洛谷P4774 [NOI2018]屠龙勇士

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题解

这题到底是什么东西……数学题太珂怕了……

//minamoto
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<set>
#define ll long long
#define GG {puts("-1");return;}
using namespace std;
const int N=1e5+5;
#define getc() (p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++)
char buf[1<<21],*p1=buf,*p2=buf;
template<class T>inline bool cmax(T&a,const T&b){return a<b?a=b,1:0;}
inline ll read(){
    #define num ch-'0'
    char ch;bool flag=0;ll res;
    while((ch=getc())>'9'||ch<'0')
    (ch=='-')&&(flag=true);
    for(res=num;(ch=getc())<='9'&&ch>='0';res=res*10+num);
    (flag)&&(res=-res);
    #undef num
    return res;
}
multiset<ll> s;int n,m;ll mod[N],xs[N],cs[N],st[N],gif[N];int T;
inline void exgcd(ll a,ll &x,ll b,ll &y){
    if(!b) return (void)(x=1,y=0);
    exgcd(b,x,a%b,y);ll t=x;x=y,y=t-(a/b)*y;
}
inline ll gcd(ll a,ll b){
    if(a<b) swap(a,b);
    while(b^=a^=b^=a%=b);return a;
}
inline ll inv(ll a,ll p){a%=p;ll x,y;exgcd(a,x,p,y);return x<0?x+p:x;}
inline ll mul(ll a,ll b,const ll &mod){
    ll res=0;b%=mod,b=b>0?b:b+mod;
    for(;b;b>>=1,a=(a+a)%mod) (res+=a*(b&1))%=mod;
    return res;
}
inline void spj(){
    ll res=0;
    for(int i=1;i<=n;++i) cmax(res,(cs[i]+xs[i]-1)/xs[i]);
    printf("%lld\n",res);
}
inline void spj2(){
    ll lc=1;
    for(int i=1;i<=n;++i){
        ll ds=mod[i]/gcd(mod[i],xs[i]);
        lc=lc/gcd(lc,ds)*ds;
    }
    printf("%lld\n",lc);
}
void solve(){
    n=read(),m=read();
    for(int i=1;i<=n;++i) cs[i]=read();
    for(int i=1;i<=n;++i) mod[i]=read();
    for(int i=1;i<=n;++i) gif[i]=read();
    for(int i=1;i<=m;++i) st[i]=read();
    for(int i=1;i<=m;++i) s.insert(st[i]);
    multiset<ll>::iterator ii;
    for(int i=1;i<=n;++i){
        ii=(cs[i]<(*s.begin()))?s.begin():(--s.upper_bound(cs[i]));
        xs[i]=*ii,s.erase(ii),s.insert(gif[i]);
    }
    for(int i=1;i<=m;++i)
    if(mod[i]==cs[i]){spj2();return;}
    for(int i=1;i<=n;++i)
    if(mod[i]==1){spj();return;}
    for(int i=1;i<=n;++i) xs[i]%=mod[i];
    for(int i=1;i<=n;++i)
    if(xs[i]==0){
        if(mod[i]==cs[i]) xs[i]=1,mod[i]=1,cs[i]=0;
        else GG;
    }
    for(int i=1;i<=n;++i){
        ll sx,sy,g=gcd(xs[i],mod[i]);
        if(cs[i]%g!=0) GG;
        exgcd(xs[i],sx,mod[i],sy);
        mod[i]=mod[i]/g;sx=(sx%mod[i]+mod[i])%mod[i],cs[i]=mul(sx,cs[i]/g,mod[i]);
    }
    for(int i=1;i<n;++i){
        ll g=gcd(mod[i],mod[i+1]);if((cs[i+1]-cs[i])%g!=0) GG;
        ll ncs=mul(inv(mod[i]/g,mod[i+1]/g),(cs[i+1]-cs[i])/g,mod[i+1]/g);
        ll nmod=mod[i]/g*mod[i+1];
        ncs=mul(ncs,mod[i],nmod),(ncs+=cs[i])%=nmod,cs[i+1]=ncs,mod[i+1]=nmod;
    }printf("%lld\n",cs[n]);
}
inline void clear(){s.clear();}
int main(){
//    freopen("testdata.in","r",stdin);
    T=read();
    for(int i=1;i<=T;++i) solve(),clear();
    return 0;
}