結果
問題 | No.1706 Many Bus Stops (hard) |
ユーザー |
![]() |
提出日時 | 2021-10-08 23:02:18 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 3 ms / 2,000 ms |
コード長 | 14,005 bytes |
コンパイル時間 | 2,762 ms |
コンパイル使用メモリ | 202,260 KB |
最終ジャッジ日時 | 2025-01-24 23:11:57 |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 41 |
ソースコード
#define LOCAL#include <bits/stdc++.h>using namespace std;#pragma region Macrostypedef long long ll;typedef __int128_t i128;typedef unsigned int uint;typedef unsigned long long ull;#define ALL(x) (x).begin(), (x).end()template <typename T> istream& operator>>(istream& is, vector<T>& v) {for (T& x : v) is >> x;return is;}template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {for (int i = 0; i < (int)v.size(); i++) {os << v[i] << (i + 1 == (int)v.size() ? "" : " ");}return os;}template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {os << '(' << p.first << ',' << p.second << ')';return os;}template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {os << '{';for (auto itr = m.begin(); itr != m.end();) {os << '(' << itr->first << ',' << itr->second << ')';if (++itr != m.end()) os << ',';}os << '}';return os;}template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {os << '{';for (auto itr = m.begin(); itr != m.end();) {os << '(' << itr->first << ',' << itr->second << ')';if (++itr != m.end()) os << ',';}os << '}';return os;}template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {os << '{';for (auto itr = s.begin(); itr != s.end();) {os << *itr;if (++itr != s.end()) os << ',';}os << '}';return os;}template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {os << '{';for (auto itr = s.begin(); itr != s.end();) {os << *itr;if (++itr != s.end()) os << ',';}os << '}';return os;}template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {os << '{';for (auto itr = s.begin(); itr != s.end();) {os << *itr;if (++itr != s.end()) os << ',';}os << '}';return os;}template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {for (int i = 0; i < (int)v.size(); i++) {os << v[i] << (i + 1 == (int)v.size() ? "" : " ");}return os;}template <int i, typename T> void print_tuple(ostream&, const T&) {}template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {if (i) os << ',';os << get<i>(t);print_tuple<i + 1, T, Args...>(os, t);}template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {os << '{';print_tuple<0, tuple<Args...>, Args...>(os, t);return os << '}';}void debug_out() { cerr << '\n'; }template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {cerr << head;if (sizeof...(Tail) > 0) cerr << ", ";debug_out(move(tail)...);}#ifdef LOCAL#define debug(...) \cerr << " "; \cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \cerr << " "; \debug_out(__VA_ARGS__)#else#define debug(...) 42#endiftemplate <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }int popcount(signed t) { return __builtin_popcount(t); }int popcount(long long t) { return __builtin_popcountll(t); }bool ispow2(int i) { return i && (i & -i) == i; }template <class T> T ceil(T x, T y) {assert(y >= 1);return (x > 0 ? (x + y - 1) / y : x / y);}template <class T> T floor(T x, T y) {assert(y >= 1);return (x > 0 ? x / y : (x - y + 1) / y);}template <class T1, class T2> inline bool chmin(T1& a, T2 b) {if (a > b) {a = b;return true;}return false;}template <class T1, class T2> inline bool chmax(T1& a, T2 b) {if (a < b) {a = b;return true;}return false;}#pragma endregion#include <cassert>#include <cstdint>#include <iostream>template <uint64_t Modulus> class modint {using i64 = int64_t;using u32 = uint32_t;using u64 = uint64_t;static_assert(Modulus < static_cast<uint32_t>(1) << 31, "Modulus must be less than 2**31");static constexpr u32 mod = Modulus;u32 v;public:constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}constexpr u32& val() noexcept { return v; }constexpr const u32& val() const noexcept { return v; }constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }constexpr modint& operator+=(const modint& rhs) noexcept {v += rhs.v;if (v >= mod) v -= mod;return *this;}constexpr modint& operator-=(const modint& rhs) noexcept {if (v < rhs.v) v += mod;v -= rhs.v;return *this;}constexpr modint& operator*=(const modint& rhs) noexcept {v = (u64)v * rhs.v % mod;return *this;}constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.inv(); }constexpr modint pow(long long n) const noexcept {assert(0 <= n);modint self(*this), res(1);while (n > 0) {if (n & 1) res *= self;self *= self;n >>= 1;}return res;}constexpr modint inv() const noexcept {assert(*this != 0);return pow(mod - 2);}constexpr modint& operator++() noexcept {if (++v == mod) v = 0;return *this;}constexpr modint& operator--() noexcept {if (v == 0) v = mod;return --v, *this;}constexpr modint operator++(int) noexcept {modint t = *this;return ++*this, t;}constexpr modint operator--(int) noexcept {modint t = *this;return --*this, t;}constexpr modint operator-() const noexcept { return modint(mod - v); }template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }constexpr bool operator!