uva 11916 Emoogle Grid （BSGS）

UVA 11916

　　BSGS的一道简单题，不过中间卡了一下没有及时取模，其他这里的100000007是素数，所以不用加上拓展就能做了。

代码如下：

 #include <cstdio>
 #include <iostream>
 #include <algorithm>
 #include <cstring>
 #include <vector>
 #include <cmath>
 #include <map>

 using namespace std;

 template<class T> T gcd(T a, T b) { return b ? a : gcd(b, a % b);}
 typedef long long LL;
 void gcd(LL a, LL b, LL &d, LL &x, LL &y) {
     if (b) { gcd(b, a % b, d, y, x); y -= a / b * x;}
     else d = a, x = , y = ;
 }
 const LL MOD = ;
 const int N = ;

 LL multi(LL a, LL p) {
     LL ret = ;
     a %= MOD;
     while (p > ) {
         if (p & ) ret *= a, ret %= MOD;
         a *= a, a %= MOD, p >>= ;
     }
     return ret;
 }
 map<LL, int> id;
 vector<LL> rec[N];
 LL mincol;

 void bs(LL b, LL x, LL rt) {
     id.clear();
     for (int i = ; i <= rt; i++) {
         if (id.find(b) != id.end()) break;
         id[b] = i;
         b *= x, b %= MOD;
     }
 }

 LL gs(LL b, LL x, LL r) {
     LL cur = b;
     //for (int i = 0; i < 50; i++) {
         //if (cur == r) return mincol + i + 1;
         //cur *= x, cur %= MOD;
     //}
     int rt = (int) ceil(sqrt((double) MOD)) + ;
     bs(b, x, rt);
     LL st = multi(x, rt), p, q, d;
     cur = ;
     for (int i = ; i <= rt; i++) {
         gcd(cur, MOD, d, p, q);
         p %= MOD, p += MOD, p %= MOD, p *= r / d, p %= MOD;
         if (id.find(p) != id.end()) return (LL) i * rt + id[p] + mincol + ;
         cur *= st, cur %= MOD;
     }
     return -;
 }

 LL bf(LL b, LL x, LL r) {
     LL cur = b;
     for (int i = ; i < MOD; i++) {
         if (cur == r) return mincol + i + ;
         cur *= x, cur %= MOD;
     }
     return -;
 }
 int main() {
     //freopen("in", "r", stdin);
     LL n, k, b, r, x, y, bres;
     int T, cas = ;
     cin >> T;
     while (T-- && cin >> n >> k >> b >> r) {
         for (int i = ; i < N; i++) rec[i].clear();
         id.clear();
         mincol = ;
         for (int i = ; i < b; i++) {
             cin >> x >> y;
             if (id.find(y) == id.end()) id[y] = id.size() - ;
             rec[id[y]].push_back(x);
             mincol = max(mincol, x);
         }
         bres = ;
         for (int i = , sz = id.size(); i < sz; i++) {
             rec[i].push_back();
             rec[i].push_back(mincol + );
             sort(rec[i].begin(), rec[i].end());
             for (int j = , szj = rec[i].size(); j < szj; j++) {
                 if (rec[i][j] - rec[i][j - ] -  >= ) bres *= k * multi(k - , (LL) rec[i][j] - rec[i][j - ] - ) % MOD, bres %= MOD;
             }
         }
         LL tmp = k * multi(k - , mincol - );
         bres *= multi(tmp, n - id.size());
         bres %= MOD;
         cout << "Case " << cas++ << ": ";
         if (bres == r) { cout << mincol << endl; continue; }
         int cnt = ;
         for (int i = , sz = id.size(); i < sz; i++) {
             rec[i].pop_back();
             if (rec[i][rec[i].size() - ] == mincol) bres *= k, bres %= MOD, cnt++;
         }
         bres *= multi(k - , n - cnt);
         bres %= MOD;
         k = multi(k - , n);
         cout << gs(bres, k, r) << endl;
         //cout << bf(bres, k, r) << endl;
     }
     return ;
 }

——written by Lyon