結果
問題 | No.1907 DETERMINATION |
ユーザー | 👑 ygussany |
提出日時 | 2022-04-15 23:18:44 |
言語 | C++17(clang) (17.0.6 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 710 ms / 4,000 ms |
コード長 | 3,887 bytes |
コンパイル時間 | 1,001 ms |
コンパイル使用メモリ | 96,496 KB |
実行使用メモリ | 5,140 KB |
最終ジャッジ日時 | 2023-08-26 08:46:04 |
合計ジャッジ時間 | 25,871 ms |
ジャッジサーバーID (参考情報) |
judge13 / judge14 |
テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
4,376 KB |
testcase_01 | AC | 2 ms
4,376 KB |
testcase_02 | AC | 1 ms
4,380 KB |
testcase_03 | AC | 2 ms
4,376 KB |
testcase_04 | AC | 2 ms
4,376 KB |
testcase_05 | AC | 1 ms
4,376 KB |
testcase_06 | AC | 2 ms
4,380 KB |
testcase_07 | AC | 219 ms
4,436 KB |
testcase_08 | AC | 94 ms
4,376 KB |
testcase_09 | AC | 155 ms
4,376 KB |
testcase_10 | AC | 508 ms
5,036 KB |
testcase_11 | AC | 255 ms
4,712 KB |
testcase_12 | AC | 490 ms
4,988 KB |
testcase_13 | AC | 463 ms
5,020 KB |
testcase_14 | AC | 430 ms
4,972 KB |
testcase_15 | AC | 91 ms
4,380 KB |
testcase_16 | AC | 37 ms
4,376 KB |
testcase_17 | AC | 479 ms
4,992 KB |
testcase_18 | AC | 332 ms
4,656 KB |
testcase_19 | AC | 13 ms
4,380 KB |
testcase_20 | AC | 471 ms
4,948 KB |
testcase_21 | AC | 52 ms
4,380 KB |
testcase_22 | AC | 455 ms
4,692 KB |
testcase_23 | AC | 546 ms
5,020 KB |
testcase_24 | AC | 163 ms
4,376 KB |
testcase_25 | AC | 2 ms
4,380 KB |
testcase_26 | AC | 502 ms
5,016 KB |
testcase_27 | AC | 600 ms
4,996 KB |
testcase_28 | AC | 604 ms
4,996 KB |
testcase_29 | AC | 595 ms
5,004 KB |
testcase_30 | AC | 2 ms
4,380 KB |
testcase_31 | AC | 515 ms
5,016 KB |
testcase_32 | AC | 500 ms
5,116 KB |
testcase_33 | AC | 503 ms
5,004 KB |
testcase_34 | AC | 502 ms
5,140 KB |
testcase_35 | AC | 2 ms
4,376 KB |
testcase_36 | AC | 2 ms
4,380 KB |
testcase_37 | AC | 2 ms
4,376 KB |
testcase_38 | AC | 504 ms
5,080 KB |
testcase_39 | AC | 502 ms
5,016 KB |
testcase_40 | AC | 705 ms
5,004 KB |
testcase_41 | AC | 505 ms
5,128 KB |
testcase_42 | AC | 709 ms
5,004 KB |
testcase_43 | AC | 710 ms
5,020 KB |
testcase_44 | AC | 566 ms
5,116 KB |
testcase_45 | AC | 603 ms
5,108 KB |
testcase_46 | AC | 500 ms
5,064 KB |
testcase_47 | AC | 498 ms
5,088 KB |
testcase_48 | AC | 503 ms
5,128 KB |
testcase_49 | AC | 529 ms
4,996 KB |
testcase_50 | AC | 504 ms
5,092 KB |
testcase_51 | AC | 503 ms
5,100 KB |
testcase_52 | AC | 2 ms
4,380 KB |
testcase_53 | AC | 542 ms
4,816 KB |
testcase_54 | AC | 541 ms
4,816 KB |
testcase_55 | AC | 2 ms
4,380 KB |
testcase_56 | AC | 543 ms
4,732 KB |
testcase_57 | AC | 542 ms
4,812 KB |
testcase_58 | AC | 415 ms
4,980 KB |
testcase_59 | AC | 352 ms
5,068 KB |
testcase_60 | AC | 355 ms
5,128 KB |
testcase_61 | AC | 430 ms
5,084 KB |
testcase_62 | AC | 359 ms
5,072 KB |
testcase_63 | AC | 503 ms
5,008 KB |
testcase_64 | AC | 2 ms
4,376 KB |
testcase_65 | AC | 1 ms
4,376 KB |
testcase_66 | AC | 2 ms
4,380 KB |
ソースコード
