CHKSEL - Editorial

chksel
combinatorics
editorial
flfi2016
lucas-theorem
medium-hard
number-theory

#1

PROBLEM LINK :

contest

practice

Author : Rahul Agarwal

Tester : Rahul Agarwal

Editorialist : Rahul Agarwal

DIFFICULTY :

Medium-Hard

PREREQUISITES :

Number Theory, Lucas Theorem

PROBLEM :

Find the number of ways of selecting K distinct items from a group of N distinct items.

As the output can be large print the answer modulo P.

Flawed Code :

#include

#define ll long long

ll fact[1000000];

int pwr(int x,int p,int mod){

ll t = 1,a=x;

while§
{
a=(a*a)%mod;p=p>>1;
}
return t;}

ll abc(int n,int r,int MOD){

ll tem=(fact[r]*fact[n-r])%MOD;

tem=pwr(tem,MOD-1,MOD);

return (tem*fact[n])%MOD;}

ll xyz(ll n,ll m,int p){

if(n==0)return 1;

if(m==0)return 1;

int ni=n%p;
int mi=m%p;

return xyz(n/p,m/p,p)*abc(ni,mi,p)%p;}

ll C(ll n,ll r,int MOD){

fact[0]=1; for(int i=1;i!=MOD;i++) fact*=(i*fact[i-1])%MOD;

return xyz(n,r,MOD);}

int main(){

int t;cin>>t;

while(t–){

ll n,k;int p;

cin>>n>>k>>p;

printf("%lld",C(n,k,p));

}}

EXPLANATION :

This question was a simple implementation of the Lucas Theorem

The corrected code can be view at, Corrected Code.