poj 2417

Accepted    8508K    391MS    C++   2004B
相比下边，，优化太多太多了。。。
/**
baby-step-giant-step  因为数据量太大，，自己写hash

**/
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
using namespace std;
long long n,a,b;
const int maxn = 499991;
bool Hash[maxn];
long long idx[maxn];
long long val[maxn];

void ex_gcd(long long a,long long b,long long &x,long long &y){
    if(b==0){
        x=1;
        y=0;
        return ;
    }
    ex_gcd(b,a%b,x,y);
    long long tmp = x-(a/b)*y;
    x = y;
    y = tmp;
}

long long euler(long long n){
    long long i,tmp = n;
    for(i=2;i*i<=n;i++)if(n%i==0){
        tmp = tmp/i*(i-1);
        while(n%i==0)
            n = n/i;
    }
    if(n>1)
        tmp = tmp/n*(n-1);
    return tmp;
}

void Insert(long long id,long long num){
    long long k = num%maxn;
    while(Hash[k]&&val[k]!=num){
        k++;
        if(k==maxn) k = k-maxn;
    }
    if(!Hash[k]){
        Hash[k] =1;
        idx[k] = id;
        val[k] = num;
    }
}

long long found(long long num){
    long long k = num%maxn;
    while(Hash[k]&&val[k]!=num){
        k++;
        if(k==maxn) k = k-maxn;
    }
    if(!Hash[k]){
        return -1;
    }
    return idx[k];
}

long long baby_step(long long a,long long b,long long n){
    long long m = ceil(sqrt(euler(n)+0.5));
    memset(Hash,false,sizeof(Hash));
    memset(idx,-1,sizeof(idx));
    memset(val,-1,sizeof(val));
    long long d=1;
    for(long long i=0;i<m;i++){
        Insert(i,d);
        d = d*a%n;
    }
    long long res =1;
    long long x,y;
    for(long long i=0;i<m;i++){
        ex_gcd(res,n,x,y);
        long long tmp = x*b%n;
        tmp = (tmp%n+n)%n;
        long long k = found(tmp);
        if(k!=-1){
            return (i)*m+k;
        }
        res = res*d%n;
    }
    return -1;
}

int main()
{
    while(scanf("%I64d%I64d%I64d",&n,&a,&b)==3){
        long long res = baby_step(a,b,n);
        if(res==-1)
            printf("no solution
");
        else
            printf("%I64d
",res);
    }
    return 0;
}

-----------------------------------分割线---------------------------------------
/**
106 高次方程。。。baby-step-giant-step 算法
Accepted   4592K4     516MS      C++1104B
**/
#include <iostream>
#include <cstdio>
#include <math.h>
#include <map>
using namespace std;

long long powmod(long long a,long long b,long long n){
    if(b==0)
        return 1;
    long long c =1;
    while(b){
        if(b&1)
            c =c*a%n;
        a =a*a%n;
        b>>=1;
    }
    return c;
}

long long logmod(long long a,long long b,long long n){
    long long m,v,e=1,i;
    m = ceil(sqrt(n+0.5));
    //cout<<(double)(n-1)*1.0/m<<endl;
    //long long m_n = powmod(a,m,n);
    v = powmod(a,n-1-m,n);
    map<long long ,long long >x;
    x.clear();
    x[1] =m;
    for(i=1;i<m;i++){
        e = e*a%n;
        if(!x[e]) x[e]=i;
    }
    for(i=0;i<m;i++){
        if(x[b]){
            long long num = x[b];
            x.clear();
            return i*m+(m==num?0:num);
        }
        b = b*v%n;
    }
    return -1;
}

int main()
{
    long long a,b,n;
    while(scanf("%I64d%I64d%I64d",&n,&a,&b)==3){
        long long res = logmod(a,b,n);
        if(res==-1)
            printf("no solution
");
        else
            printf("%I64d
",res);
    }
    return 0;
}