Submission #408646

#	Time	Username	Problem	Language	Result	Execution time	Memory
408646		tranxuanbach	Boat (APIO16_boat)	C++17	100 / 100	1061 ms	7368 KiB

boat

#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 / 9
• Subtask 2: 22 / 22
• Subtask 3: 27 / 27
• Subtask 4: 42 / 42