結果

問題 No.2255 Determinant Sum
ユーザー 👑 hos.lyrichos.lyric
提出日時 2023-03-24 21:29:28
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 419 ms / 2,000 ms
コード長 7,143 bytes
コンパイル時間 1,424 ms
コンパイル使用メモリ 113,040 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-18 16:46:13
合計ジャッジ時間 5,749 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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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
5,376 KB
testcase_02 AC 4 ms
5,376 KB
testcase_03 AC 4 ms
5,376 KB
testcase_04 AC 4 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 419 ms
5,376 KB
testcase_07 AC 305 ms
5,376 KB
testcase_08 AC 327 ms
5,376 KB
testcase_09 AC 338 ms
5,376 KB
testcase_10 AC 304 ms
5,376 KB
testcase_11 AC 15 ms
5,376 KB
testcase_12 AC 151 ms
5,376 KB
testcase_13 AC 16 ms
5,376 KB
testcase_14 AC 401 ms
5,376 KB
testcase_15 AC 149 ms
5,376 KB
testcase_16 AC 131 ms
5,376 KB
testcase_17 AC 139 ms
5,376 KB
testcase_18 AC 104 ms
5,376 KB
testcase_19 AC 120 ms
5,376 KB
testcase_20 AC 135 ms
5,376 KB
testcase_21 AC 178 ms
5,376 KB
testcase_22 AC 131 ms
5,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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; }

////////////////////////////////////////////////////////////////////////////////
struct ModInt {
  static unsigned 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) { x = (static_cast<unsigned long long>(x) * a.x) % 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;
////////////////////////////////////////////////////////////////////////////////


// det(a + x I)
// O(n^3)
//   Call by value: Modifies a (Watch out when using C-style array!)
template <class T> vector<T> charPoly(vector<vector<T>> a) {
  const int n = a.size();
  // upper Hessenberg
  for (int j = 0; j < n - 2; ++j) {
    for (int i = j + 1; i < n; ++i) {
      if (a[i][j]) {
        swap(a[j + 1], a[i]);
        for (int ii = 0; ii < n; ++ii) swap(a[ii][j + 1], a[ii][i]);
        break;
      }
    }
    if (a[j + 1][j]) {
      const T s = 1 / a[j + 1][j];
      for (int i = j + 2; i < n; ++i) {
        const T t = s * a[i][j];
        for (int jj = j; jj < n; ++jj) a[i][jj] -= t * a[j + 1][jj];
        for (int ii = 0; ii < n; ++ii) a[ii][j + 1] += t * a[ii][i];
      }
    }
  }
  // fss[i] := det(a[0..i][0..i] + x I_i)
  vector<vector<T>> fss(n + 1);
  fss[0] = {1};
  for (int i = 0; i < n; ++i) {
    fss[i + 1].assign(i + 2, 0);
    for (int k = 0; k <= i; ++k) fss[i + 1][k + 1] = fss[i][k];
    for (int k = 0; k <= i; ++k) fss[i + 1][k] += a[i][i] * fss[i][k];
    T prod = 1;
    for (int j = i - 1; j >= 0; --j) {
      prod *= -a[j + 1][j];
      const T t = prod * a[j][i];
      for (int k = 0; k <= j; ++k) fss[i + 1][k] += t * fss[j][k];
    }
  }
  return fss[n];
}

// det(a + x b)
// O(n^3)
//   Call by value: Modifies a, b (Watch out when using C-style array!)
template <class T> vector<T> detPoly(vector<vector<T>> a, vector<vector<T>> b) {
  const int n = a.size();
  T prod = 1;
  int off = 0;
  for (int h = 0; h < n; ++h) {
    for (; ; ) {
      if (b[h][h]) break;
      for (int j = h + 1; j < n; ++j) {
        if (b[h][j]) {
          prod *= -1;
          for (int i = 0; i < n; ++i) {
            swap(a[i][h], a[i][j]);
            swap(b[i][h], b[i][j]);
          }
          break;
        }
      }
      if (b[h][h]) break;
      if (++off > n) return vector<T>(n + 1, 0);
      for (int j = 0; j < n; ++j) {
        b[h][j] = a[h][j];
        a[h][j] = 0;
      }
      for (int i = 0; i < h; ++i) {
        const T t = b[h][i];
        for (int j = 0; j < n; ++j) {
          a[h][j] -= t * a[i][j];
          b[h][j] -= t * b[i][j];
        }
      }
    }
    prod *= b[h][h];
    const T s = 1 / b[h][h];
    for (int j = 0; j < n; ++j) {
      a[h][j] *= s;
      b[h][j] *= s;
    }
    for (int i = 0; i < n; ++i) if (h != i) {
      const T t = b[i][h];
      for (int j = 0; j < n; ++j) {
        a[i][j] -= t * a[h][j];
        b[i][j] -= t * b[h][j];
      }
    }
  }
  const vector<T> fs = charPoly(a);
  vector<T> gs(n + 1, 0);
  for (int i = 0; off + i <= n; ++i) gs[i] = prod * fs[off + i];
  return gs;
}


using Mint = ModInt;


int N, P;
int A[60][60];

int main() {
  for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    scanf("%d%d", &N, &P);
    for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) {
      scanf("%d", &A[i][j]);
    }
    Mint::M = P;
    
    int K = 0;
    vector<vector<Mint>> a(N, vector<Mint>(N, 0));
    vector<vector<Mint>> b(N, vector<Mint>(N, 0));
    for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) {
      if (~A[i][j]) {
        a[i][j] = A[i][j];
      } else {
        ++K;
        b[i][j] = 1;
      }
    }
    const auto res = detPoly(a, b);
// cerr<<"res = "<<res<<endl;
    
    Mint ans = 0;
    for (int i = 0; i <= N; ++i) {
      Mint prod = res[i];
      if (i > 0) {
        if (P != 2) prod = 0;
      }
      if (K - i > 0) {
        prod = 0;
      }
      ans += prod;
    }
    printf("%u\n", ans.x);
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}
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