oj.uz

Submission #312585

# Submission time Handle Problem Language Result Execution time Memory
312585 2020-10-13T19:58:05 Z Lawliet Semafor (COI20_semafor) C++17
100 / 100
 1117 ms 17528 KB 
#include <bits/stdc++.h>
 
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define REP(i, n) FOR(i, 0, n)
#define TRACE(x) cerr << #x << " " << x << endl
#define _ << " " <<
#define debug(...) fprintf(stderr, __VA_ARGS__)
typedef long long ll;
typedef std::pair<ll, ll> pii;
#define double long double
typedef double db;
using namespace std;
 
 ll MaxN = 200100;
 ll mod = 1e9 + 7;
 
struct Matrix {
  vector<vector<ll>> a;
  int dim;
  vector<ll>& operator [] (ll r) { return a[r]; };
 
  Matrix(int DIM, ll x = 0) {
    dim = DIM;
    REP(i, DIM) a.emplace_back();
    REP(i, DIM) REP(j, DIM) a[i].push_back(0);
    if (x) REP(i, DIM) a[i][i] = x; // identity
  }
};
 
Matrix operator * ( Matrix &A,  Matrix &B) {
  int DIM = A.dim;
   ll mod2 = ll(mod) * mod;
  Matrix C(DIM);
  REP(i, DIM) REP(j, DIM) {
    ll w = 0;
    REP(k, DIM) {
      w += ll(A[i][k]) * B[k][j];
      if (w >= mod2) w -= mod2;
    }
    C[i][j] = w % mod;
  }
  return C;
}
 
Matrix operator ^ ( Matrix &A, ll b) {
  Matrix R = Matrix(A.dim, 1);
  for (; b > 0; b /= 2) {
    if (b % 2) R = R*A;
    A = A*A;
  }
  return R;
}
 
ostream& operator<< (ostream& f,  Matrix &A) {
  for (int i = 0; i < A.dim; i++) {
    for (int j = 0; j < A.dim; j++) {
      f << A.a[i][j];
      f << " ";
    }
    f << endl;
  }
  return f;
}
 
ll modpot(ll b, ll pot) {
  ll ret = 1;
  for (; pot; pot >>= 1) {
    if (pot & 1) ret = (ret * b) % mod;
    b = (b * b) % mod;
  }
  return ret;
}
 
ll modinv(ll b) {
  return modpot(b, mod-2);
}
 
int binom[55][55];
void precompute_binoms(int n) {
  for (int i = 0; i <= n; i++) {
    binom[i][0] = 1;
    for (int j = 1; j <= i; j++) {
      binom[i][j] = binom[i-1][j] + binom[i-1][j-1];
    }
  }
}
 
ll N, M, K;
int X;
int sz;
int nums;
int numbits;
vector<int> halves = {31, 31 << 5};
vector<int> digits = {2+8,    2,    1+8,  1+2+4,     2+16,
                      1+4+16, 4+8,  1+2,  1+4+8+16, 1+2+4+16};
bool is_digit[33];
 
int to_mask(int Y) {
  int ret = digits[Y % 10];
  if (M == 2) {
    ret += (digits[Y / 10] << 5);
    }
  return ret;
}
 
bool is_good(int mask) {
  bool ok = is_digit[mask & halves[0]];
  if (M == 2) { /* maybe unnecessary */
    ok &= is_digit[(mask & halves[1]) >> 5];
  }
  return ok;
}
 
Matrix power_hypercube(ll pot) {
  Matrix H(sz, 0);  
  REP(i, sz) REP(j, sz) {
    if (__builtin_popcount(i ^ j) == 1) {
      H.a[i][j] = 1;
    }
  }
  return H ^ pot; 
}
 
Matrix get_intermediate_matrix(ll pot) {
  Matrix P(numbits + 1, 0);
  P.a[0][1] = numbits;
  for (int i = 1; i < numbits; i++) {
    P.a[i][i-1] = i;
    P.a[i][i+1] = numbits - i; 
  } 
  P.a[numbits][numbits-1] = numbits;
  //cerr << P << endl;
 
  P = P ^ pot; 
  //cerr << P << endl;
 
