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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#311887#7612. Matrix InversePlentyOfPenaltyTL 0ms28300kbC++203.8kb2024-01-22 22:30:042024-01-22 22:30:05

Judging History

你现在查看的是最新测评结果

  • [2024-01-22 22:30:05]
  • 评测
  • 测评结果:TL
  • 用时:0ms
  • 内存:28300kb
  • [2024-01-22 22:30:04]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
typedef std::pair<int, int> pii;
typedef long long ll;
const int MAXN = 2011, mod = 1e9 + 7;
void Add(int &a, int t) {
  a += t;
  if (a >= mod) a -= mod;
}
ll Qpow(ll a, ll p) {
  ll res = 1;
  while (p) {
    if (p & 1) res = res * a % mod;
    a = a * a % mod, p >>= 1;
  }
  return res;
}
int a[MAXN][MAXN], ra[MAXN][MAXN], b[MAXN][MAXN], rb[MAXN][MAXN], res[MAXN][MAXN];
int f[MAXN][MAXN];
int row[MAXN], col[MAXN], cr, cc;
bool type[MAXN];

void gauss(int a[15][15], int n) {
  for (int i = 1; i <= n; ++i) {
    for (int j = i; j <= n; ++j)
      if (a[j][i]) {
        std::swap(a[i], a[j]);
        break;
      }
    int inv = Qpow(a[i][i], mod - 2);
    for (int k = 1; k <= n + 1; ++k) a[i][k] = ll(a[i][k]) * inv % mod;
    for (int j = 1; j <= n; ++j)
      if (i != j && a[j][i]) {
        int r = a[j][i];
        for (int k = i; k <= n + 1; ++k) a[j][k] = ((a[j][k] - ll(r) * a[i][k]) % mod + mod) % mod;
      }
  }
}
int eq[15][15];

struct one {
  int x, y, v;
  inline bool operator<(const one &rhs) const {
    if (x != rhs.x) return x < rhs.x;
    if (y != rhs.y) return y < rhs.y;
    return v < rhs.v;
  }
};
std::vector<one> ans;
vector<pii> seq;

int main() {
#ifdef popteam
  // freopen("I.in", "r", stdin);
#endif
  mt19937 rd(std::chrono::steady_clock::now().time_since_epoch().count());
  cin.tie(0)->sync_with_stdio(0);
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= n; ++j) cin >> a[i][j], ra[i][j] = a[i][j];
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= n; ++j) cin >> b[i][j], rb[i][j] = b[i][j], res[i][j] = b[i][j];
  for (int i = 1; i <= n; ++i) f[i][i] = 1;
  int lst = rd() % n + 1;
  for (int w = 1; w <= n; ++w) {
    int x = rd() % n + 1;
    seq.emplace_back(pii(lst, x));
    lst = x;
  }
  for (auto [x, y] : seq)
    for (int k = 1; k <= n; ++k) Add(ra[y][k], ra[x][k]), Add(f[y][k], f[x][k]);
  for (int c = 1; c <= n; ++c) {
    bool err = 0;
    for (int w = 1; w <= 15; ++w) {
      int i = rd() % n + 1;
      int sum = 0;
      for (int k = 1; k <= n; ++k) sum = (sum + ll(ra[i][k]) * b[k][c]) % mod;
      // printf("c=%d,i=%d,sum=%d\n", i, c, sum);
      if (sum != f[i][c]) {
        err = 1;
        break;
      }
    }
    if (err) col[++cc] = c; //, printf("Err,c=%d\n", c);
  }
  assert(cc <= 12);
  memset(f, 0, sizeof f);
  for (int i = 1; i <= n; ++i) f[i][i] = 1;
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= n; ++j) ra[i][j] = a[i][j];
  for (auto [x, y] : seq)
    for (int k = 1; k <= n; ++k) Add(ra[k][y], ra[k][x]), Add(f[k][y], f[k][x]);
  for (int r = 1; r <= n; ++r) {
    bool err = 0;
    for (int w = 1; w <= 15; ++w) {
      int j = rd() % n + 1;
      int sum = 0;
      for (int k = 1; k <= n; ++k) sum = (sum + ll(b[r][k]) * ra[k][j]) % mod;
      if (sum != f[r][j]) {
        err = 1;
        break;
      }
    }
    if (err) row[++cr] = r, type[r] = 1; //, printf("Err,r=%d\n", r);
  }
  fprintf(stderr, "cr=%d\n", cr);
  assert(cr <= 12);
  for (int w = 1; w <= cc; ++w) {
    memset(eq, 0, sizeof eq);
    int c = col[w];
    for (int i = 1; i <= cr; ++i) {
      if (i == c) ++eq[i][cr + 1];
      int cur = 0;
      for (int r = 1; r <= n; ++r)
        if (type[r]) eq[i][++cur] = a[i][r];
        else
          eq[i][cr + 1] = ((eq[i][cr + 1] - ll(a[i][r]) * b[r][c]) % mod + mod) % mod;
    }
    gauss(eq, cr);
    int cur = 0;
    for (int r = 1; r <= n; ++r)
      if (type[r]) {
        ++cur;
        if (res[r][c] != eq[cur][cr + 1]) ans.emplace_back(one{r, c, eq[cur][cr + 1]});
      }
  }
  cout << ans.size() << '\n';
  sort(ans.begin(), ans.end());
  for (auto P : ans) {
    cout << P.x << " " << P.y << " " << P.v << '\n';
  }
}

Details

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Test #1:

score: 100
Accepted
time: 0ms
memory: 28300kb

input:

1
953176428
107682094

output:

0

result:

ok single line: '0'

Test #2:

score: -100
Time Limit Exceeded

input:

1995
586309310 548144807 578573993 437893403 641164340 712256053 172321263 108058526 768610920 123320669 762746291 856047593 979279376 29067913 309867338 292286426 45124325 239705174 675003623 213743652 620561338 116308277 695369179 669459894 682522334 846995555 159510341 999359657 645579085 7499563...

output:


result: