oj.uz

Submission #969449

# Submission time Handle Problem Language Result Execution time Memory
969449 2024-04-25T07:32:41 Z kilkuwu Boat (APIO16_boat) C++17
100 / 100
 1363 ms 8656 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>;

template <typename M>
struct Comb {
  std::vector<M> _fact, _finv;

  Comb() : _fact(1, 1), _finv(1, 1) {}

  inline int size() const { return static_cast<int>(_fact.size()); }

  void _double_extend() {
    int old_size = size();
    int new_size = std::min(M::mod(), size() * 2);

    _fact.resize(new_size);
    _finv.resize(new_size);

    for (int i = old_size; i < new_size; i++) {
      _fact[i] = _fact[i - 1] * i;
    }
    
    _finv[new_size - 1] = _fact[new_size - 1].inv();
    for (int i = new_size - 2; i >= old_size; i--) {
      _finv[i] = _finv[i + 1] * (i + 1);
    }
  }

  /**
   * Calculate ***n** choose **k***.
  */
  M operator()(int n, int k) {
    if (k > n || k < 0) return M();
    while (size() <= n) {
      _double_extend();
    }
    return _fact[n] * _finv[n - k] * _finv[k];
  }

  M lucas(int64_t n, int64_t k) {
    if (k > n) return 0;
    if (n < md) return this->operator()(n, k);
    return lucas(n / md, k / md) * this->operator()(n % md, k % md);
  }
};

Comb<Mint> C;
 
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());
  dbg(vals);
 
  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();
    dbg(a[i], b[i]);
  }
 
  std::vector<std::vector<Mint>> choose(num_segments, std::vector<Mint>(n + 1));
  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];
    choose[i][0] = 1;
    for (int j = 0; j < n; j++) {
      choose[i][j + 1] = choose[i][j] * (len - j) / (j + 1);
    }
    for (int cnt = 1; cnt <= n; cnt++) {
      prepared[i][cnt] = 0;
      for (int j = 0; j < cnt; j++) {
        prepared[i][cnt] += C(cnt - 1, j) * choose[i][j + 1];
      }
    }
  }

  
 
 
  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];
          Mint mul = prepared[j][cnt];
          dbg(i, j, k, cnt, mul, ff[k + 1][j + 1], mul * ff[k + 1][j + 1]);
          dp[i][j] += ff[k + 1][j + 1] * mul;
        }
      }
      ans += dp[i][j];
      dbg(i, j, dp[i][j]);
      ff[i][j] = ff[i][j + 1] + dp[i][j];
    }
  }
 
