結果

問題 No.1665 quotient replace
コンテスト
ユーザー keijak
提出日時 2021-09-04 04:25:13
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 968 ms / 3,000 ms
コード長 5,593 bytes
コンパイル時間 2,464 ms
コンパイル使用メモリ 212,992 KB
最終ジャッジ日時 2025-01-24 07:37:16
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 41
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 # 

#include <bits/stdc++.h>
#define REP_(i, a_, b_, a, b, ...) \
  for (int i = (a), END_##i = (b); i < END_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using i64 = long long;

template<typename T, typename U>
inline bool chmax(T &a, U b) {
  return a < b and ((a = std::move(b)), true);
}
template<typename T, typename U>
inline bool chmin(T &a, U b) {
  return a > b and ((a = std::move(b)), true);
}
template<typename T>
inline int ssize(const T &a) {
  return (int) std::size(a);
}

template<typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &a) {
  for (auto &x: a) is >> x;
  return is;
}
template<typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &a) {
  return os << "(" << a.first << ", " << a.second << ")";
}
template<typename Container>
std::ostream &print_seq(const Container &a, std::string_view sep = " ",
                        std::string_view ends = "\n",
                        std::ostream &os = std::cout) {
  auto b = std::begin(a), e = std::end(a);
  for (auto it = std::begin(a); it != e; ++it) {
    if (it != b) os << sep;
    os << *it;
  }
  return os << ends;
}
template<typename T, typename = void>
struct is_iterable : std::false_type {};
template<typename T>
struct is_iterable<T, std::void_t<decltype(std::begin(std::declval<T>())),
                                  decltype(std::end(std::declval<T>()))>>
    : std::true_type {
};

template<typename T, typename = std::enable_if_t<
    is_iterable<T>::value &&
        !std::is_same<T, std::string_view>::value &&
        !std::is_same<T, std::string>::value>>
std::ostream &operator<<(std::ostream &os, const T &a) {
  return print_seq(a, ", ", "", (os << "{")) << "}";
}

void print() { std::cout << "\n"; }
template<class T>
void print(const T &x) {
  std::cout << x << "\n";
}
template<typename Head, typename... Tail>
void print(const Head &head, Tail... tail) {
  std::cout << head << " ";
  print(tail...);
}

struct Input {
  template<typename T>
  operator T() const {
    T x;
    std::cin >> x;
    return x;
  }
} in;

#ifdef MY_DEBUG
#include "debug_dump.hpp"
#else
#define DUMP(...)
#endif

using namespace std;

const int L = 1'000'005;

struct PrimeSieve {
  std::vector<int> spf;  // smallest prime factors table.
  std::vector<int> primes;

  explicit PrimeSieve(int n) : spf(n + 1) {
    // O(n)
    for (int i = 2; i <= n; ++i) {
      if (spf[i] == 0) {
        spf[i] = i;
        primes.push_back(i);
      }
      for (const auto &p: primes) {
        if (i * p > n or p > spf[i]) break;
        spf[i * p] = p;
      }
    }
  }

  inline bool is_prime(int n) const { return spf[n] == n; }

  auto factorize(int n) const {
    assert(0 < n and n < int(spf.size()));
    std::vector<std::pair<int, int>> res;
    while (n > 1) {
      const int p = spf[n];
      int count = 0;
      do {
        n /= p;
        ++count;
      } while (n % p == 0);
      res.emplace_back(p, count);
    }
    return res;
  }
} sieve(L);

// O(d(n)) + sorting
std::vector<i64> enumerate_divisors(
    const std::vector<std::pair<int, int>> &fac) {
  std::vector<i64> res = {1};
  for (auto[p, k]: fac) {
    int sz = res.size();
    for (int i = 0; i < sz; ++i) {
      i64 pp = 1;
      for (int j = 0; j < k; ++j) {
        pp *= p;
        res.push_back(res[i] * pp);
      }
    }
  }
  //std::sort(res.begin(), res.end());
  return res;
}

// Disjoint closed intervals [l, r] (mapping l to r).
class ClosedIntervalSet : public std::map<i64, i64> {
 private:
  // If true, automatically merges [l, c] and [c+1, r].
  bool merge_adjacent;

 public:
  ClosedIntervalSet(bool merge_adjacent = true)
      : merge_adjacent(merge_adjacent) {}

  // Returns the interval [l, r] which contains p if available.
  // Otherwise returns this->end().
  std::map<i64, i64>::iterator get(i64 p) {
    auto it = upper_bound(p);
    if (it == begin() || (--it)->second < p) return end();
    return it;
  }

  // Inserts interval [l, r]
  void insert(i64 l, i64 r) {
    auto itl = upper_bound(l), itr = upper_bound(r + merge_adjacent);
    if (itl != begin()) {
      if ((--itl)->second < l - merge_adjacent) ++itl;
    }
    if (itl != itr) {
      l = std::min(l, itl->first);
      r = std::max(r, std::prev(itr)->second);
      erase(itl, itr);
    }
    (*this)[l] = r;
  }

  // Removes interval [l, r]
  void remove(i64 l, i64 r) {
    auto itl = upper_bound(l), itr = upper_bound(r);
    if (itl != begin()) {
      if ((--itl)->second < l) ++itl;
    }
    if (itl == itr) return;
    i64 tl = std::min(l, itl->first);
    i64 tr = std::max(r, std::prev(itr)->second);
    erase(itl, itr);
    if (tl < l) (*this)[tl] = l - 1;
    if (r < tr) (*this)[r + 1] = tr;
  }

  // Are p and q in the same interval?
  bool same(i64 p, i64 q) {
    const auto &it = get(p);
    return it != end() && it->first <= q && q <= it->second;
  }

  i64 mex() {
    auto it = get(0);
    if (it == end()) return 0;
    return it->second + 1;
  }
};

auto main() -> int {
  ios_base::sync_with_stdio(false), cin.tie(nullptr);

  const int n = in;
  vector<int> a(n);
  cin >> a;
  int amax = *max_element(ALL(a));
  vector<int> g(amax + 1, -1);
  g[1] = 0;
  for (int x = 2; x <= amax; ++x) {
    auto ds = enumerate_divisors(sieve.factorize(x));
    ClosedIntervalSet cis;
    for (auto d: ds) {
      if (d == x) continue;
      cis.insert(g[d], g[d]);
    }
    g[x] = cis.mex();
  }
  int gall = 0;
  REP(i, n) {
    gall ^= g[a[i]];
  }
  print(gall == 0 ? "black" : "white");
}
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