Submission #408646

#TimeUsernameProblemLanguageResultExecution timeMemory
408646tranxuanbachBoat (APIO16_boat)C++17
100 / 100
1061 ms7368 KiB
#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: | --------------------------------------------------| --------------------------------------------------| ==================================================+ */
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