第十五届吉林省赛The 15th Jilin Provincial Collegiate Programming Contest C.Random Number Generator（数学 BSGS)

Posted 2022-10-16 quinn18

文章目录

• • 题意
  • 题解
  • 代码
• 总结

题目链接

---

题意

：

题解

：
BSGS

代码

：

#include <bits/stdc++.h>
#include <unordered_map>
using namespace std;
#define ll long long
#define int long long
const ll N=1e8+5;
ll ksm(ll a, ll p, ll mod) 
	ll res=1;
	while(p) 
		if(p&1) res=res*a%mod;
		a=a*a%mod;
		p>>=1;
	
	return res;

ll exgcd(ll a, ll b, ll &x, ll &y) 
	if(!b) 
		x=1;
		y=0;
		return a;
	
	ll ans=exgcd(b, a%b, y, x);
	y=y-a/b*x;
	return ans;

ll inv(ll a, ll mod) //存在逆元条件：gcd(a,mod)=1
	ll x, y;
	ll g=exgcd(a, mod, x, y);
	if(g!=1) return -1;
	return (x%mod+mod)%mod;

ll bsgs(ll a,ll b,ll p)

    b%=p;
    if(b==1||p==1)return 0;
    ll n=sqrt(p);
    static unordered_map<ll,ll>Bmp;
    Bmp.clear();
    ll inva=inv(ksm(a,n-1,p),p)*b%p;
    for(ll i=n-1;i>=0;i--)
    
        Bmp[inva]=i;inva=inva*a%p;
    
    ll ta=1,powa=ksm(a,n,p);
    for(ll k=0;k<=p;k+=n)
    
        if(Bmp.count(ta))return k+Bmp[ta];
        ta=ta*powa%p;
    
    return -1;

signed main() 
	ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
	int a, b, M, x0, x;
	cin>>a>>b>>M>>x0>>x;
	bool q=0;
	if(x==x0) q=1;
	else if(a==0) 
		if(b==x) q=1;
		else q=0;
	else if(a==1) 
		if(b) q=1;
		else q=0;
	else 
		int aa=ksm(a-1,M-2,M)%M; 
		int t=((x+b*aa)%M*ksm(x0+b%M*aa%M,M-2,M)%M)%M;
		if(bsgs(a,t,M)==-1) q=0;
		else q=1;
	
	if(q) cout<<"YES"<<endl;
	else cout<<"NO"<<endl;
    return 0;

---

总结

Qaq