結果

問題 No.97 最大の値を求めるくえり
コンテスト
ユーザー Komaki__
提出日時 2014-12-07 21:19:36
言語 C++11（廃止可能性あり）
(gcc 13.3.0)
結果
AC  
実行時間 688 ms / 5,000 ms
コード長 9,677 bytes
コンパイル時間 1,593 ms
コンパイル使用メモリ 172,016 KB
実行使用メモリ 8,536 KB
最終ジャッジ日時 2024-06-11 17:19:38
合計ジャッジ時間 7,758 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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ファイルパターン 結果
other AC * 19
権限があれば一括ダウンロードができます

ソースコード

diff # 

#ifdef KOMAKI_LOCAL
#include <omp.h>
#else
#define NDEBUG
#endif

#include <bits/stdc++.h>
#include <sys/time.h>
#include <unistd.h>
using namespace std;
#define i64         int64_t
#define rep(i, n)   for(i64 i = 0; i < ((i64)(n)); ++i)
#define sz(v)       ((i64)((v).size()))
#define bit(n)      (((i64)1)<<((i64)(n)))
#define all(v)      (v).begin(), (v).end()

template <int POS, class TUPLE> void deploy(std::ostream &os, const TUPLE &tuple){}
template <int POS, class TUPLE, class H, class ...Ts> void deploy(std::ostream &os, const TUPLE &t){ os << (POS == 0 ? "" : ", ") << get<POS>(t); deploy<POS + 1, TUPLE, Ts...>(os, t); }
template <class ...Ts> std::ostream& operator<<(std::ostream &os, const std::tuple<Ts...> &t){ os << "("; deploy<0, std::tuple<Ts...>, Ts...>(os, t); os << ")"; return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::vector<T> &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "" : ", "); os << "}"; return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::set<T> &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "" : ", "); os << "}"; return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::queue<T> &q){ auto qq = q; os << "{"; for(; !qq.empty(); qq.pop()){ os << qq.front() << (qq.size() != 1 ? ", " : ""); } os << "}"; return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::priority_queue<T> &q){ auto qq = q; os << "{"; for(; !qq.empty(); qq.pop()){ os << qq.top() << (qq.size() != 1 ? ", " : ""); } os << "}"; return os; }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::pair<T, K> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::map<T, K> &mp){ int remain = mp.size(); os << "{"; for(auto e: mp) os << "(" << e.first << " -> " << e.second << ")" << (--remain == 0 ? "" : ", "); os << "}"; return os; }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::unordered_map<T, K> &mp){ int remain = mp.size(); os << "{"; for(auto e: mp) os << "(" << e.first << " -> " << e.second << ")" << (--remain == 0 ? "" : ", "); os << "}"; return os; }
#define DEBUG0() { char buf[1000]; sprintf(buf, "line:%3d | ", __LINE__); std::cout << buf << std::endl; }
#define DEBUG1(var0) { char buf[1000]; sprintf(buf, "line:%3d | ", __LINE__); std::cout << buf << (#var0) << "=" << (var0) << std::endl; }
#define DEBUG2(var0, var1) { char buf[1000]; sprintf(buf, "line:%3d | ", __LINE__); std::cout << buf << (#var0) << "=" << (var0) << ", " << (#var1) << "=" << (var1) << std::endl; }
#define DEBUG3(var0, var1, var2) { char buf[1000]; sprintf(buf, "line:%3d | ", __LINE__); std::cout << buf << (#var0) << "=" << (var0) << ", " << (#var1) << "=" << (var1) << ", " << (#var2) << "=" << (var2) << std::endl; }
#define DEBUG4(var0, var1, var2, var3) { char buf[1000]; sprintf(buf, "line:%3d | ", __LINE__); std::cout << buf << (#var0) << "=" << (var0) << ", " << (#var1) << "=" << (var1) << ", " << (#var2) << "=" << (var2) << ", " << (#var3) << "=" << (var3) << std::endl; }
#define DEBUG5(var0, var1, var2, var3, var4) { char buf[1000]; sprintf(buf, "line:%3d | ", __LINE__); std::cout << buf << (#var0) << "=" << (var0) << ", " << (#var1) << "=" << (var1) << ", " << (#var2) << "=" << (var2) << ", " << (#var3) << "=" << (var3) << ", " << (#var4) << "=" << (var4) << std::endl; }
#define DEBUG6(var0, var1, var2, var3, var4, var5) { char buf[1000]; sprintf(buf, "line:%3d | ", __LINE__); std::cout << buf << (#var0) << "=" << (var0) << ", " << (#var1) << "=" << (var1) << ", " << (#var2) << "=" << (var2) << ", " << (#var3) << "=" << (var3) << ", " << (#var4) << "=" << (var4) << ", " << (#var5) << "=" << (var5) << std::endl; }
















