結果
問題 | No.891 隣接3項間の漸化式 |
ユーザー |
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提出日時 | 2020-02-26 23:14:25 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 9,081 bytes |
コンパイル時間 | 2,025 ms |
コンパイル使用メモリ | 180,088 KB |
実行使用メモリ | 6,824 KB |
最終ジャッジ日時 | 2024-10-13 15:34:15 |
合計ジャッジ時間 | 3,129 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 31 WA * 8 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define FOR(i,a,b) for(int i=(a);i<(b);++i)#define REP(i,n) FOR(i,0,n)#define ALL(v) begin(v),end(v)#define fi first#define se secondtemplate<typename A, typename B> inline bool chmax(A &a, B b) { if (a<b) { a=b; return 1; } return 0; }template<typename A, typename B> inline bool chmin(A &a, B b) { if (a>b) { a=b; return 1; } return 0; }using ll = long long;using pii = pair<int, int>;constexpr ll INF = 1ll<<30;constexpr ll longINF = 1ll<<60;constexpr ll MOD = 1000000007;constexpr bool debug = 0;//---------------------------------//template<typename T>struct Matrix {public:using value_type = T;using size_type = std::size_t;Matrix() {}Matrix(size_type h, size_type w, const value_type & x = 0) : h(h), w(w), val(h, std::vector<value_type>(w, x)) {assert(h > 0 && w > 0);}Matrix(std::vector<std::vector<value_type>> val) : h(val.size()), w(val.size() ? val[0].size() : 0), val(val) {assert(h > 0 && w > 0);for (size_type i = 1; i < h; ++i) assert(val[i].size() == w);}Matrix(std::initializer_list<std::vector<value_type>> init) : val(init.begin(), init.end()) {h = val.size();w = val.size() ? val[0].size() : 0;assert(h > 0 && w > 0);for (size_type i = 1; i < h; ++i) assert(val[i].size() == w);}std::vector<value_type> & operator [](size_type i) noexcept { return val[i]; }const std::vector<value_type> & operator [](size_type i) const noexcept { return val[i]; };value_type & operator ()(size_type i, size_type j) noexcept { return val[i][j]; };const value_type & operator ()(size_type i, size_type j) const noexcept { return val[i][j]; }value_type & at(size_type i, size_type j) {assert(i < h && j < w);return val[i][j];}const value_type & at(size_type i, size_type j) const {assert(i < h & j < w);return val[i][j];}bool empty() const { return !(h || w); }std::pair<size_type, size_type> type() const { return std::make_pair(h, w); }bool match_type(const Matrix & rhs) const noexcept { return h == rhs.h && w == rhs.w; }bool is_square() const { return h == w; }const std::vector<std::vector<value_type>> & get() const noexcept { return val; }bool operator ==(const Matrix & rhs) const noexcept { return match_type(rhs) && val == rhs.val; }bool operator !=(const Matrix & rhs) const noexcept { return !(*this == rhs); }Matrix operator +() const { return Matrix(*this); }Matrix operator -() const { return Matrix(h, w) - Matrix(*this); }Matrix operator +(const Matrix & rhs) const { return Matrix(*this) += rhs; }Matrix operator -(const Matrix & rhs) const { return Matrix(*this) -= rhs; }Matrix operator *(const Matrix & rhs) const {assert(w == rhs.h);Matrix res(h, rhs.w);for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < rhs.w; ++j) for (size_type k = 0; k < w; ++k)res.val[i][j] += val[i][k] * rhs.val[k][j];return res;}Matrix operator /(const Matrix & rhs) const { return Matrix(*this) /= rhs; }friend Matrix operator *(const value_type & lhs, const Matrix & rhs) {Matrix res(rhs.val);for (size_type i = 0; i < res.h; ++i) for (size_type j = 0; j < res.w; ++j)res.val[i][j] = lhs * res.val[i][j];return res;}Matrix operator *(const value_type & rhs) const {Matrix res(val);for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < w; ++j)res.val[i][j] *= rhs;return res;}Matrix operator /(const value_type & rhs) const {Matrix res(val);for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < w; ++j)res.val[i][j] /= rhs;return res;}Matrix & operator +=(const Matrix & rhs) {assert(match_type(rhs));for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < w; ++j)val[i][j] += rhs.val[i][j];return *this;}Matrix & operator -=(const Matrix & rhs) {assert(match_type(rhs));for (size_type i = 0; i < h; ++i) for(size_type j = 0; j < w; ++j)val[i][j] -= rhs.val[i][j];return *this;}Matrix & operator *=(const Matrix & rhs) {*this = *this * rhs;return *this;}Matrix & operator /=(const Matrix & rhs) {*this *= rhs.inverse();return *this;}Matrix pow(long long n) const {Matrix res = identity(h), x(*this);if (n < 0) { x = x.inverse(); n = -n; }while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }return res;}Matrix trans() const {Matrix res(w, h);for (size_type i = 0; i < h; ++i) for (size_type j = 0; j < w; ++j)res.val[j][i] = val[i][j];return res;}Matrix inverse() const {assert(is_square());Matrix aug_mat = this->hstack(identity(h));if (aug_mat.gauss_jordan() != h) return Matrix();return aug_mat.submat(0, w, h, 2 * w);}Matrix vstack(const Matrix & A) const {assert(w == A.w);Matrix res(h + A.h, w);std::copy(val.begin(), val.end(), res.val.begin());std::copy(A.val.begin(), A.val.end(), res.val.begin() + h);return res;}Matrix hstack(const Matrix & A) const {assert(h == A.h);Matrix res(h, w + A.w);for (int i = 0; i < h; ++i) {std::copy(val[i].begin(), val[i].end(), res.val[i].begin());std::copy(A.val[i].begin(), A.val[i].end(), res.val[i].begin() + w);}return res;}Matrix submat(size_type i1, size_type j1, size_type i2, size_type j2) const {assert(i1 < i2 && j1 < j2 && i2 <= h && j2 <= w);Matrix res(i2 - i1, j2 - j1);for (size_type i = 0; i < i2 - i1; ++i)std::copy(val[i + i1].begin() + j1, val[i + i1].begin() + j2, res.val[i].begin());return res;}static Matrix identity(size_type n) {Matrix res(n, n);for (size_type i = 0; i < n; ++i) res(i, i) = 1;return res;}size_type gauss_jordan(size_type colnum = -1) {if (colnum == -1) colnum = w;size_type rank = 0;for (size_type k = 0; k < colnum; ++k) {size_type pivot = -1;for (size_type i = rank; i < h; ++i) {if (val[i][k] != 0) {pivot = i;break;}}if (pivot == -1) continue;if (pivot != rank) std::swap(val[rank], val[pivot]);value_type div = static_cast<value_type>(1) / val[rank][k];for (size_type j = k; j < w; ++j) val[rank][j] *= div;for (size_type i = 0; i < h; ++i) if (i != rank) {for (size_type j = k + 1; j < w; ++j) val[i][j] -= val[rank][j] * val[i][k];val[i][k] = 0;}++rank;}return rank;}friend std::ostream & operator <<(std::ostream & os, const Matrix & rhs) {os << "type = (" << rhs.h << "," << rhs.w << ") [\n";for (size_type i = 0; i < rhs.h; ++i) for (size_type j = 0; j < rhs.w; ++j)os << (j == 0 ? " " : "") << rhs.val[i][j] << (j + 1 == rhs.w ? '\n' : ' ');return os << "]";}private:size_type h, w;std::vector<std::vector<value_type>> val;};template<int M>struct ModInt {public:using value_type = long long;ModInt(value_type val = 0) : val(val < 0 ? (M - (-val % M)) % M : val % M) {}explicit operator bool() const noexcept { return val; }bool operator ==(const ModInt & rhs) const noexcept { return val == rhs.val; }bool operator !=(const ModInt & rhs) const noexcept { return !(*this == rhs); }ModInt operator +() const noexcept { return ModInt(*this); }ModInt operator -() const noexcept { return ModInt(0) -= *this; }ModInt operator +(const ModInt & rhs) const noexcept { return ModInt(*this) += rhs; }ModInt operator -(const ModInt & rhs) const noexcept { return ModInt(*this) -= rhs; }ModInt operator *(const ModInt & rhs) const noexcept { return ModInt(*this) *= rhs; }ModInt operator /(const ModInt & rhs) const noexcept { return ModInt(*this) /= rhs; }ModInt & operator +=(const ModInt & rhs) noexcept {val += rhs.val;if (val >= M) val -= M;return *this;}ModInt & operator -=(const ModInt & rhs) noexcept {if (val < rhs.val) val += M;val -= rhs.val;return *this;}ModInt & operator *=(const ModInt & rhs) noexcept {val = val * rhs.val % M;return *this;}ModInt & operator /=(const ModInt & rhs) noexcept {*this *= rhs.inverse();return *this;}ModInt pow(value_type n) const {ModInt res = 1, x = val;if (n < 0) { x = x.inverse(); n = -n; }while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }return res;}ModInt inverse() const {value_type a = val, a1 = 1, a2 = 0, b = M, b1 = 0, b2 = 1;while (b > 0) {value_type q = a / b, r = a % b;value_type nb1 = a1 - q * b1, nb2 = a2 - q * b2;a = b; b = r;a1 = b1; b1 = nb1;a2 = b2; b2 = nb2;}assert(a == 1);return a1;}const value_type & get() const noexcept { return val; }static decltype(M) get_mod() noexcept { return M; }friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val; }friend std::istream & operator >>(std::istream & is, ModInt & rhs) {value_type x;is >> x;rhs = ModInt(x);return is;}private:value_type val;};using mint = ModInt<MOD>;int main() {ll a, b, n;cin >> a >> b >> n;mint ans;if (n <= 1) ans = n;else {Matrix<mint> A{{a, b}, {1, 0}};Matrix<mint> b{{1}, {0}};cout << (A.pow(n - 1) * b)[0][0] << endl;}return 0;}