oj.uz

Submission #969436

# Submission time Handle Problem Language Result Execution time Memory
969436 2024-04-25T06:59:12 Z kilkuwu Boat (APIO16_boat) C++17
0 / 100
 81 ms 6400 KB 
#include <bits/stdc++.h>

#define nl '\n'

#ifdef LOCAL
#include "template/debug.hpp"
#else
#define dbg(...) ;
#define timer(...) ;
#endif

template <int md>
struct Modular {
  int v;

  constexpr Modular() : v(0) {}

  template <typename T>
  static inline int normalize(const T& x) {
    int res = -md <= x && x < md ? static_cast<int>(x) : static_cast<int>(x % md);
    return res + (res < 0) * md;
  }
  
  static constexpr int mod() {
    return md;
  }

  template <typename U>
  Modular(const U& x) : v(normalize(x)) {}

  const int& operator()() const { return v; }

  template <typename U>
  explicit operator U() const {
    return static_cast<U>(v);
  }

  using M = Modular;

  constexpr static inline M _raw(int x) {
    static_assert(x >= 0 && x < md);
    M res;
    res.v = x;
    return res;
  }

  template <typename U>
  friend std::enable_if_t<std::is_integral_v<U>, M> power(M b, U e) {
    assert(e >= 0);
    M ans = 1;
    while (e) {
      if (e & 1) ans *= b;
      b *= b;
      e >>= 1;
    }
    return ans;
  }

  M inv() const {
    M res = power(*this, md - 2);
    return res;
  }

  M& operator+=(const M& y) { return v += y.v, v -= (v >= md) * md, *this; }
  M& operator-=(const M& y) { return v -= y.v, v += (v < 0) * md, *this; }
  M& operator*=(const M& y) { return v = (int64_t) v * y.v % md, *this; }
  M& operator/=(const M& y) { return *this *= y.inv(); }

  M& operator++() { return *this += _raw(1); }
  M& operator--() { return *this -= _raw(1); }

  M operator++(int) {
    M res(*this);
    return *this += _raw(1), res;
  }

  M operator--(int) {
    M res(*this);
    return *this -= _raw(1), res;
  }

  M operator-() const { return M(-v); }

  friend bool operator==(const M& x, const M& y) { return x.v == y.v; }
  friend bool operator<(const M& x, const M& y) { return x.v < y.v; }
  friend bool operator>(const M& x, const M& y) { return x.v > y.v; }
  friend bool operator<=(const M& x, const M& y) { return x.v <= y.v; }
  friend bool operator>=(const M& x, const M& y) { return x.v >= y.v; }
  friend bool operator!=(const M& x, const M& y) { return x.v != y.v; }

  template <typename Istream>
  friend Istream& operator>>(Istream& is, M& y) {
    int64_t x;
    is >> x;
    y.v = y.normalize(x);
    return is;
  }

  template <typename Ostream>
  friend Ostream& operator<<(Ostream& os, const M& y) {
    return os << y.v;
  }

  friend M operator+(const M& x, const M& y) { return M(x) += y; }
  friend M operator-(const M& x, const M& y) { return M(x) -= y; }
  friend M operator*(const M& x, const M& y) { return M(x) *= y; }
  friend M operator/(const M& x, const M& y) { return M(x) /= y; }
};

constexpr int md = 1e9 + 7;
using Mint = Modular<md>;

signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  
  int n;
  std::cin >> n;
  std::vector<int> a(n), b(n);
  for (int i = 0; i < n; i++) std::cin >> a[i] >> b[i], b[i]++;

  std::vector<int> vals(a.begin(), a.end());
  vals.insert(vals.end(), b.begin(), b.end());
  std::sort(vals.begin(), vals.end());
  vals.erase(std::unique(vals.begin(), vals.end()), vals.end());

  int num_segments = vals.size() - 1;

  for (int i = 0; i < n; i++) {
    a[i] = std::lower_bound(vals.begin(), vals.end(), a[i]) - vals.begin();
    b[i] = std::lower_bound(vals.begin(), vals.end(), b[i]) - vals.begin();
  }

  std::vector<std::vector<Mint>> prepared(num_segments, std::vector<Mint>(n + 1));

