結果
| 問題 | No.1175 Simultaneous Equations |
| ユーザー |
 tkmst201
|
| 提出日時 | 2021-01-12 18:22:10 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 7,070 bytes |
| コンパイル時間 | 2,147 ms |
| コンパイル使用メモリ | 199,380 KB |
| 最終ジャッジ日時 | 2025-01-17 16:35:45 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 11 |
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)template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }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 = false;//---------------------------------//struct Matrix {public:using value_type = double;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().first != 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;}std::pair<size_type, value_type> gauss_jordan(size_type colnum = -1) {if (colnum == -1) colnum = w;size_type rank = 0;value_type det = 1;for (size_type k = 0; k < colnum; ++k) {size_type pivot = -1;value_type mx = EPS;for (size_type i = rank; i < h; ++i) {value_type cur = std::abs(val[i][k]);if (cur > mx) {mx = cur;pivot = i;}}if (pivot == -1) continue;if (pivot != rank) {det *= -1;std::swap(val[rank], val[pivot]);}value_type div = val[rank][k];det *= div;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;}if (!is_square() || rank != h) det = 0;return {rank, det};}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:static constexpr value_type EPS = 1e-6;size_type h, w;std::vector<std::vector<value_type>> val;};int main() {Matrix mat(2, 3);REP(i, 2) REP(j, 3) cin >> mat[i][j];mat.gauss_jordan();printf("%.15f %.15f\n", mat[0][2], mat[1][2]);}