test/1_mytest/EGZ.test.cpp

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• Last update: 2026-09-01 06:31:29+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• ds/csr.hpp
• mod/mod_inv.hpp
• my_template.hpp
• nt/EGZ.hpp
• random/base.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"

#include "random/base.hpp"
#include "nt/EGZ.hpp"

void test(int N) {
  FOR(1000) {
    vc<ll> A(2 * N - 1);
    FOR(i, len(A)) A[i] = RNG(0, N);
    vc<int> I = EGZ(N, A);
    ll sm = 0;
    for (int i : I) sm += A[i];
    assert(len(I) == N && sm % N == 0);
    sort(all(I));
    FOR(i, len(I) - 1) assert(I[i] != I[i + 1]);
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  FOR(N, 1, 100) test(N);
  solve();
  return 0;
}

#line 1 "test/1_mytest/EGZ.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(USE_PCH)
#include <my_template_compiled.hpp>
#else
#if defined(__GNUC__)
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
// 環境によってはコンパイル成功かつ実行時エラー
#pragma GCC target("avx2,popcnt")
#endif
#include <bits/stdc++.h>
#include <cassert>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class>
constexpr bool dependent_false = false;

template <class T>
constexpr T infty = [] {
  static_assert(dependent_false<T>, "infty<T> is not defined");
  return T{};
}();
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<i128>;
template <>
constexpr long double infty<long double> = infty<i128>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using pq_max = priority_queue<T>;
template <class T>
using pq_min = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = ll(a) - 1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = ll(a) - 1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define all(x) (x).begin(), (x).end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

// require y > 0
template <typename T>
T floor(T x, T y) {
  return x / y - (x % y < 0);
}

// require y > 0
template <typename T>
T ceil(T x, T y) {
  return (x / y) + (x % y > 0);
}

// require y > 0
template <typename T>
T bmod(T x, T y) {
  T r = x % y;
  return (r < 0 ? r + y : r);
}

// require y > 0
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = x / y, r = x % y;
  if (r < 0) --q, r += y;
  return {q, r};
}

constexpr auto TEN = [] {
  array<u64, 20> A{};
  A[0] = 1;
  for (int i = 1; i < 20; ++i) A[i] = 10 * A[i - 1];
  return A;
}();

template <typename T, typename U>
T SUM(const U &A) {
  return std::accumulate(A.begin(), A.end(), T{});
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
template <class C, class T>
inline long long LB(const C &c, const T &x) {
  return lower_bound(c.begin(), c.end(), x) - c.begin();
}
template <class C, class T>
inline long long UB(const C &c, const T &x) {
  return upper_bound(c.begin(), c.end(), x) - c.begin();
}
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <class T, class Container, class Compare>
T POP(priority_queue<T, Container, Compare> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
i128 binary_search(F check, i128 ok, i128 ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (1) {
    i128 x = (ok + ng) / 2;
    if (x == ok || x == ng) break;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}

template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  T c = max<T>(a, b);
  bool changed = (c != a);
  a = c;
  return changed;
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  T c = min<T>(a, b);
  bool changed = (c != a);
  a = c;
  return changed;
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vc<T> cumsum(const vc<U> &A, int off = 1) {
  int N = A.size();
  vc<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vc<int> argsort(const vc<T> &A) {
  vc<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
      [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &...others) {
  first.reserve(first.size() + (others.size() + ... + 0));
  (first.insert(first.end(), others.begin(), others.end()), ...);
}

// i128
template <class T, enable_if_t<is_same_v<T, i128>, int> = 0>
constexpr i128 abs(T x) {
  return x < 0 ? -x : x;
}

constexpr i128 gcd(i128 a, i128 b) {
  while (b != 0) {
    i128 c = a % b;
    a = b, b = c;
  }
  return abs(a);
}
#endif
#line 3 "test/1_mytest/EGZ.test.cpp"

#line 1 "random/base.hpp"

u64 RNG_64() {
  static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(
                      chrono::high_resolution_clock::now().time_since_epoch())
                          .count()) *
                  10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) {
  assert(lim > 0);
  return RNG_64() % lim;
}

ll RNG(ll l, ll r) {
  assert(l < r);
  return l + RNG_64() % (r - l);
}
#line 1 "ds/csr.hpp"

template <typename T>
struct CSR {
  int n;
  bool prepared;
  vc<int> ptr;
  vc<int> I;
  vc<T> dat;

