test/unittest/binomial-prefix-sum-query.test.cpp

• View this file on GitHub
• Last update: 2026-07-17 15:50:59+00:00

Depends on

• Binomial Coefficient Prefix Sum Query (math/combinatorics/binomial-prefix-sum-query.hpp)
• Binomial Table (二項係数テーブル) (math/combinatorics/binomial-table.hpp)
• Enumeration (組み合わせ) (math/combinatorics/enumeration.hpp)
• Montgomery Mod Int (math/combinatorics/montgomery-mod-int.hpp)
• template/template.hpp

Code

// competitive-verifier: STANDALONE

#include "../../template/template.hpp"

#include "../../math/combinatorics/binomial-prefix-sum-query.hpp"
#include "../../math/combinatorics/binomial-table.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"

using mint = modint998244353;

int main() {
  constexpr int N = 50;
  auto binom = binomial_table<mint>(N);
  vector<vector<mint> > prefix(N + 1, vector<mint>(N + 2));
  for (int n = 0; n <= N; n++) {
    for (int k = 0; k <= n; k++) {
      prefix[n][k + 1] = prefix[n][k] + binom[n][k];
    }
  }

  BinomialPrefixSumQuery<mint> query(N);
  assert(query.value() == mint(0));
  for (int n = 0; n <= N; n++) {
    for (int k = -1; k <= n; k++) {
      assert(query.move(n, k) == prefix[n][k + 1]);
      assert(query.value() == prefix[n][k + 1]);
    }
  }
  for (int n = N; n >= 0; n--) {
    for (int k = n; k >= -1; k--) {
      assert(query.move(n, k) == prefix[n][k + 1]);
    }
  }

  mt19937 rng(123456789);
  for (int rep = 0; rep < 1000; rep++) {
    int n = rng() % (N + 1);
    int k = (int)(rng() % (n + 2)) - 1;
    assert(query.move(n, k) == prefix[n][k + 1]);
  }

  query.reset();
  assert(query.value() == mint(0));
  assert(query.move(N, N) == mint(2).pow(N));

  int k = N / 2;
  assert(query.move(N, k) == prefix[N][k + 1]);
  for (int n = N - 1; n >= 0; n--) {
    if ((n & 1) && k > 0) --k;
    k = min(k, n);
    assert(query.move(n, k) == prefix[n][k + 1]);
  }
}

#line 1 "test/unittest/binomial-prefix-sum-query.test.cpp"
// competitive-verifier: STANDALONE

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  for (size_t i = 0; i < v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (T& in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
bool chmax(T1& a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
bool chmin(T1& a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
enable_if_t<is_class_v<T> == 0> fill_v(T& t, const V& v) {
  t = v;
}

template <typename T, typename V>
enable_if_t<is_class_v<T> != 0> fill_v(T& t, const V& v) {
  for (auto& e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F&& f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args&&... args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
decltype(auto) MFP(F&& f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/unittest/binomial-prefix-sum-query.test.cpp"

#line 2 "math/combinatorics/binomial-prefix-sum-query.hpp"

#line 1 "math/combinatorics/enumeration.hpp"
/**
 * @brief Enumeration(組み合わせ)
 */
template <typename T>
struct Enumeration {
 private:
  static vector<T> _fact, _finv, _inv;

  inline static void expand(size_t sz) {
    if (_fact.size() < sz + 1) {
      int pre_sz = max(1, (int)_fact.size());
      _fact.resize(sz + 1, T(1));
      _finv.resize(sz + 1, T(1));
      _inv.resize(sz + 1, T(1));
      for (int i = pre_sz; i <= (int)sz; i++) {
        _fact[i] = _fact[i - 1] * T(i);
      }
      _finv[sz] = T(1) / _fact[sz];
      for (int i = (int)sz - 1; i >= pre_sz; i--) {
        _finv[i] = _finv[i + 1] * T(i + 1);
      }
      for (int i = pre_sz; i <= (int)sz; i++) {
        _inv[i] = _finv[i] * _fact[i - 1];
      }
    }
  }

 public:
  explicit Enumeration(size_t sz = 0) { expand(sz); }

  static inline T fact(int k) {
    expand(k);
    return _fact[k];
  }

  static inline T finv(int k) {
    expand(k);
    return _finv[k];
  }

  static inline T inv(int k) {
    expand(k);
    return _inv[k];
  }

  static T P(int n, int r) {
    if (r < 0 || n < r) return 0;
    return fact(n) * finv(n - r);
  }

  static T C(int p, int q) {
    if (q < 0 || p < q) return 0;
    return fact(p) * finv(q) * finv(p - q);
  }

  static T H(int n, int r) {
    if (n < 0 || r < 0) return 0;
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

template <typename T>
vector<T> Enumeration<T>::_fact = vector<T>();
template <typename T>
vector<T> Enumeration<T>::_finv = vector<T>();
template <typename T>
vector<T> Enumeration<T>::_inv = vector<T>();
#line 4 "math/combinatorics/binomial-prefix-sum-query.hpp"

