oj.uz

Submission #801987

# Submission time Handle Problem Language Result Execution time Memory
801987 2023-08-02T08:55:55 Z peijar Boat (APIO16_boat) C++17
100 / 100
 1037 ms 1504 KB 
#include <bits/stdc++.h>
#define int long long
using namespace std;

string to_string(string s) { return s; }
template <typename T> string to_string(T v) {
  bool first = true;
  string res = "[";
  for (const auto &x : v) {
    if (!first)
      res += ", ";
    first = false;
    res += to_string(x);
  }
  res += "]";
  return res;
}

void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
  cout << ' ' << to_string(H);
  dbg_out(T...);
}

#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif

template <const int32_t MOD> struct ModInt {
  int32_t x;
  ModInt() : x(0) {}
  ModInt(long long u) : x(u % MOD) {
    if (x < 0)
      x += MOD;
  }
  friend bool operator==(const ModInt &a, const ModInt &b) {
    return a.x == b.x;
  }
  friend bool operator!=(const ModInt &a, const ModInt &b) {
    return a.x != b.x;
  }
  friend bool operator<(const ModInt &a, const ModInt &b) { return a.x < b.x; }
  friend bool operator>(const ModInt &a, const ModInt &b) { return a.x > b.x; }
  friend bool operator<=(const ModInt &a, const ModInt &b) {
    return a.x <= b.x;
  }
  friend bool operator>=(const ModInt &a, const ModInt &b) {
    return a.x >= b.x;
  }
  static ModInt sign(long long k) {
    return ((k & 1) ? ModInt(MOD - 1) : ModInt(1));
  }

  ModInt &operator+=(const ModInt &m) {
    x += m.x;
    if (x >= MOD)
      x -= MOD;
    return *this;
  }
  ModInt &operator-=(const ModInt &m) {
    x -= m.x;
    if (x < 0LL)
      x += MOD;
    return *this;
  }
  ModInt &operator*=(const ModInt &m) {
    x = (1LL * x * m.x) % MOD;
    return *this;
  }

  friend ModInt operator-(const ModInt &a) {
    ModInt res(a);
    if (res.x)
      res.x = MOD - res.x;
    return res;
  }
  friend ModInt operator+(const ModInt &a, const ModInt &b) {
    return ModInt(a) += ModInt(b);
  }
  friend ModInt operator-(const ModInt &a, const ModInt &b) {
    return ModInt(a) -= ModInt(b);
  }
  friend ModInt operator*(const ModInt &a, const ModInt &b) {
    return ModInt(a) *= ModInt(b);
  }

  static long long fp(long long u, long long k) {
    long long res = 1LL;
    while (k > 0LL) {
      if (k & 1LL)
        res = (res * u) % MOD;
      u = (u * u) % MOD;
      k /= 2LL;
    }
    return res;
  }

  static constexpr int mod() { return MOD; }

  ModInt fastpow(long long k) { return ModInt(fp(x, k)); }
  ModInt inv() {
    assert(x);
    return ModInt(fp(x, MOD - 2));
  }
  ModInt &operator/=(const ModInt &m) { return *this *= ModInt(m).inv(); }
  friend ModInt operator/(const ModInt &a, const ModInt &b) {
    return ModInt(a) *= ModInt(b).inv();
  }

  friend ostream &operator<<(ostream &out, const ModInt &a) {
    return out << a.x;
  }
  friend istream &operator>>(istream &in, ModInt &a) { return in >> a.x; }
  friend string to_string(ModInt u) { return to_string(u.x); }
};

const int MOD = 1e9 + 7;
using Mint = ModInt<MOD>;

const int MAXN = 1e5;
Mint fact[MAXN], invFact[MAXN];

void initFact() {
  fact[0] = 1;
  for (int i = 1; i < MAXN; ++i)
    fact[i] = i * fact[i - 1];
  invFact[MAXN - 1] = fact[MAXN - 1].inv();
  for (int i = MAXN - 1; i; --i)
    invFact[i - 1] = invFact[i] * i;
}

map<pair<int, int>, Mint> cache;

