Clever Y POJ - 3243 （扩展BSGS）

Posted 2020-10-03 yijiull

Clever Y

 POJ - 3243 

题意：给a，c，b，求最小的x使得 a^x≡b (mod c)。

扩展BSGS算法~

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <iostream>
 4 #include <cmath>
 5 #define ll long long
 6 using namespace std;
 7 const int mod=99991;
 8 ll head[mod],nex[mod];
 9 ll cnt;
10 ll hs[mod],id[mod];
11 void init(){
12     memset(head,-1,sizeof(head));
13     cnt=0;
14 }
15 void insert_(ll x,ll i){
16     hs[cnt]=x;id[cnt]=i;
17     ll u=x%mod;
18     nex[cnt]=head[u];
19     head[u]=cnt++;
20 }
21 ll find_(ll x){
22     int u=x%mod;
23     for(int i=head[u];~i;i=nex[i]){
24         if(hs[i]==x) return id[i];
25     }
26     return -1;
27 }
28 ll gcd(ll a,ll b){
29     ll r=a%b;
30     while(r){a=b;b=r;r=a%b;}
31     return b;
32 }
33 ll BSGS(ll a,ll b,ll c){
34     a%=c;b%=c;
35     if(b==1) return 0;
36     ll g=1,d=1,k=0;
37     while((g=gcd(a,c))!=1){
38         if(b%g) return -1;
39         b/=g;c/=g;
40         k++;
41         d=d*(a/g)%c;
42         if(b==d) return k;
43     }
44     ll m=ceil(sqrt(c*1.0)),q=1;
45     for(ll i=0;i<=m;i++){
46         if(i==0) insert_(b,i);
47         else {
48             q=q*a%c;
49             insert_(q*b%c,i);
50         }
51     }
52     for(ll i=1;i<=m;i++){
53         d=d*q%c;
54         ll j=find_(d);
55         if(j!=-1) return i*m-j+k;
56     }
57     return -1;
58 }
59 int main(){
60     ll a,b,c;
61     while(scanf("%lld%lld%lld",&a,&c,&b)&&(a+b+c)){
62         init();
63         ll ans=BSGS(a,b,c);
64         if(ans==-1) puts("No Solution");
65         else printf("%lld\n",ans);
66     }
67 }

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