unsigned xor128_x = 123456789, xor128_y = 362436069, xor128_z = 521288629, xor128_w = 88675123;
unsigned xor128() {
	unsigned t = xor128_x ^ (xor128_x << 11);
	xor128_x = xor128_y; xor128_y = xor128_z; xor128_z = xor128_w;
	return xor128_w = xor128_w ^ (xor128_w >> 19) ^ (t ^ (t >> 8));
}
/*
const i64 LIMIT = 8000;
const i64 MOD = 100003;
void generate()
{
  vector<i64> a;
  rep(i, MOD) a.push_back(xor128() % MOD);

  i64 bests[MOD];
  rep(i, MOD) bests[i] = 0;
  vector<i64> updates[MOD];

  i64 cnt = 0;
  rep(i, MOD){
    //if(i % 100 == 0) DEBUG1(i);
    rep(q, MOD){
      i64 t = (a[i] * q) % MOD;
      if(bests[q] < t){
        if(LIMIT <= i){
          ++cnt;
          updates[q].push_back(i);
          cout << q << ", " << i << ", ";
          if(cnt % 100 == 0) cout << endl;
        }
        bests[q] = t;
      }
    }
  }

  DEBUG1(cnt);
}

vector<i64> updates[MOD];
int t[] = 


int main()
{
  generate();
  return 0;

  i64 n, q;
  cin >> n >> q;
  
  vector<i64> a;
  rep(i, n) a.push_back(xor128() % MOD);

  i64 bests[MOD];
  rep(i, MOD) bests[i] = 0;

  rep(i, min(LIMIT, n)){
    rep(j, MOD) bests[j] = max(bests[j], (a[i] * j) % MOD);
  }
  rep(j, MOD){
    for(auto t: updates[j])if(t < n) bests[j] = max(bests[j], (a[t] * j) % MOD);
  }

  rep(i, q){
    i64 t;
    cin >> t;
    cout << bests[t] << endl;
  }

}


*/


/******************************************************************/
/*                                                                */
/* Undefine "GF_USE_FIXED_GF" to use various mods, but slower.    */
/* To use fixed one, set your mod at "static const int mod = ;"   */
/*                                                                */
/******************************************************************/

#define GF_USE_FIXED_GF
template <typename T> class GF
{
public:
  #ifdef GF_USE_FIXED_GF
  static const T mod = 100003; // Set your mod!
  GF() { permutation_memo = std::vector<T>(1, 1); inverse_memo = std::vector<T>(2, 1); permutation_inverse_memo = std::vector<T>(2, 1); }
  #else
  T mod;
  GF(T mod) : mod(mod) { permutation_memo = std::vector<T>(1, 1); inverse_memo = std::vector<T>(2, 1); permutation_inverse_memo = std::vector<T>(2, 1); } 
  #endif 


  T norm(T i);

  T add(T i0, T i1);
  T sub(T i0, T i1);
  T mul(T i0, T i1);
  T div(T i0, T i1);
  T pow(T i, int64_t p);
  T inv(T i);
  T permInv(T i);
  