Mint binom(int n, int k) {
  if (k < 0 or k > n)
    return 0;
  if (n < MAXN)
    return fact[n] * invFact[k] * invFact[n - k];

  Mint ret = 1;
  for (int i = n; i > n - k; --i)
    ret *= i;
  ret *= invFact[k];
  return ret;
}

signed main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);

  initFact();

  int nbEcoles;
  cin >> nbEcoles;

  map<int, vector<int>> events;

  vector<array<Mint, 2>> precalc(nbEcoles);

  for (int iEcole = 0; iEcole < nbEcoles; ++iEcole) {
    int lo, up;
    cin >> lo >> up;
    events[lo - 1].push_back(-1);
    events[lo].push_back(iEcole);
    events[up].push_back(-1);
    events[1 + up].push_back(iEcole);
  }
  vector<Mint> dp(nbEcoles);
  vector<Mint> prefDp(nbEcoles + 1);
  set<int> on;
  int prev = 0;
  for (auto [timeStamp, toUpdate] : events) {
    for (int x : toUpdate) {
      if (x == -1)
        continue;
      if (on.count(x))
        on.erase(x);
      else
        on.insert(x);
    }
    int lo = prev + 1, up = timeStamp;
    if (lo > up)
      continue;
    vector<Mint> revProd(nbEcoles + 1);
    int szInt = up - lo + 1;
    revProd[0] = 1;
    for (int i = 0; i < nbEcoles; ++i)
      revProd[i + 1] = revProd[i] * (szInt - i);
    auto calc = [&](int szInt, int cntMiddle, bool midDiff) {
      Mint ret = 0;
      for (int takeMiddle = 0; takeMiddle <= cntMiddle; ++takeMiddle)
        if (szInt >= takeMiddle + 1 + midDiff)
          ret += revProd[takeMiddle + 1 + midDiff] *
                 invFact[takeMiddle + 1 + midDiff] *
                 binom(cntMiddle, takeMiddle);
      precalc[cntMiddle][midDiff] = ret;
    };