  for (int i = 0; i < num_segments; i++) {
    int len = vals[i + 1] - vals[i];
    prepared[i][0] = 1;
    for (int j = 0; j < n; j++) {
      prepared[i][j + 1] = prepared[i][j] * (len - j) / (j + 1);
    }
    for (int j = 0; j < n; j++) {
      prepared[i][j + 1] += prepared[i][j];
    }
  }


  std::vector<std::vector<Mint>> dp(n + 1, std::vector<Mint>(num_segments + 1));
  std::vector<std::vector<Mint>> ff(n + 1, std::vector<Mint>(num_segments + 1));


  dp[n].back() = 1;
  for (int j = 0; j <= num_segments; j++) {
    ff[n][j] = 1;
  }

  Mint ans = 0;

  for (int i = n - 1; i >= 0; i--) {
    for (int j = num_segments - 1; j >= 0; j--) {
      if (a[i] <= j && j < b[i]) {
        int cnt = 0;
        for (int k = i; k < n; k++) {
          cnt += a[k] <= j && j < b[k];
          int rem = cnt - 1;
          Mint mul = prepared[j][rem];
          dp[i][j] += ff[k + 1][j + 1] * mul;
        }
      }
      ans += dp[i][j];
      ff[i][j] = ff[i][j + 1] + dp[i][j];
    }
  }

  std::cout << ans << nl;
}

Subtask #1
0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 79 ms 6400 KB Output is correct
2 Correct 78 ms 6228 KB Output is correct
3 Correct 78 ms 6276 KB Output is correct
4 Correct 79 ms 6272 KB Output is correct
5 Correct 80 ms 6224 KB Output is correct
6 Correct 78 ms 6276 KB Output is correct
7 Correct 78 ms 6228 KB Output is correct
8 Correct 79 ms 6276 KB Output is correct
9 Correct 78 ms 6276 KB Output is correct
10 Correct 81 ms 6228 KB Output is correct
11 Correct 80 ms 6276 KB Output is correct
12 Correct 78 ms 6288 KB Output is correct
13 Correct 78 ms 6228 KB Output is correct
14 Correct 79 ms 6292 KB Output is correct
15 Correct 79 ms 6292 KB Output is correct
16 Incorrect 16 ms 1612 KB Output isn't correct
17 Halted 0 ms 0 KB -

Subtask #2
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 79 ms 6400 KB Output is correct
2 Correct 78 ms 6228 KB Output is correct
3 Correct 78 ms 6276 KB Output is correct
4 Correct 79 ms 6272 KB Output is correct
5 Correct 80 ms 6224 KB Output is correct
6 Correct 78 ms 6276 KB Output is correct
7 Correct 78 ms 6228 KB Output is correct
8 Correct 79 ms 6276 KB Output is correct
9 Correct 78 ms 6276 KB Output is correct
10 Correct 81 ms 6228 KB Output is correct
11 Correct 80 ms 6276 KB Output is correct
12 Correct 78 ms 6288 KB Output is correct
13 Correct 78 ms 6228 KB Output is correct
14 Correct 79 ms 6292 KB Output is correct
15 Correct 79 ms 6292 KB Output is correct
16 Incorrect 16 ms 1612 KB Output isn't correct
17 Halted 0 ms 0 KB -

Subtask #3
0 / 27.0

# Verdict Execution time Memory Grader output
1 Incorrect 5 ms 604 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 79 ms 6400 KB Output is correct
2 Correct 78 ms 6228 KB Output is correct
3 Correct 78 ms 6276 KB Output is correct
4 Correct 79 ms 6272 KB Output is correct
5 Correct 80 ms 6224 KB Output is correct
6 Correct 78 ms 6276 KB Output is correct
7 Correct 78 ms 6228 KB Output is correct
8 Correct 79 ms 6276 KB Output is correct
9 Correct 78 ms 6276 KB Output is correct
10 Correct 81 ms 6228 KB Output is correct
11 Correct 80 ms 6276 KB Output is correct
12 Correct 78 ms 6288 KB Output is correct
13 Correct 78 ms 6228 KB Output is correct
14 Correct 79 ms 6292 KB Output is correct
15 Correct 79 ms 6292 KB Output is correct
16 Incorrect 16 ms 1612 KB Output isn't correct
17 Halted 0 ms 0 KB -