HDU 2815 扩展baby step giant step 算法

题目大意就是求 a^x = b(mod c) 中的x

用一般的baby step giant step 算法会超时

这里参考的是http://hi.baidu.com/aekdycoin/item/236937318413c680c2cf29d4

map平衡树查找值

 #include <cstdio>
 #include <cstring>
 #include <iostream>
 #include <cmath>
 #include <map>
 using namespace std;
 #define ll long long

 int q_pow(int a , int b , int mod)
 {
     ll ans = ;
     while(b)
     {
         if(b&) ans =((ll)ans*a)%mod;
         a = ((ll)a*a)%mod;
         b>>=;
     }
     return ans;
 }

 int gcd(int a , int b)
 {
     if(b == )return a;
     else return gcd(b,a%b);
 }

 int ex_gcd(int a , int &x , int b , int &y)
 {
     if(b == ){
         x= , y=;
         return a;
     }
     int ans = ex_gcd(b , x , a%b , y);
     int t = x;
     x=y , y = t-a/b*y;
     return ans;
 }

 int inv(int a , int b , int mod)
 {
     int x , y , d;
     d = ex_gcd(a , x , mod , y);
     int e = (ll)x*b%mod;
     return e<?e+mod:e;
 }

 int BabyStep(int A,int B,int C){
     map<int,int> Hash;
     ll buf=%C,D=buf,K;
     int i,d=,tmp;
     for(i=;i<=;buf=buf*A%C,++i)
         if(buf==B) return i;
     while((tmp=gcd(A,C))!=)
     {
         if(B%tmp)return -;
         ++d;
         C/=tmp;
         B/=tmp;
         D=D*A/tmp%C;
     }
     Hash.clear();
     int M=(int)ceil(sqrt((double)C));
     for(buf=%C,i=;i<=M;buf=buf*A%C,++i)
         if(!Hash.count((int)buf))Hash[(int)buf]=i;
     for(i=,K=q_pow((ll)A,M,C);i<=M;D=D*K%C,++i)
     {
         tmp=inv(D,B,C);
         if(tmp>=&&Hash.count(tmp))return i*M+Hash[tmp]+d;
     }
     return -;
 }
 int main()
 {
    // freopen("a.in" ,"r" , stdin);
     int k , p , n;
     while(scanf("%d%d%d" , &k , &p , &n) == )
     {
         if(n>=p){
             puts("Orz,I can’t find D!");
             continue;
         }
         int ans = BabyStep(k , n , p);
         if(ans == -) puts("Orz,I can’t find D!");
         else printf("%d\n" , ans);
     }
     return ;
 }

hash表查找值（效率高很多）hash是线性查找：

 #include<iostream>
 #include<map>
 #include<cmath>
 #include <cstdio>
 using namespace std;
 typedef long long LL;
 const int maxn = ;
 struct hash{
     int a,b,next;
 }Hash[maxn << ];
 int flg[maxn + ];
 int top,idx;
 //hash值插入
 void ins(int a,int b){
     int k = b & maxn;
     if(flg[k] != idx){
         flg[k] = idx;
         Hash[k].next = -;
         Hash[k].a = a;
         Hash[k].b = b;
         return ;
     }
     while(Hash[k].next != -){
         if(Hash[k].b == b) return ;
         k = Hash[k].next;
     }
     Hash[k].next = ++ top;
     Hash[top].next = -;
     Hash[top].a = a;
     Hash[top].b = b;
 }
 //hash值查找
 int find(int b){
     int k = b & maxn;
     if(flg[k] != idx) return -;
     while(k != -){
         if(Hash[k].b == b) return Hash[k].a;
         k = Hash[k].next;
     }
     return -;
 }
 int gcd(int a,int b)
 {
     return b?gcd(b,a%b):a;
 }
 int ext_gcd(int a,int b,int& x,int& y)
 {
     int t,ret;
     if (!b){x=,y=;return a;}
     ret=ext_gcd(b,a%b,x,y);
     t=x,x=y,y=t-a/b*y;
     return ret;
 }
 int Inval(int a,int b,int n){
     int x,y,e;
     ext_gcd(a,n,x,y);
     e=(LL)x*b%n;
     return e<?e+n:e;
 }
 int pow_mod(LL a,int b,int c)
 {
     LL ret=%c;
     a%=c;
     while(b){
         if(b&)ret=ret*a%c;
         a=a*a%c;
         b>>=;
     }
     return ret;
 }
 int BabyStep(int A,int B,int C){
     top = maxn; ++ idx;
     LL buf=%C,D=buf,K;
     int i,d=,tmp;
     for(i=;i<=;buf=buf*A%C,++i)
         if(buf==B)return i;
     while((tmp=gcd(A,C))!=){
         if(B%tmp)return -;
         ++d;
         C/=tmp;
         B/=tmp;
         D=D*A/tmp%C;
     }
     int M=(int)ceil(sqrt(C+0.5));
     for(buf=%C,i=;i<=M;buf=buf*A%C,++i)
         ins(i,buf);
     for(i=,K=pow_mod((LL)A,M,C);i<=M;D=D*K%C,++i){
         tmp=Inval((int)D,B,C);
         int w ;
         if(tmp>=&&(w = find(tmp)) != -) return i*M+w+d;
     }
     return -;
 }
 int main(){
     int A,B,C;
     while(scanf("%d%d%d",&A,&C,&B)!=EOF){
         if(B>C){
             puts("Orz,I can’t find D!");
             continue;
         }
         int tmp=BabyStep(A,B,C);
         if(tmp<)
             puts("Orz,I can’t find D!");
         else printf("%d\n",tmp);
     }
     return ;
 }