    for (int cntMiddle = 0; cntMiddle < (int)on.size(); ++cntMiddle)
      for (int midDiff : {0, 1})
        calc(szInt, cntMiddle, midDiff);
    vector<int> vec(on.begin(), on.end());
    vector<Mint> nxtDp(on.size());
    for (int fst = 0; fst < (int)on.size(); ++fst)
      for (int lst = fst; lst < (int)on.size(); ++lst) {
        int middle = max(0LL, lst - fst - 1);
        Mint choixAvant = 1 + prefDp[vec[fst]];
        Mint choixMiddle = precalc[middle][fst != lst];
        nxtDp[lst] += choixMiddle * choixAvant;
      }
    for (int i = 0; i < (int)vec.size(); ++i)
      dp[vec[i]] += nxtDp[i];
    for (int i = 0; i < nbEcoles; ++i)
      prefDp[i + 1] = prefDp[i] + dp[i];
    dbg(lo, up, on, dp);
    prev = up;
  }
  cout << accumulate(dp.begin(), dp.end(), Mint(0)) << endl;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 1240 KB Output is correct
2 Correct 7 ms 1244 KB Output is correct
3 Correct 8 ms 1236 KB Output is correct
4 Correct 7 ms 1232 KB Output is correct
5 Correct 7 ms 1236 KB Output is correct
6 Correct 7 ms 1236 KB Output is correct
7 Correct 6 ms 1292 KB Output is correct
8 Correct 7 ms 1240 KB Output is correct
9 Correct 7 ms 1292 KB Output is correct
10 Correct 7 ms 1236 KB Output is correct
11 Correct 7 ms 1236 KB Output is correct
12 Correct 6 ms 1236 KB Output is correct
13 Correct 7 ms 1240 KB Output is correct
14 Correct 7 ms 1236 KB Output is correct
15 Correct 7 ms 1248 KB Output is correct
16 Correct 3 ms 1108 KB Output is correct
17 Correct 4 ms 1104 KB Output is correct
18 Correct 3 ms 1120 KB Output is correct
19 Correct 3 ms 1108 KB Output is correct
20 Correct 4 ms 1112 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 1240 KB Output is correct
2 Correct 7 ms 1244 KB Output is correct
3 Correct 8 ms 1236 KB Output is correct
4 Correct 7 ms 1232 KB Output is correct
5 Correct 7 ms 1236 KB Output is correct
6 Correct 7 ms 1236 KB Output is correct
7 Correct 6 ms 1292 KB Output is correct
8 Correct 7 ms 1240 KB Output is correct
9 Correct 7 ms 1292 KB Output is correct
10 Correct 7 ms 1236 KB Output is correct
11 Correct 7 ms 1236 KB Output is correct
12 Correct 6 ms 1236 KB Output is correct
13 Correct 7 ms 1240 KB Output is correct
14 Correct 7 ms 1236 KB Output is correct
15 Correct 7 ms 1248 KB Output is correct
16 Correct 3 ms 1108 KB Output is correct
17 Correct 4 ms 1104 KB Output is correct
18 Correct 3 ms 1120 KB Output is correct
19 Correct 3 ms 1108 KB Output is correct
20 Correct 4 ms 1112 KB Output is correct
21 Correct 209 ms 1340 KB Output is correct
22 Correct 190 ms 1340 KB Output is correct
23 Correct 153 ms 1336 KB Output is correct
24 Correct 181 ms 1340 KB Output is correct
25 Correct 178 ms 1336 KB Output is correct
26 Correct 353 ms 1340 KB Output is correct
27 Correct 364 ms 1468 KB Output is correct
28 Correct 348 ms 1344 KB Output is correct
29 Correct 358 ms 1344 KB Output is correct
30 Correct 8 ms 1236 KB Output is correct
31 Correct 8 ms 1236 KB Output is correct
32 Correct 8 ms 1236 KB Output is correct
33 Correct 8 ms 1240 KB Output is correct
34 Correct 8 ms 1344 KB Output is correct
35 Correct 7 ms 1236 KB Output is correct
36 Correct 7 ms 1292 KB Output is correct
37 Correct 7 ms 1240 KB Output is correct
38 Correct 7 ms 1236 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 1104 KB Output is correct
2 Correct 5 ms 1108 KB Output is correct
3 Correct 6 ms 1108 KB Output is correct
4 Correct 7 ms 1160 KB Output is correct
5 Correct 7 ms 1160 KB Output is correct
6 Correct 11 ms 1108 KB Output is correct
7 Correct 15 ms 1108 KB Output is correct
8 Correct 11 ms 1108 KB Output is correct
9 Correct 11 ms 1108 KB Output is correct
10 Correct 11 ms 1108 KB Output is correct
11 Correct 6 ms 1108 KB Output is correct
