TJOI2018 Day1 T1

http://www.elijahqi.win/archives/3274

题意：每次乘一个数每次除一个以前乘过的数，每次询问求总答案 模数不为质数且不一定于前面的互质

线段树，以位置建树即可 每次除法相当于把以前的位置改成1即可

#include<cstdio>
#include<cctype>
#define lc (x<<1)
#define rc (x<<1|1)
#include<algorithm>
#define ll long long
using namespace std;
inline char gc(){
    static char now[1<<16],*S,*T;
    if (T==S){T=(S=now)+fread(now,1,1<<16,stdin);if (T==S) return EOF;}
    return *S++;
}
inline int read(){
    int x=0,f=1;char ch=gc();
    while(!isdigit(ch)) {if (ch=='-') f=-1;ch=gc();}
    while(isdigit(ch)) x=x*10+ch-'0',ch=gc();
    return x*f;
}
const int N=1e5+10; 
struct node{int sum;}tree[N<<2];int mod;
inline void update(int x){tree[x].sum=(ll)tree[lc].sum*tree[rc].sum%mod;}
inline void modify(int x,int l,int r,int p,int v){
    if (l==r) {tree[x].sum=v;return;}int mid=l+r>>1;
    if (p<=mid) modify(lc,l,mid,p,v);else modify(rc,mid+1,r,p,v);update(x);
}
inline void build(int x,int l,int r){
    tree[x].sum=1;if (l==r) return;int mid=l+r>>1;
    build(lc,l,mid);build(rc,mid+1,r);
}
int main(){
    freopen("cal.in","r",stdin);
    freopen("cal.out","w",stdout);
    int T=read();
    while(T--){
        int q=read();mod=read();build(1,1,q);
        for (int owo=1;owo<=q;++owo){
            int op=read();
            if (op==1) modify(1,1,q,owo,read()),printf("%d\n",tree[1].sum);
            else modify(1,1,q,read(),1),printf("%d\n",tree[1].sum);
        }
    }
    return 0;
}

辣鸡elijahqi考场做法

#include<map>
#include<queue>
#include<cstdio>
#include<cctype>
#include<vector>
#include<cstring>
#define pa pair<int,int>
#include<algorithm>
#define ll long long
using namespace std;
inline char gc(){
       static char now[1<<16],*S,*T;
       if (T==S){T=(S=now)+fread(now,1,1<<16,stdin);if (T==S) return EOF;}
       return *S++;            
}
inline int read(){
       int x=0,f=1;char ch=gc();
       while(!isdigit(ch)) {if (ch=='-') f=-1;ch=gc();}
       while(isdigit(ch)) x=x*10+ch-'0',ch=gc();
       return x*f;       
}
const int N=100010;
int T,prime[N],m_prime[N],cnt,nm[N],pos[N],p1[N],inv[N],Q,mod,tot;
bool not_prime[N],flag[N];ll ans;map<int,int> mm;
map<int,int>::iterator it;
inline int ksm(ll b,int t){static ll tmp;
       for (tmp=1;t;b=b*b%mod,t>>=1) if (t&1) tmp=tmp*b%mod;return tmp;
}
inline void exgcd(int a,int b,int &x,int &y){
       if (!b) {x=1;y=0;return;}exgcd(b,a%b,x,y);
       int t=x;x=y;y=t-a/b*y;       
}
inline int gcd(int x,int y){
       if(!y) return x;return gcd(y,x%y);       
}
inline void gao(int m){
       int x=m;
       for (int i=1;i<=tot&&prime[i]<=x;++i){
           if (x%prime[i]) continue;
           if(flag[prime[i]]){
                 while(x%prime[i]==0) ++nm[p1[prime[i]]],x/=prime[i];
           }else{
                 while(x%prime[i]==0) ans=ans*prime[i]%mod,x/=prime[i];  
           }
       }
       if (x>1) {
          if(x==m_prime[cnt]) ++nm[cnt];
          else if (gcd(x,mod)==1)ans=ans*x%mod;
               else ++mm[x];
       }ll ans1=ans;
       for (int i=1;i<=cnt;++i) ans1=ans1*ksm(m_prime[i],nm[i])%mod;
       for (it=mm.begin();it!=mm.end();++it){
           ans1=ans1*ksm(it->first,it->second);
       }printf("%lld\n",ans1);
}
inline int get_inv(int a,int b){
       static int t1,t2;
       exgcd(a,b,t1,t2);
       t1=(t1%b+b)%b;
       return t1;       
}
inline void gao1(int p){
       int m=pos[p];int x=m;
       for (int i=1;i<=tot&&prime[i]<=x;++i){
           if (x%prime[i]) continue;
           if (flag[prime[i]]){
              while(x%prime[i]==0) --nm[p1[prime[i]]],x/=prime[i];
           }else{
              while(x%prime[i]==0) ans=ans*inv[i]%mod,x/=prime[i];
           }  
       }if (x>1) {
           if (x==m_prime[cnt]) --nm[cnt];
           else if (gcd(x,mod)==1) ans=ans*get_inv(x,mod)%mod;
           else{
                --mm[x];
           }  
       }ll ans1=ans;
       for (int i=1;i<=cnt;++i) ans1=ans1*ksm(m_prime[i],nm[i])%mod;
       for (it=mm.begin();it!=mm.end();++it){
           ans1=ans1*ksm(it->first,it->second);
       }printf("%lld\n",ans1);
}

int main(){
    freopen("cal.in","r",stdin);
    freopen("cal.out","w",stdout);
    T=read();
    for (int i=2;i<=1e5;++i) {
        if (!not_prime[i]) prime[++tot]=i;
        for (int j=1;prime[j]*i<=1e5&&j<=tot;++j){
            not_prime[prime[j]*i]=1;
            if (i%prime[j]==0) break;    
        }    
    }
    while(T--){
               Q=read();mod=read();int x=mod;ans=1;cnt=0;mm.clear();
               memset(nm,0,sizeof(nm));memset(flag,0,sizeof(flag));
               memset(inv,0,sizeof(inv));memset(pos,0,sizeof(pos));
               for (int i=1;i<=tot&&x>=prime[i];++i){
                   if (x%prime[i]) continue;
                   m_prime[++cnt]=prime[i];p1[prime[i]]=cnt;flag[prime[i]]=1;
                   while(x%prime[i]==0) x/=prime[i];   
               }if (x>1) m_prime[++cnt]=x;
               //for (int i=1;i<=cnt;++i) printf("%d ",m_prime[i]);puts("");
               for (int i=1;i<=tot;++i){
                   if (flag[prime[i]]) continue;
                   //printf("%d\n",get_inv(prime[i],mod));
                   inv[i]=get_inv(prime[i],mod);
               }
               for (int owo=1;owo<=Q;++owo){
                   int op=read(),m=read();pos[owo]=m;
                   if (op==1)gao(m);else gao1(m);
                 //  printf("%d\n",ans);
               }
    }
    return 0;    
}