#898105 (C++14) No.2405 Minimal Matrix Decomposition

提出ソース

結果

問題	No.2405 Minimal Matrix Decomposition
ユーザー	👑 hos.lyric
提出日時	2023-08-04 21:33:58
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	88 ms / 2,000 ms
コード長	6,325 bytes
コンパイル時間	1,151 ms
コンパイル使用メモリ	115,196 KB
実行使用メモリ	6,528 KB
最終ジャッジ日時	2024-10-14 19:32:18
合計ジャッジ時間	5,317 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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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 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	19 ms 5,248 KB
testcase_05	AC	88 ms 6,528 KB
testcase_06	AC	2 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	2 ms 5,248 KB
testcase_09	AC	2 ms 5,248 KB
testcase_10	AC	46 ms 5,248 KB
testcase_11	AC	59 ms 5,248 KB
testcase_12	AC	3 ms 5,248 KB
testcase_13	AC	14 ms 5,248 KB
testcase_14	AC	16 ms 5,248 KB
testcase_15	AC	8 ms 5,248 KB
testcase_16	AC	6 ms 5,248 KB
testcase_17	AC	24 ms 5,248 KB
testcase_18	AC	17 ms 5,248 KB
testcase_19	AC	17 ms 5,248 KB
testcase_20	AC	3 ms 5,248 KB
testcase_21	AC	6 ms 5,248 KB
testcase_22	AC	45 ms 5,248 KB
testcase_23	AC	2 ms 5,248 KB
testcase_24	AC	3 ms 5,248 KB
testcase_25	AC	4 ms 5,248 KB
testcase_26	AC	34 ms 5,248 KB
testcase_27	AC	12 ms 5,248 KB
testcase_28	AC	31 ms 5,248 KB
testcase_29	AC	10 ms 5,248 KB
testcase_30	AC	43 ms 5,248 KB
testcase_31	AC	16 ms 5,248 KB
testcase_32	AC	4 ms 5,248 KB
testcase_33	AC	30 ms 5,248 KB
testcase_34	AC	8 ms 5,248 KB
testcase_35	AC	2 ms 5,248 KB
testcase_36	AC	13 ms 5,248 KB
testcase_37	AC	19 ms 5,248 KB
testcase_38	AC	20 ms 5,248 KB
testcase_39	AC	33 ms 5,248 KB
testcase_40	AC	16 ms 5,248 KB
testcase_41	AC	4 ms 5,248 KB
testcase_42	AC	38 ms 5,248 KB
testcase_43	AC	11 ms 5,248 KB
testcase_44	AC	11 ms 5,248 KB
testcase_45	AC	5 ms 5,248 KB
testcase_46	AC	9 ms 5,248 KB
testcase_47	AC	11 ms 5,248 KB
testcase_48	AC	6 ms 5,248 KB
testcase_49	AC	3 ms 5,248 KB

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ソースコード

raw source code

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }

////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
  static unsigned M;
  static unsigned long long NEG_INV_M;
  static void setM(unsigned long long m) { M = m; NEG_INV_M = -1ULL / M; }
  unsigned x;
  ModInt() : x(0U) {}
  ModInt(unsigned x_) : x(x_ % M) {}
  ModInt(unsigned long long x_) : x(x_ % M) {}
  ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) {
    const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
    const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
    const unsigned long long r = y - M * q;
    x = r - M * (r >= M);
    return *this;
  }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////


// a \in Mat(m, n), rank(a) = r
// b \in Mat(m, r), c \in Mat(r, n), a = b c
// O(m n min(m, n))
//   Call by value: Modifies a (Watch out when using C-style array!)
template <class T>
pair<vector<vector<T>>, vector<vector<T>>> rankDecompose(vector<vector<T>> a) {
  assert(!a.empty());
  const int m = a.size(), n = a[0].size();
  vector<int> is(m);
  for (int i = 0; i < m; ++i) is[i] = i;
  vector<vector<T>> b(m, vector<T>(min(m, n), 0));
  int r = 0;
  for (int h = 0; r < m && h < n; ++h) {
    for (int i = r; i < m; ++i) if (a[i][h]) {
      swap(a[r], a[i]);
      swap(is[r], is[i]);
      break;
    }
    if (a[r][h]) {
      const T s = a[r][h].inv();
      for (int i = r + 1; i < m; ++i) {
        const T t = b[is[i]][r] = s * a[i][h];
        for (int j = h; j < n; ++j) a[i][j] -= t * a[r][j];
      }
      ++r;
    }
  }
  for (int i = 0; i < m; ++i) b[i].resize(r);
  for (int k = 0; k < r; ++k) b[is[k]][k] = 1;
  a.resize(r);
  return std::make_pair(b, a);
}
////////////////////////////////////////////////////////////////////////////////


using Mint = ModInt;

int P, M, N;
vector<vector<Mint>> A;

int main() {
  for (; ~scanf("%d", &P); ) {
    Mint::setM(P);
    scanf("%d%d", &M, &N);
    A.assign(M, vector<Mint>(N));
    for (int i = 0; i < M; ++i) for (int j = 0; j < N; ++j) {
      scanf("%u", &A[i][j].x);
    }
    
    auto ans = rankDecompose(A);
    int r = ans.second.size();
    if (r == 0) {
      r = 1;
      ans.first.assign(M, vector<Mint>(r, 0));
      ans.second.assign(r, vector<Mint>(N, 0));
    }
    if (M * N <= M * r + r * N) {
      puts("1");
      printf("%d %d\n", M, N);
      for (int i = 0; i < M; ++i) {
        for (int j = 0; j < N; ++j) {
          if (j) printf(" ");
          printf("%u", A[i][j].x);
        }
        puts("");
      }
    } else {
      puts("2");
      printf("%d %d\n", M, r);
      for (int i = 0; i < M; ++i) {
        for (int j = 0; j < r; ++j) {
          if (j) printf(" ");
          printf("%u", ans.first[i][j].x);
        }
        puts("");
      }
      printf("%d %d\n", r, N);
      for (int i = 0; i < r; ++i) {
        for (int j = 0; j < N; ++j) {
          if (j) printf(" ");
          printf("%u", ans.second[i][j].x);
        }
        puts("");
      }
    }
#ifdef LOCAL
cerr<<"========"<<endl;
#endif
  }
  return 0;
}

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結果

テストケース

ソースコード