12 Correct 6 ms 1108 KB Output is correct
13 Correct 6 ms 1112 KB Output is correct
14 Correct 6 ms 1156 KB Output is correct
15 Correct 6 ms 1108 KB Output is correct
16 Correct 4 ms 1144 KB Output is correct
17 Correct 4 ms 1108 KB Output is correct
18 Correct 4 ms 1108 KB Output is correct
19 Correct 4 ms 1108 KB Output is correct
20 Correct 4 ms 1108 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 1240 KB Output is correct
2 Correct 7 ms 1244 KB Output is correct
3 Correct 8 ms 1236 KB Output is correct
4 Correct 7 ms 1232 KB Output is correct
5 Correct 7 ms 1236 KB Output is correct
6 Correct 7 ms 1236 KB Output is correct
7 Correct 6 ms 1292 KB Output is correct
8 Correct 7 ms 1240 KB Output is correct
9 Correct 7 ms 1292 KB Output is correct
10 Correct 7 ms 1236 KB Output is correct
11 Correct 7 ms 1236 KB Output is correct
12 Correct 6 ms 1236 KB Output is correct
13 Correct 7 ms 1240 KB Output is correct
14 Correct 7 ms 1236 KB Output is correct
15 Correct 7 ms 1248 KB Output is correct
16 Correct 3 ms 1108 KB Output is correct
17 Correct 4 ms 1104 KB Output is correct
18 Correct 3 ms 1120 KB Output is correct
19 Correct 3 ms 1108 KB Output is correct
20 Correct 4 ms 1112 KB Output is correct
21 Correct 209 ms 1340 KB Output is correct
22 Correct 190 ms 1340 KB Output is correct
23 Correct 153 ms 1336 KB Output is correct
24 Correct 181 ms 1340 KB Output is correct
25 Correct 178 ms 1336 KB Output is correct
26 Correct 353 ms 1340 KB Output is correct
27 Correct 364 ms 1468 KB Output is correct
28 Correct 348 ms 1344 KB Output is correct
29 Correct 358 ms 1344 KB Output is correct
30 Correct 8 ms 1236 KB Output is correct
31 Correct 8 ms 1236 KB Output is correct
32 Correct 8 ms 1236 KB Output is correct
33 Correct 8 ms 1240 KB Output is correct
34 Correct 8 ms 1344 KB Output is correct
35 Correct 7 ms 1236 KB Output is correct
36 Correct 7 ms 1292 KB Output is correct
37 Correct 7 ms 1240 KB Output is correct
38 Correct 7 ms 1236 KB Output is correct
39 Correct 6 ms 1104 KB Output is correct
40 Correct 5 ms 1108 KB Output is correct
41 Correct 6 ms 1108 KB Output is correct
42 Correct 7 ms 1160 KB Output is correct
43 Correct 7 ms 1160 KB Output is correct
44 Correct 11 ms 1108 KB Output is correct
45 Correct 15 ms 1108 KB Output is correct
46 Correct 11 ms 1108 KB Output is correct
47 Correct 11 ms 1108 KB Output is correct
48 Correct 11 ms 1108 KB Output is correct
49 Correct 6 ms 1108 KB Output is correct
50 Correct 6 ms 1108 KB Output is correct
51 Correct 6 ms 1112 KB Output is correct
52 Correct 6 ms 1156 KB Output is correct
53 Correct 6 ms 1108 KB Output is correct
54 Correct 4 ms 1144 KB Output is correct
55 Correct 4 ms 1108 KB Output is correct
56 Correct 4 ms 1108 KB Output is correct
57 Correct 4 ms 1108 KB Output is correct
58 Correct 4 ms 1108 KB Output is correct
59 Correct 445 ms 1376 KB Output is correct
60 Correct 396 ms 1376 KB Output is correct
61 Correct 388 ms 1372 KB Output is correct
62 Correct 453 ms 1372 KB Output is correct
63 Correct 468 ms 1372 KB Output is correct
64 Correct 1024 ms 1504 KB Output is correct
65 Correct 1031 ms 1400 KB Output is correct
66 Correct 1037 ms 1484 KB Output is correct
67 Correct 1037 ms 1484 KB Output is correct
68 Correct 1020 ms 1392 KB Output is correct
69 Correct 373 ms 1364 KB Output is correct
70 Correct 397 ms 1380 KB Output is correct
71 Correct 397 ms 1372 KB Output is correct
72 Correct 411 ms 1484 KB Output is correct
73 Correct 411 ms 1372 KB Output is correct
74 Correct 56 ms 1360 KB Output is correct
75 Correct 51 ms 1228 KB Output is correct
76 Correct 54 ms 1220 KB Output is correct
77 Correct 55 ms 1208 KB Output is correct
78 Correct 57 ms 1220 KB Output is correct