  Matrix A(sz, 0);
  REP(i, sz) REP(j, sz) {
    int r = __builtin_popcount(i ^ j);
    A.a[i][j] = P.a[0][r] * modinv(binom[numbits][r]) % mod;
  }
  return A;
}
 
void solve() {
  //TRACE(K);
  precompute_binoms(numbits + 1);
  Matrix A = get_intermediate_matrix(K);
  Matrix B = get_intermediate_matrix(N % K);
  map<int, int> new_index;
 
  int cnt = 0;
  REP(i, sz) {
    if (is_good(i)) {
      new_index[i] = cnt++;
    }
  }
  assert(cnt == nums);
  Matrix C(nums, 0), D(nums, 0);
 
  REP(i, sz) REP(k, sz) {
    if (is_good(i) && is_good(k)) {
      C[new_index[i]][new_index[k]] = A.a[i][k]; 
      D[new_index[i]][new_index[k]] = B.a[i][k]; 
    }
    else {
      A.a[i][k] = 0;
      B.a[i][k] = 0;
    }
  }
 
 
  C = C ^ (N/K);
 
  C = C * D;
 
 
  for (int Y = 0; Y < nums; Y++) {
    cout << C.a[new_index[to_mask(X)]][new_index[to_mask(Y)]] << endl;
  }
}
 
void load() {
  cin >> M >> N >> K >> X;
  assert(M == 1 || M == 2);
  sz = (M == 1) ? 32 : 1024;
  nums = (M == 1) ? 10 : 100;
  numbits = (M == 1) ? 5 : 10;
 
  for (auto d: digits) {
    is_digit[d] = true;
  }
 
}
 
int main() {
  ios_base::sync_with_stdio(false);
  load();
  solve();
  return 0;
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 384 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 2 ms 256 KB Output is correct
6 Correct 1 ms 256 KB Output is correct
7 Correct 2 ms 256 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 1 ms 384 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 384 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 2 ms 256 KB Output is correct
6 Correct 1 ms 256 KB Output is correct
7 Correct 2 ms 256 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 1 ms 384 KB Output is correct
11 Correct 1 ms 384 KB Output is correct
12 Correct 2 ms 384 KB Output is correct
13 Correct 2 ms 384 KB Output is correct
14 Correct 2 ms 384 KB Output is correct
15 Correct 2 ms 384 KB Output is correct
16 Correct 2 ms 384 KB Output is correct
17 Correct 2 ms 384 KB Output is correct
18 Correct 2 ms 384 KB Output is correct
19 Correct 2 ms 384 KB Output is correct
20 Correct 2 ms 384 KB Output is correct
21 Correct 2 ms 384 KB Output is correct
22 Correct 2 ms 384 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 982 ms 17352 KB Output is correct
2 Correct 979 ms 17284 KB Output is correct
3 Correct 977 ms 17400 KB Output is correct
4 Correct 987 ms 17400 KB Output is correct
5 Correct 985 ms 17400 KB Output is correct
6 Correct 978 ms 17296 KB Output is correct
7 Correct 980 ms 17352 KB Output is correct
8 Correct 975 ms 17272 KB Output is correct
9 Correct 978 ms 17400 KB Output is correct

