could you refer a number theory book..?
On Tue, Mar 6, 2012 at 7:01 AM, Gene <gene.ress...@gmail.com> wrote:
> It's a fact from number theory that
>
> x * (x^(M-2)) = 1 (mod M)
>
> if M is prime. So x^(M-2) is the multiplicative inverse of x (mod
> M). It follows by identities of modulo arithmetic that
>
> n!/(r!(n-r)!) = n! * inv(r!) * inv( (n-r)! ) (mod M)
>
> This is what the code is computing. A basic number theory book will
> cover this stuff in the early chapters.
>
>
> On Mar 5, 5:13 am, amrit harry <dabbcomput...@gmail.com> wrote:
> > #include <cstdio>
> >
> > #define MOD 1000000007
> >
> > int powmod(int base, int expo){
> > if(expo==0)
> > return 1;
> > else if(expo&1)
> > return (long long)base*powmod(base, expo-1)%MOD;
> > else{
> > int root=powmod(base, expo>>1);
> > return (long long)root*root%MOD;
> > }
> >
> > }
> >
> > int inverse(int x){
> > return powmod(x, MOD-2);
> >
> > }
> >
> > void init(){
> > fact[0]=1;
> > for(int i=1; i<=5000; i++)
> > fact[i]=(long long)i*fact[i-1]%MOD;
> > invfact[5000]=inverse(fact[5000]);
> > for(int i=5000; i>0; i--)
> > invfact[i-1]=(long long)i*invfact[i]%MOD;
> >
> > }
> >
> > int nCr(int n, int r){
> > if(r>n || r<0)
> > return 0;
> > return (long long)((long
> long)fact[n]*invfact[r]%MOD)*invfact[n-r]%MOD;
> >
> > }
> >
> > int main(){
> > init();
> > int N, K;
> > while(scanf("%d %d", &N, &K) && (N||K)){
> >
> > print("%d",nCr(N,K));
> > }
> >
> > }
> >
> > This is code for calculating binomial cofficient =
> fact(n)/fact(n-r)*fact(r) value of fact(r)*fact(n-r) lead to overflow so in
> this code they use a method of calculating inverse of fact. i could not
> able to understand how inverse function work please explain.
> >
> > Thanks.
>
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