結果

問題 No.1907 DETERMINATION
ユーザー vjudge1
提出日時 2025-03-30 13:25:48
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 788 ms / 4,000 ms
コード長 4,011 bytes
コンパイル時間 3,533 ms
コンパイル使用メモリ 279,344 KB
実行使用メモリ 7,392 KB
最終ジャッジ日時 2025-03-30 13:26:19
合計ジャッジ時間 31,030 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
sample AC * 4
other AC * 63
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 <bits/stdc++.h>

using namespace std;
using LL = long long;

const int kMaxN = 405, kM = 998244353;

LL a[kMaxN][kMaxN], b[kMaxN][kMaxN], f[kMaxN][kMaxN], n, val = 1, cnt;

LL P(LL x, LL y) {
  LL ans = 1;
  for (LL i = 1; i <= y; i <<= 1, x = x * x % kM) {
    (y & i) && (ans = ans * x % kM);
  }
  return ans;
}

void Init() {                     // ????????
  for (int i = 1; i <= n; i++) {  // ?? i ?? i+1 ??? 1
    int pos = 0;
    for (int j = i + 1; j <= n; j++) {
      if (a[j][i]) {
        pos = j;
        break;
      }
    }
    if (!pos) {
      continue;
    }
    swap(a[i + 1], a[pos]);
    for (int k = 1; k <= n; k++) {
      swap(a[k][i + 1], a[k][pos]);
    }
    LL f = a[i + 1][i], inv = P(f, kM - 2);
    for (int j = i; j <= n; j++) {
      a[i + 1][j] = a[i + 1][j] * inv % kM;
    }
    for (int j = 1; j <= n; j++) {
      a[j][i + 1] = a[j][i + 1] * f % kM;
    }
    for (int j = i + 2; j <= n; j++) {
      LL val = a[j][i];
      for (int k = 1; k <= n; k++) {
        a[k][i + 1] = (a[k][i + 1] + a[k][j] * val) % kM;
      }
      val = (kM - val) % kM;
      for (int k = i; k <= n; k++) {
        a[j][k] = (a[j][k] + a[i + 1][k] * val) % kM;
      }
    }
  }
}

void Dp() {
  f[0][0] = 1;
  for (int i = 1; i <= n; i++) {
    LL val = kM - 1;
    for (int j = i; j >= 1; j--) {
      LL g = val * a[j][i] % kM;
      for (int k = 0; k < j; k++) {
        f[i][k] = (f[i][k] + g * f[j - 1][k]) % kM;
      }
      val = val * a[j][j - 1] % kM;
    }
    for (int k = 1; k <= i; k++) {
      f[i][k] = (f[i - 1][k - 1] + f[i][k]) % kM;
    }
  }
}

void Work(int x) {               // ?(x,x)???0
  for (int i = 1; i < x; i++) {  // ?x??i?
    // ?? i ?????????
    for (int j = 1; j <= n; j++) {
      a[j][x] = (a[j][x] - a[j][i] * b[i][x]) % kM;
    }
    b[i][x] = 0;
  }
  for (int i = 1; i <= n; i++) {
    b[i][x] = a[i][x], a[i][x] = 0;
  }
}

void Debug() {
  cout << "a:\n";
  for (int x = 1; x <= n; x++) {
    for (int y = 1; y <= n; y++) {
      cout << a[x][y] << " ";
    }
    cout << "\n";
  }
  cout << "b:\n";
  for (int x = 1; x <= n; x++) {
    for (int y = 1; y <= n; y++) {
      cout << b[x][y] << " ";
    }
    cout << "\n";
  }
}

void Calc() {
  // ????????
  for (int i = 1; i <= n && cnt <= n; i++) {
    int p = 0;
    for (int j = i; j <= n; j++) {
      if (b[j][i]) {
        p = j;
        break;
      }
    }
    if (!p) {
      cnt++;
      Work(i), i--;
    } else {
      if (p != i) {
        swap(b[i], b[p]), swap(a[i], a[p]);
        val = (kM - val) % kM;
      }
      val = val * b[i][i] % kM;
      LL v = P(b[i][i], kM - 2);
      for (int j = n; j >= 1; j--) {
        a[i][j] = a[i][j] * v % kM;
        b[i][j] = b[i][j] * v % kM;
      }
      for (int j = 1; j <= n; j++) {
        if (i != j) {
          LL x = b[j][i];
          for (int k = n; k >= 1; k--) {
            a[j][k] = (a[j][k] - x * a[i][k]) % kM;
            b[j][k] = (b[j][k] - x * b[i][k]) % kM;
          }
        }
      }
      // Debug();
    }
  }
  // ???????
  for (int i = n; i >= 1; i--) {        // ?i?
    for (int j = i + 1; j <= n; j++) {  // ???j?
      LL val = b[i][j];
      for (int k = 1; k <= n; k++) {
        b[i][k] = (b[i][k] - b[j][k] * val) % kM;
        a[i][k] = (a[i][k] - a[j][k] * val) % kM;
      }
    }
  }
  // Debug();
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      a[i][j] = (a[i][j] + kM) % kM;
      a[i][j] = (kM - a[i][j]) % kM;
    }
  }
}

int main() {
  ios ::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> a[i][j];
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> b[i][j];
    }
  }
  // cout << "\n\n\n\n\n\n";
  Calc();
  Init();
  Dp();
  val = (val % kM + kM) % kM;
  for (int i = 0; i <= n - cnt; i++) {
    cout << f[n][i + cnt] * val % kM << "\n";
  }
  for (int i = 1; i <= cnt; i++) {
    cout << 0 << "\n";
  }
  return 0;
}
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