<=num[i];k++)
{
c2[k+j]+=c1[j]/fac(k);
}
}
for(j=0;j<=m;j++)
{
c1[j]=c2[j];
c2[j]=0;
}
}
printf("%.0lf\n",fac(m)*c1[m]);
}
return 0;
}
double f(int n){
if(n==0){
return 0;
}
return f(n-1)+1.0*n/(fac(n+1)*fac(n+2));
}
unsigned long long int fac(unsigned long long int a,unsigned long long int b,unsigned long long int c){
if(a==b && c>3) return 1;
else if(a==b) return 1;
else if(a==0) return 0;
else if(c>=2) return((a*fac(a-1,b,c-1))/c);
else return((a*fac(a-1,b,c-1))/1);
}
int bezcoeff(int n, int i)
{
int numer = fac(n);
int denom1 = fac(n - i);
int denom2 = fac(i);
int result = (numer/(denom1 * denom2));
return result;
}
FE_TMPL std::complex<float> FE_SYS::_Y(int n,int m,float theta,float phi){
std::complex<float> a = 1;
if(m>0 && m%2==1) a = -1;
a *= std::sqrt(fac(n-m)/float(fac(n+m)));
a *= _P(n,m,std::cos(theta));
a *= std::exp(std::complex<float>(0,m*phi));
return a;
}
void bootentry()
{
_printtst("5!=", fac(5));
_printtst("7!=", fac(7));
_printtst("fib(8)=", fib(8));
_printtst("fib(A)=", fib(0xA));
_testhalt();
}
/* ================================ SINUS ======================================== */
TMath::DOUBLE TMath::sin(DOUBLE x)
{
x = mod(x + PI, 2 * PI) - PI;
DOUBLE r = 0;
for (LONG n = 0; n <= 16L; n+=4) {
r += pow(x, n + 1) / fac(n + 1) - pow(x, n + 3) / fac(n + 3);
}
return r;
}
/* ================================ KOSINUS ======================================== */
TMath::DOUBLE TMath::cos(DOUBLE x)
{
x = mod(x + PI, 2 * PI) - PI;
DOUBLE r = 0;
for (LONG n = 0; n <= 16L; n+=4) {
r += pow(x, n + 0) / fac(n + 0) - pow(x, n + 2) / fac(n + 2);
}
return r;
}
double
I(double x, unsigned a, unsigned b)
{
double r = 0;
for (int j = a; static_cast<unsigned>(j) <= a+b-1; ++j)
r += fac(a+b-1)/(fac(j) * fac(a + b - 1 - j)) * std::pow(x, j) *
std::pow(1-x, a+b-1-j);
return r;
}
static float bernstein(unsigned n, unsigned i, float t) {
float binom = fac(n) / (fac(n-i) * fac(i));
if (i == 0) {
return binom * pow(1-t, n);
} else if (i == n) {
return binom * pow(t, i);
} else {
return binom * pow(t, i) * pow(1-t, n-i);
}
}
TMath::DOUBLE TMath::asin(DOUBLE x)
{
x = mod(x + 1, 2) - 1;
DOUBLE r = 0;
for (LONG n = 0; n <= 8L; n++)
{
r += fac(2 * n) / (pow(DOUBLE(2), 2 * n) * pow(fac(n), 2) * (2 * n + 1)) * pow(x, 2 * n + 1);
}
return r;
}
void fac(long long n) {
for (long long i = 2; i * i <= n; i++) {
if (n % i == 0) {
fac(i);
fac(n / i);
return;
}
}
f[j++] = n;
}
int _tmain(int argc, _TCHAR* argv[])
{
f(ga, 10);
int aa[10] {1, fac(2), fac(3), fac(4), fac(5), fac(6), fac(7), fac(8), fac(9), fac(10)};
f(aa, 10);
return 0;
}
int main()
{
int n = 1;
for (int i = 0; i < 10; ++i, n = n + n) gv[i] = n * 2;
int aa[10] {1, fac(2), fac(3), fac(4), fac(5), fac(6), fac(7), fac(8), fac(9), fac(10)};
return 0;
}
/*
main computes and prints the relative error to be used in myexp()
natural ln2 / 2 is cached early to avoid redunt computations.
fac() is used to quickly calculate factorials.