Subtask #4
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1006 ms 17528 KB Output is correct
2 Correct 1043 ms 17400 KB Output is correct
3 Correct 1083 ms 17400 KB Output is correct
4 Correct 1117 ms 17400 KB Output is correct
5 Correct 1107 ms 17484 KB Output is correct
6 Correct 1107 ms 17400 KB Output is correct
7 Correct 1107 ms 17400 KB Output is correct
8 Correct 1109 ms 17356 KB Output is correct
9 Correct 1107 ms 17528 KB Output is correct
10 Correct 1103 ms 17348 KB Output is correct
11 Correct 986 ms 17292 KB Output is correct
12 Correct 975 ms 17272 KB Output is correct
13 Correct 1104 ms 17528 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1006 ms 17528 KB Output is correct
2 Correct 1043 ms 17400 KB Output is correct
3 Correct 1083 ms 17400 KB Output is correct
4 Correct 1117 ms 17400 KB Output is correct
5 Correct 1107 ms 17484 KB Output is correct
6 Correct 1107 ms 17400 KB Output is correct
7 Correct 1107 ms 17400 KB Output is correct
8 Correct 1109 ms 17356 KB Output is correct
9 Correct 1107 ms 17528 KB Output is correct
10 Correct 1103 ms 17348 KB Output is correct
11 Correct 986 ms 17292 KB Output is correct
12 Correct 975 ms 17272 KB Output is correct
13 Correct 1104 ms 17528 KB Output is correct
14 Correct 993 ms 17360 KB Output is correct
15 Correct 1032 ms 17272 KB Output is correct
16 Correct 1059 ms 17376 KB Output is correct
17 Correct 1088 ms 17400 KB Output is correct
18 Correct 1095 ms 17400 KB Output is correct
19 Correct 1076 ms 17528 KB Output is correct
20 Correct 1094 ms 17420 KB Output is correct
21 Correct 1104 ms 17400 KB Output is correct
22 Correct 1106 ms 17400 KB Output is correct
23 Correct 1085 ms 17352 KB Output is correct
24 Correct 1089 ms 17400 KB Output is correct
25 Correct 1087 ms 17400 KB Output is correct
26 Correct 980 ms 17400 KB Output is correct
27 Correct 984 ms 17400 KB Output is correct
28 Correct 1056 ms 17220 KB Output is correct

Subtask #6
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 982 ms 17352 KB Output is correct
2 Correct 979 ms 17284 KB Output is correct
3 Correct 977 ms 17400 KB Output is correct
4 Correct 987 ms 17400 KB Output is correct
5 Correct 985 ms 17400 KB Output is correct
6 Correct 978 ms 17296 KB Output is correct
7 Correct 980 ms 17352 KB Output is correct
8 Correct 975 ms 17272 KB Output is correct
9 Correct 978 ms 17400 KB Output is correct
10 Correct 1006 ms 17528 KB Output is correct
11 Correct 1043 ms 17400 KB Output is correct
12 Correct 1083 ms 17400 KB Output is correct
13 Correct 1117 ms 17400 KB Output is correct
14 Correct 1107 ms 17484 KB Output is correct
15 Correct 1107 ms 17400 KB Output is correct
16 Correct 1107 ms 17400 KB Output is correct
17 Correct 1109 ms 17356 KB Output is correct
18 Correct 1107 ms 17528 KB Output is correct
19 Correct 1103 ms 17348 KB Output is correct
20 Correct 986 ms 17292 KB Output is correct
21 Correct 975 ms 17272 KB Output is correct
22 Correct 1104 ms 17528 KB Output is correct
23 Correct 993 ms 17360 KB Output is correct
24 Correct 1032 ms 17272 KB Output is correct
25 Correct 1059 ms 17376 KB Output is correct
26 Correct 1088 ms 17400 KB Output is correct
27 Correct 1095 ms 17400 KB Output is correct
28 Correct 1076 ms 17528 KB Output is correct
29 Correct 1094 ms 17420 KB Output is correct
30 Correct 1104 ms 17400 KB Output is correct
31 Correct 1106 ms 17400 KB Output is correct
32 Correct 1085 ms 17352 KB Output is correct
33 Correct 1089 ms 17400 KB Output is correct
34 Correct 1087 ms 17400 KB Output is correct
35 Correct 980 ms 17400 KB Output is correct
36 Correct 984 ms 17400 KB Output is correct
37 Correct 1056 ms 17220 KB Output is correct
38 Correct 981 ms 17400 KB Output is correct
39 Correct 980 ms 17272 KB Output is correct
40 Correct 979 ms 17400 KB Output is correct
41 Correct 987 ms 17272 KB Output is correct
42 Correct 984 ms 17356 KB Output is correct
43 Correct 987 ms 17400 KB Output is correct
44 Correct 981 ms 17400 KB Output is correct
45 Correct 1101 ms 17528 KB Output is correct
46 Correct 1107 ms 17272 KB Output is correct
47 Correct 983 ms 17272 KB Output is correct
48 Correct 985 ms 17400 KB Output is correct
49 Correct 980 ms 17400 KB Output is correct
50 Correct 984 ms 17272 KB Output is correct
51 Correct 985 ms 17288 KB Output is correct
52 Correct 1014 ms 17400 KB Output is correct