【SDOI 2010】 计算器

【题目链接】 

            https://www.lydsy.com/JudgeOnline/problem.php?id=2242

【算法】

           第一问用快速幂解决

           第二问用exgcd解决

           第三问用BSGS算法解决

【代码】

          

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

ll T,K,y,z,p,q,x,g,ans;

inline ll power(ll a,ll n,ll p)
{
        ll b = a,ret = 1;
        while (n > 0)
        {
                if (n & 1) ret = 1ll * ret * b % p;
                b = 1ll * b * b % p;
                n >>= 1;
        }
        return ret;
}
inline ll exgcd(ll a,ll b,ll &x,ll &y)
{
        ll g;
        if (b == 0)
        {
                x = 1;
                y = 0;
                return a;        
        }    else
        {
                g = exgcd(b,a%b,y,x);
                y -= a / b * x;
                return g;
        }
}
inline ll Baby_Step_Giant_Step(ll a,ll b,ll p)
{
        ll i,j,t,val;
        map<ll,ll> mp;
        mp.clear();
        b %= p;
        t = ceil(sqrt(p));
        for (j = 0; j <= t; j++)
        {
                val = 1ll * b * power(a,j,p) % p;
                mp[val] = j;
        }        
        a = power(a,t,p);
        if (a == 0) return b == 0 ? 1 : -1; 
        for (i = 0; i <= t; i++)
        {
                val = power(a,i,p);
                j = mp.find(val) == mp.end() ? -1 : mp[val];
                if (j >= 0 && i * t - j >= 0) 
                        return i * t - j;
        }
        return -1;
}

int main() 
{
        
        scanf("%lld%lld",&T,&K);
        while (T--)
        {
                scanf("%lld%lld%lld",&y,&z,&p);
                if (K == 1) printf("%lld\n",power(y,z,p));
                if (K == 2)
                {
                        g = exgcd(y,p,x,q);
                        if (z % g == 0) printf("%lld\n",((x*z/g)%p+p)%p);
                        else printf("Orz, I cannot find x!\n");
                }    
                if (K == 3)
                {
                        ans = Baby_Step_Giant_Step(y,z,p);
                        if (ans != -1) printf("%lld\n",ans);
                        else printf("Orz, I cannot find x!\n"); 
                }
        }
        
        return 0;
    
}