#include <algorithm> #include <cassert> #include <iostream> #include <numeric> #include <tuple> #include <type_traits> #include <utility> #include <vector> using namespace std; #include <atcoder/modint> using mint = atcoder::static_modint<998244353>; // Upper Hessenberg reduction of square matrices // Complexity: O(n^3) // Reference: // http://www.phys.uri.edu/nigh/NumRec/bookfpdf/f11-5.pdf template <class Tp> void hessenberg_reduction(std::vector<std::vector<Tp>> &M) { assert(M.size() == M[0].size()); const int N = M.size(); for (int r = 0; r < N - 2; r++) { int piv = -1; for (int j = r + 1; j < N; ++j) if (M[j][r] != 0) { piv = j; break; } if (piv < 0) continue; for (int i = 0; i < N; i++) std::swap(M[r + 1][i], M[piv][i]); for (int i = 0; i < N; i++) std::swap(M[i][r + 1], M[i][piv]); const auto rinv = Tp(1) / M[r + 1][r]; for (int i = r + 2; i < N; i++) { const auto n = M[i][r] * rinv; for (int j = 0; j < N; j++) M[i][j] -= M[r + 1][j] * n; for (int j = 0; j < N; j++) M[j][r + 1] += M[j][i] * n; } } } // Characteristic polynomial of matrix M (|xI - M|) // Complexity: O(n^3) // R. Rehman, I. C. Ipsen, "La Budde's Method for Computing Characteristic Polynomials," 2011. template <class Tp> std::vector<Tp> characteristic_poly(std::vector<std::vector<Tp>> &M) { hessenberg_reduction(M); const int N = M.size(); std::vector<std::vector<Tp>> p(N + 1); // p[i + 1] = (Characteristic polynomial of i-th leading principal minor) p[0] = {1}; for (int i = 0; i < N; i++) { p[i + 1].assign(i + 2, 0); for (int j = 0; j < i + 1; j++) p[i + 1][j + 1] += p[i][j]; for (int j = 0; j < i + 1; j++) p[i + 1][j] -= p[i][j] * M[i][i]; Tp betas = 1; for (int j = i - 1; j >= 0; j--) { betas *= M[j + 1][j]; Tp hb = -M[j][i] * betas; for (int k = 0; k < j + 1; k++) p[i + 1][k] += hb * p[j][k]; } } return p[N]; } int main() { int N, a, b = 0; mint prod = 1; cin >> N; vector mat0(N, vector<mint>(N)); vector mat1(N, vector<mint>(N)); for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { cin >> a; mat0[i][j] = a; } for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { cin >> a; mat1[i][j] = a; } for (int i = 0; i < N; ++i) { int piv = -1; for (int h = i; h < N; ++h) { if (mat1[h][i] != 0) piv = h; } if (piv < 0) { for (int h = 0; h < i; h++) { for (int hh = 0; hh < N; hh++) mat0[hh][i] -= mat0[hh][h] * mat1[h][i]; mat1[h][i] = 0; } b++; for (int h = 0; h < N; h++) { mat1[h][i] = mat0[h][i]; mat0[h][i] = 0; } if (b <= N) { i--; continue; } for (int h = 0; h <= N; h++) cout << "0\n"; return 0; } assert(piv >= i); swap(mat0[i], mat0[piv]); swap(mat1[i], mat1[piv]); if (i != piv) { for (int w = 0; w < N; ++w) { mat0[i][w] *= -1; mat1[i][w] *= -1; } } mint inv = mat1[i][i].inv(); prod *= mat1[i][i]; for (int w = 0; w < N; ++w) { mat0[i][w] *= inv; mat1[i][w] *= inv; } for (int h = 0; h < N; ++h) { if (h == i) continue; if (mat1[h][i] == 0) continue; const mint coeff = mat1[h][i]; for (int w = 0; w < N; ++w) { mat1[h][w] -= coeff * mat1[i][w]; mat0[h][w] -= coeff * mat0[i][w]; } } } for(auto &v : mat0) for (auto &x : v) x = -x; auto det_poly = characteristic_poly<mint>(mat0); for (int i = b; i <= N; i++) cout << (det_poly[i] * prod).val() << '\n'; for (int i = N + 1; i <= N + b; i++) cout << "0\n"; return 0; }