  std::cout << ans << nl;
  // 4 
  // 4 7 
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1036 ms 8276 KB Output is correct
2 Correct 1074 ms 8272 KB Output is correct
3 Correct 1065 ms 8276 KB Output is correct
4 Correct 1052 ms 8272 KB Output is correct
5 Correct 1035 ms 8276 KB Output is correct
6 Correct 1034 ms 8272 KB Output is correct
7 Correct 1029 ms 8272 KB Output is correct
8 Correct 1031 ms 8272 KB Output is correct
9 Correct 1043 ms 8280 KB Output is correct
10 Correct 1039 ms 8272 KB Output is correct
11 Correct 1067 ms 8272 KB Output is correct
12 Correct 1045 ms 8272 KB Output is correct
13 Correct 1072 ms 8276 KB Output is correct
14 Correct 1060 ms 8296 KB Output is correct
15 Correct 1054 ms 8272 KB Output is correct
16 Correct 181 ms 1876 KB Output is correct
17 Correct 207 ms 1964 KB Output is correct
18 Correct 187 ms 2128 KB Output is correct
19 Correct 206 ms 1724 KB Output is correct
20 Correct 199 ms 1692 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1036 ms 8276 KB Output is correct
2 Correct 1074 ms 8272 KB Output is correct
3 Correct 1065 ms 8276 KB Output is correct
4 Correct 1052 ms 8272 KB Output is correct
5 Correct 1035 ms 8276 KB Output is correct
6 Correct 1034 ms 8272 KB Output is correct
7 Correct 1029 ms 8272 KB Output is correct
8 Correct 1031 ms 8272 KB Output is correct
9 Correct 1043 ms 8280 KB Output is correct
10 Correct 1039 ms 8272 KB Output is correct
11 Correct 1067 ms 8272 KB Output is correct
12 Correct 1045 ms 8272 KB Output is correct
13 Correct 1072 ms 8276 KB Output is correct
14 Correct 1060 ms 8296 KB Output is correct
15 Correct 1054 ms 8272 KB Output is correct
16 Correct 181 ms 1876 KB Output is correct
17 Correct 207 ms 1964 KB Output is correct
18 Correct 187 ms 2128 KB Output is correct
19 Correct 206 ms 1724 KB Output is correct
20 Correct 199 ms 1692 KB Output is correct
21 Correct 1074 ms 7700 KB Output is correct
22 Correct 1115 ms 7808 KB Output is correct
23 Correct 1101 ms 7916 KB Output is correct
24 Correct 1061 ms 7508 KB Output is correct
25 Correct 1089 ms 7760 KB Output is correct
26 Correct 1129 ms 7456 KB Output is correct
27 Correct 1117 ms 7560 KB Output is correct
28 Correct 1116 ms 7508 KB Output is correct
29 Correct 1118 ms 7428 KB Output is correct
30 Correct 1057 ms 8532 KB Output is correct
31 Correct 1055 ms 8280 KB Output is correct
32 Correct 1046 ms 8532 KB Output is correct
33 Correct 1057 ms 8280 KB Output is correct
34 Correct 1069 ms 8268 KB Output is correct
35 Correct 1027 ms 8532 KB Output is correct
36 Correct 1053 ms 8276 KB Output is correct
37 Correct 1051 ms 8276 KB Output is correct
38 Correct 1060 ms 8268 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 600 KB Output is correct
2 Correct 13 ms 800 KB Output is correct
3 Correct 13 ms 604 KB Output is correct
4 Correct 14 ms 604 KB Output is correct
5 Correct 13 ms 604 KB Output is correct
6 Correct 14 ms 604 KB Output is correct
7 Correct 13 ms 632 KB Output is correct
8 Correct 13 ms 604 KB Output is correct
9 Correct 13 ms 632 KB Output is correct
10 Correct 13 ms 604 KB Output is correct
11 Correct 13 ms 636 KB Output is correct
12 Correct 13 ms 604 KB Output is correct
13 Correct 13 ms 604 KB Output is correct
14 Correct 13 ms 604 KB Output is correct
15 Correct 14 ms 604 KB Output is correct
16 Correct 9 ms 660 KB Output is correct
17 Correct 7 ms 600 KB Output is correct
18 Correct 7 ms 600 KB Output is correct
19 Correct 7 ms 604 KB Output is correct
20 Correct 7 ms 552 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1036 ms 8276 KB Output is correct
2 Correct 1074 ms 8272 KB Output is correct
3 Correct 1065 ms 8276 KB Output is correct
4 Correct 1052 ms 8272 KB Output is correct
5 Correct 1035 ms 8276 KB Output is correct
6 Correct 1034 ms 8272 KB Output is correct
7 Correct 1029 ms 8272 KB Output is correct
8 Correct 1031 ms 8272 KB Output is correct
9 Correct 1043 ms 8280 KB Output is correct
10 Correct 1039 ms 8272 KB Output is correct
11 Correct 1067 ms 8272 KB Output is correct
12 Correct 1045 ms 8272 KB Output is correct
13 Correct 1072 ms 8276 KB Output is correct
14 Correct 1060 ms 8296 KB Output is correct
15 Correct 1054 ms 8272 KB Output is correct
16 Correct 181 ms 1876 KB Output is correct
17 Correct 207 ms 1964 KB Output is correct
18 Correct 187 ms 2128 KB Output is correct
19 Correct 206 ms 1724 KB Output is correct
20 Correct 199 ms 1692 KB Output is correct
21 Correct 1074 ms 7700 KB Output is correct
22 Correct 1115 ms 7808 KB Output is correct
23 Correct 1101 ms 7916 KB Output is correct
24 Correct 1061 ms 7508 KB Output is correct
25 Correct 1089 ms 7760 KB Output is correct
26 Correct 1129 ms 7456 KB Output is correct
27 Correct 1117 ms 7560 KB Output is correct
28 Correct 1116 ms 7508 KB Output is correct
29 Correct 1118 ms 7428 KB Output is correct
30 Correct 1057 ms 8532 KB Output is correct
31 Correct 1055 ms 8280 KB Output is correct
32 Correct 1046 ms 8532 KB Output is correct
33 Correct 1057 ms 8280 KB Output is correct
34 Correct 1069 ms 8268 KB Output is correct
35 Correct 1027 ms 8532 KB Output is correct
36 Correct 1053 ms 8276 KB Output is correct
37 Correct 1051 ms 8276 KB Output is correct
38 Correct 1060 ms 8268 KB Output is correct
39 Correct 16 ms 600 KB Output is correct
40 Correct 13 ms 800 KB Output is correct
41 Correct 13 ms 604 KB Output is correct
42 Correct 14 ms 604 KB Output is correct
43 Correct 13 ms 604 KB Output is correct
44 Correct 14 ms 604 KB Output is correct
45 Correct 13 ms 632 KB Output is correct
46 Correct 13 ms 604 KB Output is correct
47 Correct 13 ms 632 KB Output is correct
48 Correct 13 ms 604 KB Output is correct
49 Correct 13 ms 636 KB Output is correct
50 Correct 13 ms 604 KB Output is correct
51 Correct 13 ms 604 KB Output is correct
52 Correct 13 ms 604 KB Output is correct
53 Correct 14 ms 604 KB Output is correct
54 Correct 9 ms 660 KB Output is correct
55 Correct 7 ms 600 KB Output is correct
56 Correct 7 ms 600 KB Output is correct
57 Correct 7 ms 604 KB Output is correct
58 Correct 7 ms 552 KB Output is correct
59 Correct 1194 ms 8528 KB Output is correct
60 Correct 1208 ms 8656 KB Output is correct
61 Correct 1198 ms 8288 KB Output is correct
62 Correct 1294 ms 8292 KB Output is correct
63 Correct 1202 ms 8412 KB Output is correct
64 Correct 1301 ms 8416 KB Output is correct
65 Correct 1336 ms 8288 KB Output is correct
66 Correct 1298 ms 8284 KB Output is correct
67 Correct 1363 ms 8288 KB Output is correct
68 Correct 1279 ms 8288 KB Output is correct
69 Correct 1206 ms 8284 KB Output is correct
70 Correct 1188 ms 8288 KB Output is correct
71 Correct 1208 ms 8288 KB Output is correct
72 Correct 1205 ms 8292 KB Output is correct
73 Correct 1217 ms 8308 KB Output is correct
74 Correct 212 ms 1924 KB Output is correct
75 Correct 229 ms 1712 KB Output is correct
76 Correct 228 ms 1876 KB Output is correct
77 Correct 241 ms 1692 KB Output is correct
78 Correct 221 ms 1944 KB Output is correct