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  • 【题解】多少个$1$(exBSGS)

    【题解】多少个(1)(exBSGS)

    解方程:

    [underbrace {1dots1}_{n}equiv k mod m ]

    其实就是

    [dfrac {10^n-1} {9}equiv k mod m ]

    就是

    [10^nequiv 9k+1 mod m ]

    直接exBSGS【总结】皇冠上的明珠——初等数论初步

    //@winlere
    #include<iostream>
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    #include<map>
    #include<cmath>
    
    using namespace std;  typedef long long ll;
    inline ll qr(){
          register ll ret=0,f=0;
          register char c=getchar();
          while(c<48||c>57)f|=c==45,c=getchar();
          while(c>=48&&c<=57) ret=ret*10+c-48,c=getchar();
          return f?-ret:ret;
    }
    
    map < ll , ll > s;
    inline ll exBSGS(ll a,ll b,ll m){
          ll AD=1,d;
          ll cnt=0;
          while(d=__gcd(a,m),d!=1) {
    	    b/=d,m/=d,AD=AD*(a/d),++cnt;
    	    if(AD==b) return cnt;
          }
          ll sq=sqrt(m)+1,ret=1;
          map < ll ,ll >().swap(s);
          for(ll t=0;t<sq;++t,ret=(__int128)ret*a%m)
    	    s[(__int128)ret*b%m]=t;
          for(ll t=1,w=AD*ret;t<=sq;++t,w=(__int128)w*ret%m)
    	    if(s.find(w)!=s.end())
    		  return cnt+t*sq-s[w];
          return -1;
    }
    
    int main(){
          ll k=qr(),m=qr();
          printf("%lld
    ",exBSGS(10,9ll*k+1,m));
          return 0;
    }
    
    
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  • 原文地址:https://www.cnblogs.com/winlere/p/11279308.html
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