BZOJ 2242: [SDOI2011]计算器

2242

思路：BSGS+逆元

代码：

#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pii pair<int, int>
#define piii pair<int,pii>
#define mem(a, b) memset(a, b, sizeof(a))
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
//head

map<int, int>mp;
LL q_pow(LL n, LL k, LL p) {
    LL ans = 1;
    if(k == -1) return 0;
    while(k) {
        if(k&1) ans = (ans*n) % p;
        n = (n*n) % p;
        k >>= 1;
    }
    return ans;
}

int BSGS(int a, int b, int c) {
    if(a%c == 0 && b%c != 0 ) return -1;
    int m = ceil(sqrt(c)), base = 1;
    mp.clear();
    for (int i = 0; i < m; i++) {
        if(mp.find(base) == mp.end()) mp[base] = i;
        base = (1LL * base * a) % c;
    }
    int D = 1;
    for (int i = 0; i < m; i++) {
        int x = (b * q_pow(D, c - 2, c)) % c;
        if(mp.find(x) != mp.end()) return i*m + mp[x];
        D = (1LL * D * base) % c;
    }
    return -1;
}
int main() {
    int T, op, y, z, p;
    while( ~scanf("%d %d", &T, &op)) {
        for (int i = 1; i <= T; i++) {
            scanf("%d %d %d", &y, &z, &p);
            if(op == 1) {
                printf("%lld
", q_pow(y, z, p));
            }
            else if(op == 2) {
                if(y%p == 0 && z%p != 0) printf("Orz, I cannot find x!
");
                else printf("%lld
", (1LL* z * q_pow(y, p-2, p)) % p);
            }
            else if(op == 3) {
                int ans = BSGS(y, z, p);
                if(ans == -1) printf("Orz, I cannot find x!
");
                else printf("%d
", ans);
            }
        }
    }
    return 0;
}