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Submission #408646

# Submission time Handle Problem Language Result Execution time Memory
408646 2021-05-19T12:07:28 Z tranxuanbach Boat (APIO16_boat) C++17
100 / 100
 1061 ms 7368 KB 
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;

#define endl '\n'
#define fi first
#define se second
#define For(i, l, r) for (int i = l; i < r; i++)
#define ForE(i, l, r) for (int i = l; i <= r; i++)
#define FordE(i, l, r) for (int i = l; i >= r; i--)
#define Fora(v, a) for (auto v: a)
#define bend(a) a.begin(), a.end()
#define isz(a) ((signed)a.size())

typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef vector <int> vi;
typedef vector <pii> vpii;
typedef vector <vi> vvi;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) { Modular result(*this); *this += 1; return result; }
  Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename U>
  friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

 private:
  Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}


template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}

template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

/*
using ModType = int;

struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/

constexpr int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

const int N = 5e2 + 5, mod = 1e9 + 7;

int n;
pii a[N];

Mint invfac[N], C[N][N];

void init_C(){
    invfac[0] = 1;
    For(i, 1, N){
        invfac[i] = invfac[i - 1] / i;
    }
    C[0][0] = 1;
    For(i, 1, N){
        ForE(j, 0, i){
            C[i][j] = C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
        }
    }
}

int m;
vpii ranges;

void coordinate_compress(){
    vpii vcac;
    ForE(i, 1, n){
        vcac.emplace_back(a[i].fi, 0);
        vcac.emplace_back(a[i].se + 1, 0);
    }
    sort(bend(vcac));
    ForE(i, 1, n){
        For(j, 0, isz(vcac)){
            if (a[i].fi <= vcac[j].fi and vcac[j].fi <= a[i].se){
                vcac[j].se = 1;
            }
        }
    }
    ranges.emplace_back(-1, -1);
    For(j, 0, isz(vcac) - 1){
        if (vcac[j].se){
            ranges.emplace_back(vcac[j].fi, vcac[j + 1].fi - 1);
        }
    }
    ForE(i, 1, n){
        a[i].fi = lower_bound(bend(ranges), make_pair(a[i].fi, -1)) - ranges.begin();
        a[i].se = (--lower_bound(bend(ranges), make_pair(a[i].se + 1, -1))) - ranges.begin();
    }
    m = isz(ranges) - 1;
}

Mint Crange[2 * N][N];

void init_Crange(){
    ForE(i, 1, m){
        int len = ranges[i].se - ranges[i].fi + 1;
        Mint ans = 1;
        ForE(j, 0, n){
            if (j > len){
                Crange[i][j] = 0;
                continue;
            }
            Crange[i][j] = ans;
            ans /= j + 1; ans *= len - j;
        }
    }
}

Mint calchoose[N][2 * N];

void init_calchoose(){
    ForE(i, 1, n){
        ForE(j, 1, m){
            For(neg1, 0, i){
                calchoose[i][j] += C[i - 1][neg1] * Crange[j][i - neg1];
            }
        }
    }
}

Mint dp[N][2 * N];

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    // freopen("KEK.inp", "r", stdin);
    // freopen("KEK.out", "w", stdout);
    init_C();
    cin >> n;
    ForE(i, 1, n){
        cin >> a[i].fi >> a[i].se;
    }
    coordinate_compress();
    init_Crange();
    init_calchoose();
    ForE(i, 0, n){
        dp[i][0] = 1;
    }
    ForE(j, 1, m){
        dp[0][j] = 1;
    }
    ForE(i, 1, n){
        ForE(j, 1, m){
            dp[i][j] = dp[i][j - 1];
            int len = 0;
            FordE(ti, i, 1){
                if (a[ti].fi > j or a[ti].se < j){
                    continue;
                }
                len++;
                dp[i][j] += calchoose[len][j] * dp[ti - 1][j - 1];
            }
        }
    }
    cout << dp[n][m] - 1 << endl;
}

/*
Tim so day so A = (A_1, A_2, ..., A_n) thoa man dieu kien sau:
- A_i = -1 hoac a_i <= A_i <= b_i
- Neu i < j, A_i != -1 va A_j != -1 thi A_i < A_j.