  CSR(int n = 0) : n(n), prepared(false) {}
  void reserve(int n) { dat.reserve(n); }

  void add(int i, const T& x) {
    assert(0 <= i && i < n && !prepared);
    I.eb(i), dat.eb(x);
  }

  void build() {
    assert(!prepared);
    prepared = 1;
    ptr.assign(n + 1, 0);
    for (auto& i : I) ptr[1 + i]++;
    FOR(i, len(ptr) - 1) ptr[i + 1] += ptr[i];
    vc<T> tmp(len(dat));
    FOR(k, len(dat)) {
      int i = I[k];
      tmp[ptr[i]++] = dat[k];
    }
    swap(dat, tmp);
    ptr.pop_back();
    ptr.insert(ptr.begin(), 0);
    I.clear();
  }

  struct range {
    T *first, *last;
    T* begin() const { return first; }
    T* end() const { return last; }
    bool empty() const { return first == last; }
    int size() const { return last - first; }
  };

  range operator[](int i) {
    assert(prepared);
    return range{dat.data() + ptr[i], dat.data() + ptr[i + 1]};
  }
};
#line 1 "mod/mod_inv.hpp"

// long でも大丈夫
// (val * x - 1) が mod の倍数になるようにする
// 特に mod=0 なら x=0 が満たす
ll mod_inv(ll val, ll mod) {
  if (mod == 0) return 0;
  mod = abs(mod);
  val %= mod;
  if (val < 0) val += mod;
  ll a = val, b = mod, u = 1, v = 0, t;
  while (b > 0) {
    t = a / b;
    swap(a -= t * b, b), swap(u -= t * v, v);
  }
  if (u < 0) u += mod;
  return u;
}
#line 3 "nt/EGZ.hpp"

// p-subset で総和が 0 mod p のものを作る
// return: indices
vc<int> EGZ_prime(int p, vc<ll> A) {
  assert(len(A) == p + p - 1);
  for (auto& x : A) x = bmod<ll>(x, p);
  CSR<int> ids(p);
  FOR(i, len(A)) { ids.add(A[i], i); }
  ids.build();

  A.clear();
  FOR(x, p) FOR(len(ids[x])) A.eb(x);

  [&]() -> void {
    FOR(i, p) {
      if (A[i] == A[i + p - 1]) {
        A = {A.begin() + i, A.begin() + i + p};
        return;
      }
    }
    int t = 0;
    FOR(i, p) t = (t + p - A[i]) % p;
    vc<int> par(p, -1);
    auto exist = [&](int i) -> bool { return (i == 0 || par[i] != -1); };
    FOR(i, p - 1) {
      if (exist(t)) break;
      int d = A[i + p] - A[i];
      ll L = 0, R = mod_inv(d, p) * t % p;
      while (L + 1 < R) {
        ll M = (L + R) / 2;
        (exist(M * d % p) ? L : R) = M;
      }
      par[R * d % p] = i;
    }
    while (t != 0) {
      int i = par[t];
      int d = A[i + p] - A[i];
      t = (t + p - d) % p;
      A[i] = A[i + p];
    }
    A.resize(p);
  }();
  vc<int> CNT(p);
  for (auto& x : A) CNT[x]++;
  vc<int> res;
  FOR(x, p) {
    for (int i : ids[x]) {
      if (CNT[x]) --CNT[x], res.eb(i);
    }
  }
  return res;
}

// N-subset で総和が 0 mod p のものを作る
// return: indices
vc<int> EGZ(int N, vc<ll> A) {
  for (auto& x : A) x = bmod<ll>(x, N);
  assert(len(A) == 2 * N - 1);
  if (N == 1) return {0};
  int p = 2;
  while (N % p != 0) ++p;
  if (N == p) return EGZ_prime(N, A);

  // p is a prime factor
  int M = N / p;
  vc<int> ids;
  vc<int> yet;
  vi nxt_val;
  int k = 0;
  // p-EGZ * (2M-1)
  vc<int> used(2 * p - 1);
  FOR(2 * M - 1) {
    while (len(yet) < 2 * p - 1) {
      yet.eb(k++);
    }
    vc<ll> B = rearrange(A, yet);
    vc<int> way = EGZ_prime(p, B);
    FOR(i, 2 * p - 1) used[i] = 0;
    for (int i : way) used[i] = 1;
    vc<int> nxt;
    ll x = 0;
    FOR(i, 2 * p - 1) {
      if (used[i]) {
        x += A[yet[i]];
        ids.eb(yet[i]);
      } else {
        nxt.eb(yet[i]);
      }
    }
    swap(yet, nxt);
    assert(x % p == 0);
    nxt_val.eb(x / p);
  }
  vc<int> I = EGZ(M, nxt_val);
  vc<int> res;
  for (int i : I) {
    FOR(j, p * i, p * i + p) res.eb(ids[j]);
  }
  return res;
}
#line 6 "test/1_mytest/EGZ.test.cpp"

void test(int N) {
  FOR(1000) {
    vc<ll> A(2 * N - 1);
    FOR(i, len(A)) A[i] = RNG(0, N);
    vc<int> I = EGZ(N, A);
    ll sm = 0;
    for (int i : I) sm += A[i];
    assert(len(I) == N && sm % N == 0);
    sort(all(I));
    FOR(i, len(I) - 1) assert(I[i] != I[i + 1]);
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  FOR(N, 1, 100) test(N);
  solve();
  return 0;
}

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