BZOJ 1406: [AHOI2007]密码箱 exgcd+唯一分解定理

推出来了一个解法，但是感觉复杂度十分玄学，没想到秒过~

Code: 

#include <bits/stdc++.h>
#define ll long long 
#define N 50000 
#define setIO(s) freopen(s".in","r",stdin) 
using namespace std;  
namespace Math
{ 
    ll pp,answer;  
    ll exgcd(ll a,ll b,ll &x,ll &y)
    {
        if(b==0)
        {
            x=1,y=0;
            return a;
        }
        ll ans=exgcd(b,a%b,x,y);
        ll tmp=x;
        x=y,y=tmp-a/b*y;
        return ans;
    }
    void solve(ll A,ll B,ll C)
    {   
        ll x,y,gcd,b,ans;
        gcd = exgcd(A,B,x,y);                        
        if(C%gcd!=0) 
        {
            answer=-1; 
            return; 
        }    
        x*=C/gcd,B/=gcd;
        if(B<0) B=-B;  
        ans=x%B;     
        if(ans<=0) ans+=B; 
        answer=ans,pp=B;     
    } 
};   
priority_queue<int,vector<int>,greater<int> >q;   
map<int,int>mark;   
vector<int>v;       
int prime[N],vis[N],tot; 
void init()
{
    int i,j; 
    for(i=2;i<N;++i)
    {
        if(!vis[i]) prime[++tot]=i; 
        for(j=1;j<=tot&&prime[j]*i<N;++j)
        {
            vis[prime[j]*i]=1; 
            if(i%prime[j]==0) break;    
        }
    }
}   
int main()
{ 
    init();  
    // setIO("input"); 
    int n,i,j,h,flag=0;        
    scanf("%d",&n),h=n;     
    for(i=1;i<=tot&&h>=prime[i];++i)
    {
        if(h%prime[i]==0)
        {
            int cc=1;           
            for(;h%prime[i]==0;h/=prime[i]) cc*=prime[i];      
            v.push_back(cc);   
        }
    }   
    if(h!=1) v.push_back(h);   
    if(n%4==0) flag=1;   
    int len=v.size(); 
    for(i=0;i<(1<<len);++i)
    {
        int tmp=1;   
        for(j=0;(1<<j)<=i;++j)
        {
            if(i&(1<<j)) 
                tmp*=v[j]; 
        }
        int a=tmp,b=n/tmp,dd;   
        Math::solve(a,b,2);                     
        if(Math::answer!=-1)      
        {
            ll anss=Math::answer*a-1;
            while(anss>=0&&anss<n) 
            { 
            	if(!mark[anss]) mark[anss]=1,q.push(anss);     
            	anss+=Math::pp*a; 
            }
        }         
        swap(a,b); 
        Math::solve(a,b,2);                     
        if(Math::answer!=-1)      
        {
            ll anss=Math::answer*a-1;
            while(anss>=0&&anss<n)
            { 
            	if(!mark[anss]) mark[anss]=1,q.push(anss);   
            	anss+=Math::pp*a; 
            }
        }              
        if(flag) 
        {
        	if(b%2==0) swap(a,b);    
        	a/=2,b*=2;             
	        Math::solve(a,b,2);                        
	        dd=Math::pp;         
	        if(Math::answer!=-1)      
	        {    
	            ll anss=Math::answer*a-1;
	            while(anss>=0&&anss<n) 
	            {
	            	if(!mark[anss]) 
	            	{
	            		mark[anss]=1; 
	            		q.push(anss);   
	            	}
	            	anss+=Math::pp*a;    
	            }
	        }          
	        swap(a,b); 
	        Math::solve(a,b,2);                     
	        if(Math::answer!=-1)      
	        {
	            ll anss=Math::answer*a-1;
	            while(anss>=0&&anss<n) 
	            {
	            	if(!mark[anss]) 
	            	{
	            		mark[anss]=1; 
	            		q.push(anss);   
	            	}
	            	anss+=Math::pp*a; 
	            }
	        }  
        }
    }   
    while(!q.empty()) 
    {
    	printf("%d\n",q.top()); q.pop(); 
    }
    return 0; 
}