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  • BZOJ4891 TJOI2017龙舟(Polllard-Rho)

      对给定模数分解质因数后约分即可。依然常数巨大过不了。

    #include<iostream> 
    #include<cstdio>
    #include<cmath>
    #include<cstdlib>
    #include<cstring>
    #include<algorithm>
    using namespace std;
    #define ll long long
    #define N 10010
    char getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<'0'||c>'9')) c=getchar();return c;}
    ll gcd(ll n,ll m){return m==0?n:gcd(m,n%m);}
    ll read()
    {
        ll x=0,f=1;char c=getchar();
        while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
        while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
        return x*f;
    }
    int n,m,q,cnt,p[5000010],prime[500010],tot[100],t;
    ll g[100],a[25][N],b[N],c[N],d[N];
    bool flag[5000010];
    ll ksc(ll a,ll b,ll p)
    {
        ll t=a*b-(ll)((long double)a*b/p+0.5)*p;
        return t<0?t+p:t;
    }
    ll ksm(ll a,ll k,ll p)
    {
        ll s=1;
        for (;k;k>>=1,a=ksc(a,a,p)) if (k&1) s=ksc(s,a,p);
        return s;
    }
    void exgcd(ll &x,ll &y,ll a,ll b)
    {
        if (b==0)
        {
            x=1,y=0;
            return;
        }
        exgcd(x,y,b,a%b);
        ll t=x;x=y;y=t-a/b*x;
    }
    ll inv(ll a,ll p)
    {
        ll x,y;exgcd(x,y,a,p);
        x=(x%p+p)%p;
        return x; 
    }
    bool check(int k,ll n)
    {
        if (ksm(k,n-1,n)!=1) return 0;
        ll p=n-1;
        while (!(p&1))
        {
            p>>=1;ll x=ksm(k,p,n);
            if (x==n-1) return 1;
            if (x!=1) return 0;
        }
        return 1;
    }
    bool Miller_Rabin(ll n)
    {
        if (n<=5000000) return !flag[n];
        return check(2,n)&&check(3,n)&&check(5,n)&&check(7,n)&&check(61,n)&&check(24251,n);
    }
    ll f(ll x,ll p,int c){return (ksc(x,x,p)+c)%p;}
    void getfactor(ll n)
    {
        if (n<=5000000)
        {
            while (n>1) g[++cnt]=p[n],n/=p[n];
            return;
        }
        if (Miller_Rabin(n)) {g[++cnt]=n;return;}
        while (1)
        {
            int c=rand()%(n-1)+1;
            ll x=rand()%n,y=x;
            do
            {
                ll z=gcd(abs(x-y),n);
                if (z>1&&z<n) {getfactor(z),getfactor(n/z);return;}
                x=f(x,n,c),y=f(f(y,n,c),n,c);
            }while (x!=y);
        }
    }
    int main()
    {
    #ifndef ONLINE_JUDGE
        freopen("bzoj4891.in","r",stdin);
        freopen("bzoj4891.out","w",stdout);
        const char LL[]="%I64d
    ";
    #else
        const char LL[]="%lld
    ";
    #endif
        n=read(),m=read(),q=read();
        flag[1]=1;
        for (int i=2;i<=5000000;i++)
        {
            if (!flag[i]) prime[++t]=i,p[i]=i;
            for (int j=1;j<=t&&prime[j]*i<=5000000;j++)
            {
                flag[prime[j]*i]=1;
                p[prime[j]*i]=prime[j];
                if (i%prime[j]==0) break;
            }
        }
        for (int i=1;i<=m;i++) b[i]=read();
        for (int i=1;i<=n;i++)
            for (int j=1;j<=m;j++)
            a[i][j]=read();
        while (q--)
        {
            int x=read();ll y=read(),ans=1;cnt=0;getfactor(y);
            sort(g+1,g+cnt+1);cnt=unique(g+1,g+cnt+1)-g-1;memset(tot,0,sizeof(tot));
            memcpy(c,b,sizeof(c));memcpy(d,a[x],sizeof(d));
            for (int i=1;i<=m;i++)
            {
                for (int j=1;j<=cnt;j++)
                while (c[i]%g[j]==0) tot[j]++,c[i]/=g[j];
                for (int j=1;j<=cnt;j++)
                while (d[i]%g[j]==0) tot[j]--,d[i]/=g[j];
                ans=ksc(ksc(ans,c[i],y),inv(d[i],y),y);
            }
            for (int i=1;i<=cnt;i++)
            if (tot[i]<0) {ans=-1;break;}
            else ans=ksc(ans,ksm(g[i],tot[i],y),y);
            cout<<ans<<endl;
        }
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/Gloid/p/10281793.html
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