*/
int main ( int argc, char ** argv ) {
double l = log ( 2 ) / 2; //cache ln2/2
for ( int i = 1; i <= 15; i++ ) {
double f = 2 / fac ( i + 1 ); //f contains 2 / the factorial
double p = pow ( l, i + 1 ); //p contains l ^ i+1
double r = f * p; //r holds the result of multiplying f * p
printf ( "Relative error of %d is : %0.9lf\n", i, r );
double x = fac ( i );
printf ( "Factorial of %d is : %lf\n", i, x );
}
}
int main(){
unsigned long long int a,b;
while(1){
scanf("%lli %lli",&a,&b);
if(a==0 && b==0){break;}
if(a-b > b)
printf("%lli things taken %lli at a time is %lli exactly.\n",a,b,fac(a,a-b,b));
else printf("%lli things taken %lli at a time is %lli exactly.\n",a,b,fac(a,b,a-b));
}
return 0;
}
FE_TMPL float FE_SYS::_P(int n,int m,float u){
if(n<0) return 0;
if(n < -m || n > m) return 0;
if(m<0){
return ((-m)%2==1?-1.f:1.f) * fac(n-m) / fac(n+m) * _P(n,-m,u);
}
float a = m%2==1 ? -1 : 1;
for(int j = 1;j<=m;j++) a *= 2*j - 1;
a *= std::pow(1-u*u,m/2.0f);
return a;
}
int main(int argc, char *argv[]) {
int i;
int n;
for (n = 0; n < 20; n++) {
int f = fac(n);
printf("n=%10d f=%10d\n", n, f);
}
for (i = 0, n = 0; i < 1000; i++, n = 2*n+1) {
int f = fac(n);
printf("i=%4d n=%10d f=%10d\n", i, n, f);
}
return 0;
}
int main()
{
char s[BUFSIZ];
printf("4! == %d\n", fac(4));
printf("8! == %d\n", fac(8));
printf("12! == %d\n", fac(12));
strcpy(s, "abcdef");
printf("reversing 'abcdef', we get '%s'\n", \
reverse(s));
strcpy(s, "madam");
printf("reversing 'madam', we get '%s'\n", \
reverse(s));
return 0;
}
long long generateNum(unordered_map<int, int> &hash)
{
long long denominator = 1;
int sum=0;
for (auto val : hash)
{
if (val.second == 0)
continue;
denominator *= fac(val.second);
sum += val.second;
}
if (sum == 0)
return sum;
return fac(sum) / denominator;
}
static long int
fac (long int n)
{
if (n == 0)
return 1;
return n * fac (n - 1);
}
int main(int argc, const char *argv[])
{
int value;
value=fac(5);
printf("%d\n",value);
return 0;
}
int main(){
int i;
scanf("%d", &i);
printf("%llu\n", fac(i));
printf("%lf\n", fac_d(i));
return 0;
}
int main()
{
int n;
int len;
int i,j;
int num[10];
factorial[0][0]='1';
factorial[1][0]='1';
//create all factorial
fac();
while(scanf("%d",&n))
{
if(n==0) break;
len=strlen(factorial[n]);
//initialize all to zero
for(i=0;i<10;i++) num[i]=0;
//count the frequencies
for(i=0;i<len;i++)
{
for(j=0;j<10;j++)
{
if(factorial[n][i]==(j+'0')) num[j]++;
}
}
//output
printf("%d! --\n",n);
printf(" (0)%5d (1)%5d (2)%5d (3)%5d (4)%5d\n",num[0],num[1],num[2],num[3],num[4]);
printf(" (5)%5d (6)%5d (7)%5d (8)%5d (9)%5d\n",num[5],num[6],num[7],num[8],num[9]);
}
return 0;
}
int stf::fac(int arg) {
if (arg<=1) {
return 1;
} else {
return arg*fac(arg-1);
}
}
int product_function(int acc, int x) //@ : fold_function
//@ requires true;
//@ ensures true;
{
int f = fac(x);
return acc * f;
}
int sum_function(int acc, int x) //@ : fold_function
//@ requires true;
//@ ensures true;
{
int f = fac(x);
return acc + f;
}
poly* Plethysm(entry* lambda,_index l,_index n,poly* p)
{ if (n==0) return poly_one(Lierank(grp)); else if (n==1) return p;
{ _index i,j;
poly* sum= poly_null(Lierank(grp)),**adams=alloc_array(poly*,n+1);
poly* chi_lambda=MN_char(lambda,l);
for (i=1; i<=n; ++i) { adams[i]=Adams(i,p); setshared(adams[i]); }
for (i=0;i<chi_lambda->nrows;i++)
{ entry* mu=chi_lambda->elm[i]; poly* prod=adams[mu[0]],*t;
for (j=1; j<n && mu[j]>0; ++j)
{ t=prod; prod=Tensor(t,adams[mu[j]]); freepol(t); }
sum= Addmul_pol_pol_bin(sum,prod,mult(chi_lambda->coef[i],Classord(mu,n)));
}
freemem(chi_lambda);
setshared(p); /* protect |p|; it coincides with |adams[1]| */
for (i=1; i<=n; ++i)
{ clrshared(adams[i]); freepol(adams[i]); } freearr(adams);
clrshared(p);
{ bigint* fac_n=fac(n); setshared(fac_n); /* used repeatedly */
for (i=0; i<sum->nrows; ++i)
{ bigint** cc= &sum->coef[i]
,* c= (clrshared(*cc),isshared(*cc)) ? copybigint(*cc,NULL) : *cc;
*cc=divq(c,fac_n); setshared(*cc);
if (c->size!=0) error("Internal error (plethysm).\n"); else freemem(c);
}
clrshared(fac_n); freemem(fac_n);
}
return sum;
}
}
