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;
}