/**
 * @brief Binomial Coefficient Prefix Sum Query
 */
template <typename Mint>
struct BinomialPrefixSumQuery {
 private:
  static int check_max_n(int max_n) {
    assert(max_n >= 0);
    return max_n;
  }

  int max_n_, n_ = 0, k_ = -1;
  Mint sum_ = 0, inv_two_;
  Enumeration<Mint> binom_;

 public:
  explicit BinomialPrefixSumQuery(int max_n)
      : max_n_(check_max_n(max_n)),
        inv_two_(Mint(1) / Mint(2)),
        binom_(max_n_) {}

  void reset() {
    n_ = 0;
    k_ = -1;
    sum_ = 0;
  }

  Mint move(int n, int k) {
    assert(0 <= n && n <= max_n_);
    assert(-1 <= k && k <= n);
    while (n_ < n) {
      sum_ += sum_ + binom_.C(n_, k_ + 1);
      ++n_;
      ++k_;
    }
    while (n_ > n) {
      --n_;
      --k_;
      sum_ = (sum_ - binom_.C(n_, k_ + 1)) * inv_two_;
    }
    while (k_ < k) {
      sum_ += binom_.C(n_, k_ + 1);
      ++k_;
    }
    while (k_ > k) {
      --k_;
      sum_ -= binom_.C(n_, k_ + 1);
    }
    return sum_;
  }

  Mint value() const { return sum_; }
};
#line 1 "math/combinatorics/binomial-table.hpp"
/**
 * @brief Binomial Table(二項係数テーブル)
 *
 */
template <typename T>
vector<vector<T> > binomial_table(int N) {
  vector<vector<T> > mat(N + 1, vector<T>(N + 1));
  for (int i = 0; i <= N; i++) {
    for (int j = 0; j <= i; j++) {
      if (j == 0 || j == i)
        mat[i][j] = 1;
      else
        mat[i][j] = mat[i - 1][j - 1] + mat[i - 1][j];
    }
  }
  return mat;
}
#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64& a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64& b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint& operator+=(const mint& p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint& operator-=(const mint& p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint& operator*=(const mint& p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint& operator/=(const mint& p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint& p) const { return mint(*this) += p; }

  mint operator-(const mint& p) const { return mint(*this) -= p; }

  mint operator*(const mint& p) const { return mint(*this) *= p; }

  mint operator/(const mint& p) const { return mint(*this) /= p; }

  bool operator==(const mint& p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint& p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

  friend ostream& operator<<(ostream& os, const mint& p) {
    return os << p.val();
  }

  friend istream& operator>>(istream& is, mint& a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 8 "test/unittest/binomial-prefix-sum-query.test.cpp"

using mint = modint998244353;

int main() {
  constexpr int N = 50;
  auto binom = binomial_table<mint>(N);
  vector<vector<mint> > prefix(N + 1, vector<mint>(N + 2));
  for (int n = 0; n <= N; n++) {
    for (int k = 0; k <= n; k++) {
      prefix[n][k + 1] = prefix[n][k] + binom[n][k];
    }
  }

  BinomialPrefixSumQuery<mint> query(N);
  assert(query.value() == mint(0));
  for (int n = 0; n <= N; n++) {
    for (int k = -1; k <= n; k++) {
      assert(query.move(n, k) == prefix[n][k + 1]);
      assert(query.value() == prefix[n][k + 1]);
    }
  }
  for (int n = N; n >= 0; n--) {
    for (int k = n; k >= -1; k--) {
      assert(query.move(n, k) == prefix[n][k + 1]);
    }
  }

  mt19937 rng(123456789);
  for (int rep = 0; rep < 1000; rep++) {
    int n = rng() % (N + 1);
    int k = (int)(rng() % (n + 2)) - 1;
    assert(query.move(n, k) == prefix[n][k + 1]);
  }

  query.reset();
  assert(query.value() == mint(0));
  assert(query.move(N, N) == mint(2).pow(N));

  int k = N / 2;
  assert(query.move(N, k) == prefix[N][k + 1]);
  for (int n = N - 1; n >= 0; n--) {
    if ((n & 1) && k > 0) --k;
    k = min(k, n);
    assert(query.move(n, k) == prefix[n][k + 1]);
  }
}

Back to top page