nen so thanh n doan, sau do thi
dp[i][j] la so cach de chon i so dau va moi so <= j (sau khi nen).
dp[i][j] = dp[i][j - 1] + (so cach chon (i - i' + 1) so co gia tri = j hoac -1 sau khi nen, so dau phai bang j) * dp[i' - 1][j - 1]
so cach chon tren: goi len = i - i'.
so cach = \sum_{neg1 = 0}^{len} C(len, neg1) * C(range(j), len + 1 - neg1)
==================================================+
INPUT:                                            |
--------------------------------------------------|
2
1 2
2 3
--------------------------------------------------|
==================================================+
OUTPUT:                                           |
--------------------------------------------------|

--------------------------------------------------|
==================================================+
*/

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 251 ms 6176 KB Output is correct
2 Correct 247 ms 6468 KB Output is correct
3 Correct 248 ms 6268 KB Output is correct
4 Correct 250 ms 6156 KB Output is correct
5 Correct 247 ms 6340 KB Output is correct
6 Correct 217 ms 6248 KB Output is correct
7 Correct 214 ms 6212 KB Output is correct
8 Correct 221 ms 6180 KB Output is correct
9 Correct 219 ms 6268 KB Output is correct
10 Correct 217 ms 6268 KB Output is correct
11 Correct 215 ms 6340 KB Output is correct
12 Correct 217 ms 6192 KB Output is correct
13 Correct 216 ms 6212 KB Output is correct
14 Correct 216 ms 6280 KB Output is correct
15 Correct 218 ms 6340 KB Output is correct
16 Correct 266 ms 6244 KB Output is correct
17 Correct 251 ms 6284 KB Output is correct
18 Correct 257 ms 6284 KB Output is correct
19 Correct 252 ms 6268 KB Output is correct
20 Correct 252 ms 6228 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 251 ms 6176 KB Output is correct
2 Correct 247 ms 6468 KB Output is correct
3 Correct 248 ms 6268 KB Output is correct
4 Correct 250 ms 6156 KB Output is correct
5 Correct 247 ms 6340 KB Output is correct
6 Correct 217 ms 6248 KB Output is correct
7 Correct 214 ms 6212 KB Output is correct
8 Correct 221 ms 6180 KB Output is correct
9 Correct 219 ms 6268 KB Output is correct
10 Correct 217 ms 6268 KB Output is correct
11 Correct 215 ms 6340 KB Output is correct
12 Correct 217 ms 6192 KB Output is correct
13 Correct 216 ms 6212 KB Output is correct
14 Correct 216 ms 6280 KB Output is correct
15 Correct 218 ms 6340 KB Output is correct
16 Correct 266 ms 6244 KB Output is correct
17 Correct 251 ms 6284 KB Output is correct
18 Correct 257 ms 6284 KB Output is correct
19 Correct 252 ms 6268 KB Output is correct
20 Correct 252 ms 6228 KB Output is correct
21 Correct 749 ms 7316 KB Output is correct
22 Correct 723 ms 7312 KB Output is correct
23 Correct 697 ms 7268 KB Output is correct
24 Correct 710 ms 7352 KB Output is correct
25 Correct 732 ms 7264 KB Output is correct
26 Correct 714 ms 7336 KB Output is correct
27 Correct 708 ms 7264 KB Output is correct
28 Correct 719 ms 7368 KB Output is correct
29 Correct 727 ms 7216 KB Output is correct
30 Correct 549 ms 7336 KB Output is correct
31 Correct 540 ms 7160 KB Output is correct
32 Correct 552 ms 7272 KB Output is correct
33 Correct 540 ms 7364 KB Output is correct
34 Correct 553 ms 7268 KB Output is correct
35 Correct 606 ms 7268 KB Output is correct
36 Correct 589 ms 7364 KB Output is correct
37 Correct 618 ms 7332 KB Output is correct
38 Correct 631 ms 7280 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 2508 KB Output is correct
2 Correct 13 ms 2428 KB Output is correct
3 Correct 10 ms 2508 KB Output is correct
4 Correct 15 ms 2508 KB Output is correct
5 Correct 11 ms 2416 KB Output is correct
6 Correct 14 ms 2520 KB Output is correct
7 Correct 11 ms 2436 KB Output is correct
8 Correct 16 ms 2508 KB Output is correct
9 Correct 11 ms 2508 KB Output is correct
10 Correct 12 ms 2424 KB Output is correct
