Cod sursa(job #2432580)

Utilizator AlexPop28Pop Alex-Nicolae AlexPop28 Data 24 iunie 2019 13:27:06
Problema Pod Scor 60
Compilator cpp-64 Status done
Runda Arhiva de probleme Marime 1.78 kb
#include <bits/stdc++.h>
#define DEBUG(x) cerr << (#x) << ": " << (x) << '\n'

using namespace std;

const int MOD = 9901;

struct Matrix {
  int n;
  int a[20][20];
  Matrix(int n) : n(n) {
    clear();
  }
  int* operator[](const int pos) {
    return a[pos];
  }
  void clear() {
    memset(a, 0, sizeof(a));
  }
};

void mult(Matrix &a, Matrix &b, Matrix &res) {
  res.clear();
  int n = a.n;
  for (int i = 0; i < n; ++i) {
    for (int k = 0; k < n; ++k) {
      for (int j = 0; j < n; ++j) {
        res[i][j] += a[i][k] * b[k][j] % MOD;
        if (res[i][j] >= MOD) res[i][j] -= MOD;
      }
    }
  }
}

void toPow(Matrix b, int e, Matrix &res, Matrix &aux) {
  res = b;
  --e;
  while (e) {
    if (e & 1)
      mult(res, b, aux), swap(res, aux);
    mult(b, b, aux), swap(b, aux);
    e >>= 1;
  }
}

int main() {
  freopen("pod.in", "r", stdin);
  freopen("pod.out", "w", stdout);
  ios::sync_with_stdio(0);
  cin.tie(0);

  int n, m, k; scanf("%d%d%d", &n, &m, &k);
  vector<int> v(m);
  for (int i = 0; i < m; ++i) {
    scanf("%d", &v[i]);
  }
  sort(v.begin(), v.end()); // ffs
  v.erase(unique(v.begin(), v.end()), v.end());
  Matrix tr(k);
  for (int i = 0; i < k - 1; ++i) {
    tr[i][i + 1] = 1;
  }
  tr[k - 1][0] = tr[k - 1][k - 1] = 1;
  
  Matrix dp(k);
  dp[k - 1][0] = 1; // dp = {{dp[-i],.., 0},..., {dp[0], 0}}
  
  int last = 0;
  Matrix aux1(k), aux2(k);
  for (int i = 0; i < m; ++i) {
    int e = v[i] - last;
    toPow(tr, e, aux1, aux2);
    mult(aux1, dp, aux2);
    swap(dp, aux2);
    dp[k - 1][0] = 0; // dp[v[i]] = 0
    last = v[i];
  }
  toPow(tr, n - last, aux1, aux2);
  mult(aux1, dp, aux2);
  swap(dp, aux2);
  cout << dp[k - 1][0] << endl;

#ifdef LOCAL_DEFINE
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
  return 0;
}