lucas求组合数C(n,k)%p

Saving Beans http://acm.hdu.edu.cn/showproblem.php?pid=3037

 #include<cstdio>
 typedef __int64 LL;
 const int M=;
 class LUCAS { //lucas求组合数C(n,k)%p
     LL F[M];
     LL inv(LL a,LL mod) {
         if(a==) return ;
         return inv(mod%a,mod)*(mod-mod/a)%mod;
     }
     void init(LL p) {
         F[]=;
         for(int i=; i<=p; i++) {
             F[i]=F[i-]*i%p;
         }
     }
     LL Lucas(LL n,LL k,LL p) {
         LL ans=;
         while(n&&k) {
             LL a=n%p;
             LL b=k%p;
             if(a<b) return ;
             ans=ans*F[a]%p*inv(F[b]*F[a-b]%p,p)%p;
             n/=p;
             k/=p;
         }
         return ans;
     }
 public:
     LL solve(LL n,LL k,LL p){
         init(p);
         return Lucas(n,k,p);
     }
 }gx;
 int main() {
     int t,n,m,p;
     while(~scanf("%d",&t)) {
         while(t--) {
             scanf("%d%d%d",&n,&m,&p);
             printf("%d\n",(int)gx.solve(n+m,n,p));
         }
     }
     return ;
 }

DP? http://acm.hdu.edu.cn/showproblem.php?pid=3944

 #include<cstdio>
 #include<cstring>
 #include<vector>
 #define mt(a,b) memset(a,b,sizeof(a))
 using namespace std;
 typedef __int64 LL;
 const int M=;
 class LUCASM { //比较适合n,k<=10^9,p<=10^4的情况
     int flag[M*],prime[],pcnt;
     vector<int> rev[M],fac[M];
     int quickpow(int a,int b,int c) { //快速幂求(a^b)%c
         int ret=%c;
         for(; b; a=a*a%c,b>>=) {
             if(b&) {
                 ret=ret*a%c;
             }
         }
         return ret;
     }
 public:
     void init() {//先初始化一次即可
         pcnt=;
         mt(flag,-);
         for(int i=; i<=; i++) {
             if(flag[i]) {
                 prime[pcnt++]=i;
                 rev[i].clear();
                 fac[i].clear();
             }
             for(int j=; j<pcnt&&prime[j]<=/i; j++) {
                 flag[i*prime[j]]=;
                 if(!(i%prime[j])) break;
             }
         }
         for(int i=; i<pcnt; i++) {
             int tnum=;
             rev[prime[i]].push_back();
             fac[prime[i]].push_back();
             for (int j=; j<prime[i]; j++) {
                 tnum=(tnum*j)%prime[i];
                 int now=quickpow(tnum,prime[i]-,prime[i]);
                 fac[prime[i]].push_back(tnum);
                 rev[prime[i]].push_back(now);
             }
         }
     }
     int lucas(int n,int k,int p) {
         int ret=;
         while (n && k) {
             int num1=n%p;
             int num2=k%p;
             n/=p;
             k/=p;
             if (num1<num2) return ;
             int num=(fac[p][num1]*rev[p][num2])%p;//计算c(num1,num2)%p
             num=(num*rev[p][num1-num2])%p;
             ret=(ret*num)%p;
         }
         return ret;
     }
 } gx;
 int main() {
     int n,k,p,cas=;
     gx.init();
     while(~scanf("%d%d%d",&n,&k,&p)) {
         printf("Case #%d: ",cas++);
         if(k>n/) k=n-k;
         int o=gx.lucas(n+,k,p);
         printf("%d\n",(n-k+o)%p);
     }
     return ;
 }

end