Baby step gaint step

Given the same remainder, evaluate all the solutions including it, where there is always a prime number.

 

Analysis:The steps for resolving the same formula are as follows:

(1) An original root of the Modulus

(2) ExploitationBaby step giant stepFind one, so that, because it is a prime number, there is a unique solution.

(3) set, so that there is, where, then get.

(4) Find all, you can know that there is a total of solutions, we can find all, and then sort the order.

 

O (SQRT (N) time complexity

Bsgs is as follows (Forward star Version)

　　

const maxn=200001;type node=record        data,next,id:longint;end;type LL=int64;var edge:array [0..maxn] of node;    head:array [0..maxn] of longint;    cnt:longint;    a,b,c:ll;procedure insert(data,id:longint);var i,k:longint;begin  k:=data mod maxn;  i:=head[k];  while i<>-1 do    begin      if edge[i].data=data then exit;      edge[cnt].data:=data;      edge[cnt].id:=id;      edge[cnt].next:=head[k];      head[k]:=cnt;      inc(cnt);      i:=edge[i].next;    end;end;function find(data:ll):longint;var i,k:longint;begin  k:=data mod maxn;  i:=head[k];  while i<>-1 do    begin      if edge[i].data=data then exit(edge[i].id);      i:=edge[i].next;    end;  exit(-1);end;procedure extend_gcd(a,b:ll;var x,y:ll);var t:ll;begin  if b=0 then    begin      x:=1;      y:=0;      exit;    end;  extend_gcd(b,a mod b,x,y);  t:=x;  x:=y;  y:=t-(a div b)*y;end;function gcd(x,y:ll):ll;begin  if x mod y=0 then exit(y)  else exit(gcd(y,x mod y));end;function modd(x,p:ll):ll;begin  if x>=p then exit(x mod p);  if x<0 then exit((x mod p+p) mod p);  exit(x);end;function quick_mod(a,n,p:ll):ll;var ans,t:ll;begin  ans:=1; t:=modd(a,p);  while n<>0 do    begin      if (n and 1)=1 then ans:=modd(ans*t,c);      n:=n>>1;      t:=modd(t*t,c);    end;  exit(ans);end;function bsgs(a,b,c:ll):ll;var x,y,k,t,d,len,m:ll; i:longint;begin   fillchar(head,sizeof(head),$ff);   cnt:=0;   b:=modd(b,c);   for i:=0 to 100 do      begin        if b=t then exit(i);        t:=modd(t*a,c);      end;   d:=1; len:=0;   while true do     begin       t:=gcd(a,c);       if t=1 then break;       if (b mod t)<>0 then exit(-1);       c:=c div t;       b:=b div t;       d:=modd(d*a div t,c);       inc(len);     end;   m:=trunc(sqrt(c));   t:=1;   for i:=0 to m do      begin        insert(t,i);        t:=modd(t*a,c);      end;    k:=quick_mod(a,m,c);    for i:=0 to m do      begin        extend_gcd(d,c,x,y);        t:=modd(b*x,c);        if (y=find(t)) and (y<>-1) then exit(i*m+y+len);        d:=modd(d*k,c);      end;    exit(-1);end;begin  readln(a,b,c);  writeln(bsgs(a,b,c));end.

View code

 

Baby step gaint step