1. 程式人生 > >BZOJ 1485 [HNOI2009]有趣的數列【卡特蘭大數任意模】

BZOJ 1485 [HNOI2009]有趣的數列【卡特蘭大數任意模】

模數可以去任意值。

做法原理就是把數分解分解。

當然可以當作板子來記:

#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
#define rep(i,x,y) for(ll i=(x);i<=(y);i++)
#define red(i,x,y) for(ll i=(x);i>=(y);i--)
using namespace std;
 
const ll N=2e6+5;
 
ll n,m,ans=1,id[N],vis[N],num[N],pri[N];
 
inline ll read() {
    ll x=0;char ch=getchar();bool f=0;
    while(ch>'9'||ch<'0'){if(ch=='-')f=1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
    return f?-x:x;
}
 
inline ll mul(ll x,ll y) {
    return x*y%m;
}
 
inline ll ksm(ll x,ll y) {
    ll ret=1ll;
    while(y) {
        if(y&1) ret=mul(ret,x);
        x=mul(x,x);y>>=1;
    }
    return ret;
}
 
void File() {
    freopen("interesting.in","r",stdin);
    freopen("interesting.out","w",stdout);
}
 
int main() {
//  File();
     
    n=read(),m=read();
     
    rep(i,2,2*n) {
        if(!vis[i]) {
            pri[++pri[0]]=i;id[i]=pri[0];
        }
        rep(j,1,pri[0]) {
            if(pri[j]*i>2*n) break;
            else {
                id[pri[j]*i]=j;
                vis[pri[j]*i]=1;
                if(i%pri[j]==0) break;
            }
        }
    }
     
    rep(i,2,n+1) {
        ll x=i;
        while(x>1) {
            num[id[x]]--;x/=pri[id[x]];
        }
    }
     
    rep(i,n+1,2*n) {
        ll x=i;
        while(x>1) {
            num[id[x]]++;x/=pri[id[x]];
        }
    }
     
    rep(i,1,pri[0]) ans=mul(ans,ksm(pri[i],num[i]));
 
    printf("%lld\n",ans);
     
    return 0;
}