【BZOJ 3122】 [Sdoi2013]随机数生成器 (BSGS)

  1 #include<cstdio>
  2 #include<cstdlib>
  3 #include<cstring>
  4 #include<iostream>
  5 #include<algorithm>
  6 #include<queue>
  7 #include<cmath>
  8 using namespace std;
  9 #define LL long long
 10 #define Maxn 35000
 11 
 12 struct node
 13 {
 14     LL id,val;
 15 }t[Maxn];
 16 
 17 LL ax,ay;
 18 LL exgcd(LL a,LL b)
 19 {
 20     if(b==0) {ax=1;ay=0;return a;}
 21     LL g=exgcd(b,a%b);
 22     LL xx=ax;
 23     ax=ay;ay=xx-(a/b)*ay;
 24     return g;
 25 }
 26 
 27 bool cmp(node x,node y) {return (x.val==y.val)?(x.id<y.id):(x.val<y.val);}
 28 
 29 LL cnt;
 30 
 31 LL t_div(LL x)
 32 {
 33     LL l=0,r=cnt;
 34     while(l<r)
 35     {
 36         LL mid=(l+r)>>1;
 37         if(t[mid].val==x) return t[mid].id;
 38         if(t[mid].val>x) r=mid-1;
 39         else l=mid+1;
 40     }
 41     if(t[l].val==x) return t[l].id;
 42     return -1;
 43 }
 44 
 45 LL get_ans(LL k,LL a,LL c,LL p)
 46 {
 47     LL sq=(LL)ceil(sqrt((double)p));
 48     t[0].id=0;t[0].val=k%p;
 49     for(LL i=1;i<=sq;i++) t[i].val=(t[i-1].val*a)%p,t[i].id=i;
 50     
 51     sort(t+1,t+1+sq,cmp);
 52     cnt=0;
 53     for(LL i=1;i<=sq;i++) if(t[i].val!=t[i-1].val) t[++cnt]=t[i];
 54     
 55     LL bm=1;
 56     for(LL i=1;i<=sq;i++) bm=(bm*a)%p;
 57     LL g=exgcd(bm,p);
 58     ax=(ax%(p/g)+(p/g))%(p/g);
 59     bm=ax;
 60     
 61     LL tmp=c%p;
 62     for(LL i=0;i<=sq;i++)
 63     {
 64         LL now=t_div(tmp);
 65         if(now!=-1) return now+i*sq;
 66         tmp=(tmp*bm)%p;
 67     }
 68     return -1;
 69 }
 70 
 71 LL ffind(LL k,LL a,LL c,LL p)
 72 {
 73     LL x=k;
 74     for(LL i=0;i<=100;i++)
 75     {
 76         if(x==c) return i;
 77         x=(x*a)%p;
 78     }
 79     LL g;
 80     x=0;
 81     while((g=exgcd(a,p))!=1)
 82     {
 83         p/=g;
 84         k=(k*(a/g))%p;
 85         if(c%g!=0) return -1;
 86         c/=g;
 87         x++;
 88     }
 89     LL ans=get_ans(k,a,c,p);
 90     if(ans==-1) return -1;
 91     return ans+x;
 92 }
 93 
 94 int main()
 95 {
 96     int T,kase=0;
 97     scanf("%d",&T);
 98     while(T--)
 99     {
100         // printf("%d: ",++kase);
101         LL p,a,b,x,t,c;
102         scanf("%lld%lld%lld%lld%lld",&p,&a,&b,&x,&t);
103         // if(b==0) {printf("1\n");continue;}
104         if(t==x) {printf("1\n");continue;}
105         if(a==0&&b==t) {printf("2\n");continue;}
106         else if(a==0) {printf("-1\n");continue;}
107         if(a==1)
108         {
109             LL g=exgcd(b,p);
110             c=t-x;c=(c%p+p)%p;
111             if(c%g!=0) {printf("-1\n");continue;}
112             ax*=c/g;
113             ax=(ax%(p/g)+(p/g))%(p/g);
114             printf("%d\n",ax+1);
115             continue;
116         }
117         
118         LL phi;
119         if(b%(a-1)==0) phi=b/(a-1);
120         else
121         {
122             if(exgcd(a-1,p)!=1) {printf("-1\n");continue;}
123             ax=(ax%p+p)%p;
124             phi=(b*ax)%p;
125         }
126         LL A=x+phi,B=phi+t;
127         
128         if(b==0) A=x,B=t;
129         
130         A=(A%p+p)%p; B=(B%p+p)%p;
131         // if(A==0) {printf("-1\n");continue;}
132         
133         LL ans=ffind(A,a,B,p);
134         
135         if(ans==-1) printf("-1\n");
136         else printf("%lld\n",ans+1);
137     }
138     return 0;
139 }