() const noexcept { return !v; }friend std::istream& operator>>(std::istream& s, modint& rhs) noexcept {i64 v;rhs = modint{(s >> v, v)};return s;}friend std::ostream& operator<<(std::ostream& s, const modint& rhs) noexcept { return s << rhs.v; }};/*** @brief modint* @docs docs/modulo/modint.md*/#include <cassert>#include <iostream>#include <vector>template <typename T> struct Matrix {std::vector<std::vector<T>> A;Matrix(size_t n, size_t m) : A(n, std::vector<T>(m, 0)) {}Matrix(size_t n) : A(n, std::vector<T>(n, 0)) {}size_t size() const { return A.size(); }size_t height() const { return A.size(); }size_t width() const { return A[0].size(); }inline const std::vector<T>& operator[](int k) const { return A[k]; }inline std::vector<T>& operator[](int k) { return A[k]; }static Matrix I(size_t n) {Matrix res(n);for (size_t i = 0; i < n; i++) res[i][i] = 1;return res;}Matrix& operator+=(const Matrix& B) {size_t n = height(), m = width();assert(n == B.height() && m == B.width());for (size_t i = 0; i < n; i++) {for (size_t j = 0; j < m; j++) {(*this)[i][j] += B[i][j];}}return *this;}Matrix& operator-=(const Matrix& B) {size_t n = height(), m = width();assert(n == B.height() && m == B.width());for (size_t i = 0; i < n; i++) {for (size_t j = 0; j < m; j++) {(*this)[i][j] -= B[i][j];}}return *this;}Matrix& operator*=(const Matrix& B) {size_t n = height(), m = B.width(), p = width();assert(p == B.height());std::vector<std::vector<T>> C(n, std::vector<T>(m, 0));for (size_t i = 0; i < n; i++) {for (size_t k = 0; k < p; k++) {for (size_t j = 0; j < m; j++) {C[i][j] += (*this)[i][k] * B[k][j];}}}A.swap(C);return *this;}Matrix& operator*=(const T& v) {for (size_t i = 0; i < height(); i++) {for (size_t j = 0; j < width(); j++) {(*this)[i][j] *= v;}}return *this;}Matrix& operator/=(const T& v) {T inv = T(1) / v;for (size_t i = 0; i < height(); i++) {for (size_t j = 0; j < width(); j++) {(*this)[i][j] *= inv;}}return *this;}Matrix& operator^=(long long k) {assert(0 <= k);Matrix B = Matrix::I(size());while (k > 0) {if (k & 1) B *= *this;*this *= *this;k >>= 1;}A.swap(B.A);return *this;}Matrix operator-() const {Matrix res(height(), width());for (size_t i = 0; i < height(); i++) {for (size_t j = 0; j < width(); j++) {res[i][j] = -(*this)[i][j];}}return res;}Matrix operator+(const Matrix& B) const { return Matrix(*this) += B; }Matrix operator-(const Matrix& B) const { return Matrix(*this) -= B; }Matrix operator*(const Matrix& B) const { return Matrix(*this) *= B; }Matrix operator*(const T& v) const { return Matrix(*this) *= v; }Matrix operator/(const T& v) const { return Matrix(*this) /= v; }Matrix operator^(const long long k) const { return Matrix(*this) ^= k; }bool operator==(const Matrix& B) const {assert(height() == B.height() && width() == B.width());return A == B.A;}bool operator!=(const Matrix& B) const {assert(height() == B.height() && width() == B.width());return A != B.A;}Matrix transpose() const {Matrix res(width(), height());for (size_t i = 0; i < height(); i++) {for (size_t j = 0; j < width(); j++) {res[j][i] = (*this)[i][j];}}return res;}T determinant() const {assert(height() == width());Matrix B(*this);T res = 1;for (size_t i = 0; i < height(); i++) {int pivot = -1;for (size_t j = i; j < height(); j++) {if (B[j][i] != 0) {pivot = j;break;}}if (pivot == -1) return 0;if (pivot != (int)i) {res *= -1;std::swap(B[i], B[pivot]);}res *= B[i][i];T inv = T(1) / B[i][i];for (size_t j = 0; j < width(); j++) B[i][j] *= inv;for (size_t j = i + 1; j < height(); j++) {T a = B[j][i];for (size_t k = 0; k < width(); k++) {B[j][k] -= B[i][k] * a;}}}return res;}friend std::ostream& operator<<(std::ostream& os, const Matrix& p) {size_t n = p.height(), m = p.width();os << "[(" << n << " * " << m << " Matrix)";os << "\n[columun sums: ";for (size_t j = 0; j < m; j++) {T sum = 0;for (size_t i = 0; i < n; i++) sum += p[i][j];;os << sum << (j + 1 < m ? "," : "");}os << "]";for (size_t i = 0; i < n; i++) {os << "\n[";for (size_t j = 0; j < m; j++) os << p[i][j] << (j + 1 < m ? "," : "");os << "]";}os << "]\n";return os;}};/*** @brief 行列ライブラリ* @docs docs/linearalgebra/Matrix.md*/const int INF = 1e9;const long long IINF = 1e18;const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};const char dir[4] = {'D', 'R', 'U', 'L'};const long long MOD = 1000000007;// const long long MOD = 998244353;using mint = modint<MOD>;int main() {cin.tie(0);ios::sync_with_stdio(false);int C, N, M;cin >> C >> N >> M;Matrix<mint> M1(6), M2(6);mint invC = mint(1) / C;M1[0][0] = invC;M1[0][5] = 1;M1[1][0] = invC * (C - 1);M1[2][1] = 1;M1[3][2] = 1;M1[3][3] = invC;M1[3][5] = C - 2;M1[4][3] = invC;M1[5][4] = 1;M2[0][0] = 1;M2[0][5] = 1;M2[2][1] = 1;M2[3][2] = 1;M2[3][3] = 1;M2[3][5] = C - 2;M2[5][4] = 1;Matrix<mint> M3 = M2 * M1;M3 ^= N;mint prob = M3[0][0];mint ans = 1 - (1 - prob).pow(M);cout << ans << '\n';return 0;}