高次同余方程 专题

/**************************************************************
    Problem:hdu 2815
    User: youmi
    Language: C++
    Result: Accepted
    Time:62MS
    Memory:2764K
****************************************************************/
//#pragma comment(linker, "/STACK:1024000000,1024000000")
//#include<bits/stdc++.h>
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <map>
#include <stack>
#include <set>
#include <sstream>
#include <cmath>
#include <queue>
#include <deque>
#include <string>
#include <vector>
#define zeros(a) memset(a,0,sizeof(a))
#define ones(a) memset(a,-1,sizeof(a))
#define sc(a) scanf("%d",&a)
#define sc2(a,b) scanf("%d%d",&a,&b)
#define sc3(a,b,c) scanf("%d%d%d",&a,&b,&c)
#define scs(a) scanf("%s",a)
#define sclld(a) scanf("%I64d",&a)
#define pt(a) printf("%d\n",a)
#define ptlld(a) printf("%I64d\n",a)
#define rep0(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define rep_1(i,n) for(int i=n;i>=1;i--)
#define rep_0(i,n) for(int i=n-1;i>=0;i--)
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
#define lson (step<<1)
#define rson (lson+1)
#define esp 1e-6
#define oo 0x3fffffff
#define TEST cout<<"*************************"<<endl

using namespace std;
typedef long long ll;

int n,p,b;
const int seed=65535;
struct Hh
{
    int id,next;
    ll val;
}hs[seed<<1];
bool flag[seed<<1];
int top;
void ins(int id,ll val)
{
    int k=val&seed;
    if(flag[k]==false)
    {
        flag[k]=true;
        hs[k].next=-1;
        hs[k].id=id;
        hs[k].val=val;
        return ;
    }
    while(hs[k].next!=-1)
    {
        if(hs[k].val==val)
            return ;
        k=hs[k].next;
    }
    hs[k].next=++top;
    hs[top].next=-1;
    hs[top].id=id;
    hs[top].val=val;
}
int get_find(ll val)
{
    int k=val&seed;
    if(flag[k]==false)
        return -1;
    while(k!=-1)
    {
        if(hs[k].val==val)
            return hs[k].id;
        k=hs[k].next;
    }
    return -1;
}
ll q_mul(ll a,ll b,ll mod)
{
    ll res=0;
    a=a%mod;
    while(b)
    {
        if(b&1)
            res=(res+a)%mod;
        b>>=1;
        a=(a<<1)%mod;
    }
    return res;
}
ll q_pow(ll a,ll b,ll mod)
{
    ll res=1;
    a=a%mod;
    while(b)
    {
        if(b&1)
            res=q_mul(res,a,mod);
        b>>=1;
        a=q_mul(a,a,mod);
    }
    return res;
}
ll ex_gcd(ll a,ll b,ll &x,ll &y)
{
    if(b==0)
    {
        x=1,y=0;
        return a;
    }
    ll ans=ex_gcd(b,a%b,x,y);
    ll temp=x;
    x=y;
    y=temp-y*(a/b);
    return ans;
}
ll inval(ll a)
{
    ll x,y;
    ex_gcd(a,p,x,y);
    return (x*n%p+p)%p;
}
ll babystep()
{
    top=seed;
    ll buf=1%p;
    ll D=buf,temp,x,y;
    int d=0;
    for(int i=0;i<=100;buf=buf*b%p,i++)
        if(buf==n)
            return i;
    while((temp=ex_gcd(b,p,x,y))!=1)
    {
        if(n%temp)
            return -1;
        ++d;
        p/=temp,n/=temp;
        D=D*(b/temp)%p;
    }
    int m=(int)ceil(sqrt((double)p));
    buf=1%p;
    for(int i=0;i<=m;buf=buf*b%p,i++)
        ins(i,buf);
    ll bm=q_pow(b,m,p);
    for(int i=0;i<=m;i++,D=D*bm%p)
    {
        temp=inval(D);
        int w;
        if(temp>=0&&(w=get_find(temp))!=-1)
            return i*m+w+d;
    }
    return -1;
}
int main()
{
    //freopen("in.txt","r",stdin);
    while(~sc3(b,p,n))
    {
        if(n>=p)
        {
            puts("Orz,I can’t find D!");
            continue;
        }
        zeros(flag);
        n%=p;
        ll pos=babystep();
        if(pos==-1)
            puts("Orz,I can’t find D!");
        else
            printf("%I64d\n",pos);
    }
    return 0;
}