11 Correct 11 ms 2464 KB Output is correct
12 Correct 10 ms 2440 KB Output is correct
13 Correct 11 ms 2424 KB Output is correct
14 Correct 11 ms 2508 KB Output is correct
15 Correct 12 ms 2508 KB Output is correct
16 Correct 10 ms 2472 KB Output is correct
17 Correct 12 ms 2416 KB Output is correct
18 Correct 9 ms 2508 KB Output is correct
19 Correct 9 ms 2432 KB Output is correct
20 Correct 11 ms 2508 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 251 ms 6176 KB Output is correct
2 Correct 247 ms 6468 KB Output is correct
3 Correct 248 ms 6268 KB Output is correct
4 Correct 250 ms 6156 KB Output is correct
5 Correct 247 ms 6340 KB Output is correct
6 Correct 217 ms 6248 KB Output is correct
7 Correct 214 ms 6212 KB Output is correct
8 Correct 221 ms 6180 KB Output is correct
9 Correct 219 ms 6268 KB Output is correct
10 Correct 217 ms 6268 KB Output is correct
11 Correct 215 ms 6340 KB Output is correct
12 Correct 217 ms 6192 KB Output is correct
13 Correct 216 ms 6212 KB Output is correct
14 Correct 216 ms 6280 KB Output is correct
15 Correct 218 ms 6340 KB Output is correct
16 Correct 266 ms 6244 KB Output is correct
17 Correct 251 ms 6284 KB Output is correct
18 Correct 257 ms 6284 KB Output is correct
19 Correct 252 ms 6268 KB Output is correct
20 Correct 252 ms 6228 KB Output is correct
21 Correct 749 ms 7316 KB Output is correct
22 Correct 723 ms 7312 KB Output is correct
23 Correct 697 ms 7268 KB Output is correct
24 Correct 710 ms 7352 KB Output is correct
25 Correct 732 ms 7264 KB Output is correct
26 Correct 714 ms 7336 KB Output is correct
27 Correct 708 ms 7264 KB Output is correct
28 Correct 719 ms 7368 KB Output is correct
29 Correct 727 ms 7216 KB Output is correct
30 Correct 549 ms 7336 KB Output is correct
31 Correct 540 ms 7160 KB Output is correct
32 Correct 552 ms 7272 KB Output is correct
33 Correct 540 ms 7364 KB Output is correct
34 Correct 553 ms 7268 KB Output is correct
35 Correct 606 ms 7268 KB Output is correct
36 Correct 589 ms 7364 KB Output is correct
37 Correct 618 ms 7332 KB Output is correct
38 Correct 631 ms 7280 KB Output is correct
39 Correct 10 ms 2508 KB Output is correct
40 Correct 13 ms 2428 KB Output is correct
41 Correct 10 ms 2508 KB Output is correct
42 Correct 15 ms 2508 KB Output is correct
43 Correct 11 ms 2416 KB Output is correct
44 Correct 14 ms 2520 KB Output is correct
45 Correct 11 ms 2436 KB Output is correct
46 Correct 16 ms 2508 KB Output is correct
47 Correct 11 ms 2508 KB Output is correct
48 Correct 12 ms 2424 KB Output is correct
49 Correct 11 ms 2464 KB Output is correct
50 Correct 10 ms 2440 KB Output is correct
51 Correct 11 ms 2424 KB Output is correct
52 Correct 11 ms 2508 KB Output is correct
53 Correct 12 ms 2508 KB Output is correct
54 Correct 10 ms 2472 KB Output is correct
55 Correct 12 ms 2416 KB Output is correct
56 Correct 9 ms 2508 KB Output is correct
57 Correct 9 ms 2432 KB Output is correct
58 Correct 11 ms 2508 KB Output is correct
59 Correct 945 ms 7276 KB Output is correct
60 Correct 919 ms 7272 KB Output is correct
61 Correct 952 ms 7272 KB Output is correct
62 Correct 983 ms 7272 KB Output is correct
63 Correct 951 ms 7272 KB Output is correct
64 Correct 1043 ms 7236 KB Output is correct
65 Correct 1061 ms 7272 KB Output is correct
66 Correct 1033 ms 7304 KB Output is correct
67 Correct 980 ms 7268 KB Output is correct
68 Correct 1039 ms 7272 KB Output is correct
69 Correct 966 ms 7272 KB Output is correct
70 Correct 1016 ms 7256 KB Output is correct
71 Correct 916 ms 7272 KB Output is correct
72 Correct 994 ms 7244 KB Output is correct
73 Correct 949 ms 7268 KB Output is correct
74 Correct 677 ms 7272 KB Output is correct
75 Correct 703 ms 7232 KB Output is correct
76 Correct 679 ms 7256 KB Output is correct
77 Correct 675 ms 7256 KB Output is correct
78 Correct 658 ms 7148 KB Output is correct