  T permutation(T n, T m); // n * (n - 1) * ... * (n - m + 1), Non limited memorization, Avoid segmentation fault!
  T combination(T n, T m); // Memorized for n < MEMO_SIZE_LIMIT.
  
private:
  static const int MEMO_SIZE_LIMIT = 2000000;
  std::vector<T> permutation_memo;
  std::vector<T> inverse_memo;
  std::vector<T> permutation_inverse_memo;
};


template <typename T>
inline T GF<T>::permutation(T n, T m)
{
  if(m < 0 || n < m) return 0;
  while(permutation_memo.size() <= n){
    permutation_memo.push_back(mul(permutation_memo.back(), permutation_memo.size()));
  }
  return mul(permutation_memo[n], permInv(n - m));
}

template <typename T>
inline T GF<T>::combination(T n, T m)
{
  if(m < 0 || n < m) return 0;
  if(n - m < m) m = n - m;
  
  if(n < MEMO_SIZE_LIMIT){
    T num = permutation(n, n);
    T den = mul(permInv(m), permInv(n - m));
    return mul(num, den);
  }
  
  T num = 1, den = 1;
  for(T i = 0; i < m; ++i){
    num = mul(num, n - i);
    den = mul(den, i + 1);
  }
  return div(num, den);
}

template <typename T>
inline T GF<T>::norm(T i)
{
  return (i % mod + mod) % mod;
}

template <typename T> 
inline T GF<T>::add(T i0, T i1)
{
  T res = i0 + i1;
  if(mod <= res) return res - mod;
  return res;
}

template <typename T> 
inline T GF<T>::sub(T i0, T i1)
{
  T res = i0 - i1;
  if(res < 0) return res + mod;
  return res;
}

template <typename T> 
inline T GF<T>::mul(T i0, T i1)
{
  return (int64_t)i0 * i1 % mod;
}

template <typename T> 
inline T GF<T>::div(T i0, T i1)
{
  return mul(i0, inv(i1));
}

template <typename T>
inline T GF<T>::permInv(T i)
{
  while(permutation_inverse_memo.size() <= i){
    permutation_inverse_memo.push_back(mul(permutation_inverse_memo.back(), inv(permutation_inverse_memo.size())));
  }
  return permutation_inverse_memo[i];
}

template <typename T> 
inline T GF<T>::inv(T i)
{
  if(i < MEMO_SIZE_LIMIT){
    while(inverse_memo.size() <= i){
      // Deformation of formula. 
      // b[t] * t = (M - (M / t) * t) * b[M - (M / t) * t];
      // Divides by i over a finite field GF(mod), b[t] = - (M / t) * b[M % t].
      int size = inverse_memo.size();
      inverse_memo.push_back(mod - (int64_t)(mod / size) * inverse_memo[mod % size] % mod);
    }
    return inverse_memo[i];
  }

  return this->pow(i, mod - 2);
}

template <typename T> 
inline T GF<T>::pow(T i, int64_t p)
{
  T res = 1;
  for(; p; p >>= 1){
    if(p & 1) res = mul(res, i);
    i = mul(i, i);
  }
  return res;
}






int main()
{
  const i64 LIMIT = 1000;
  const i64 MOD = 100003;
  i64 n, q;
  cin >> n >> q;
  vector<i64> a;
  rep(i, n) a.push_back(xor128() % MOD);

  i64 bests[MOD];
  rep(i, MOD) bests[i] = 0;
  rep(i, min(LIMIT, n))rep(j, MOD) bests[j] = max(bests[j], (a[i] * j) % MOD);

  GF<int> gf;
  if(LIMIT < n){
    set<i64> s;
    rep(i, n) s.insert(a[i]);
    rep(i, MOD)if(i){
      for(i64 t = MOD - 1; bests[i] < t; --t){
        i64 inv = gf.div(t, i);
        if(s.count(inv)){
          bests[i] = t;
          break;
        }
      }
    }
  }
  rep(i, q){
    i64 t;
    cin >> t;
    cout << bests[t] << endl;
    
  }
}
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