Cod sursa(job #2429333)

Utilizator AlexPop28Pop Alex-Nicolae AlexPop28 Data 9 iunie 2019 10:22:49
Problema Cowfood Scor 4
Compilator cpp-64 Status done
Runda Arhiva de probleme Marime 2.26 kb
#include <bits/stdc++.h>
#define DEBUG(x) cerr << (#x) << ": " << (x) << '\n'

using namespace std;

const int MOD = 3210121;

int add(int a, int b) {
  a += b;
  while (a >= MOD) a -= MOD;
  while (a < 0) a += MOD;
  return a;
}

int mul(int a, int b) {
  return 1LL *a * b % MOD;  
}

void calcChoose(int n, int k, vector<vector<int>> &choose) {
  for (int i = 0; i <= n; ++i) {
    choose[i][0] = 1;
    for (int j = 1, lim = min(i, k); j <= lim; ++j) {
      choose[i][j] = add(choose[i][j - 1], choose[i - 1][j]);
    }
  }
} 

int pinex(int pos, int n, int k, int s, int sign, vector<int> curr, 
          vector<int> &dp, vector<vector<int>> &mix) {
  if (pos == n) {
    int remaining = s, non_zero = 0;
    for (int &x : curr) {
      remaining -= x;
      non_zero += x != 0;
    }
    if (remaining < 0) return 0;
    if (non_zero >= 2) return sign * dp[remaining];
    if (non_zero == 1) return sign * add(dp[remaining], -remaining);
    assert(remaining == s);
    if (non_zero == 0) return sign * add(add(dp[remaining], -k * remaining), -1);
    assert(false);
  }
  int ret = pinex(pos + 1, n, k, s, sign, curr, dp, mix);
  for (int i = 0; i < k; ++i) {
    curr[i] = max(curr[i], mix[pos][i]);
  }
  ret = add(ret, pinex(pos + 1, n, k, s, sign * -1, curr, dp, mix));
  assert(ret >= 0 && ret < MOD);
  return ret;
}

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

  int k, s, n; cin >> k >> s >> n;
  vector<vector<int>> mix(n, vector<int>(k));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < k; ++j) {
      cin >> mix[i][j];
    }
  }
  vector<vector<int>> choose(s + k + 1, vector<int>(k + 1));
  calcChoose(s + k, k, choose);
  vector<int> dp(s + 1);
  // dp[i] = nr de moduri de a pune maxim i obiecte identice in k cutii distincte
  for (int i = 1; i <= s; ++i) {
    dp[i] = add(dp[i - 1], choose[i + k - 1][k - 1]);
  }
  vector<int> curr(k);
  int ans = add(dp[s], -mul(k, s)); // configuratii de tipul [x, 0, 0, 0, .., 0]
  ans = add(ans, -1); // multimea vida
  ans = add(ans, pinex(0, n, k, s, -1, curr, dp, mix));
  assert(ans >= 0 && ans < MOD);
  
  cout << ans << endl;
  
#ifdef LOCAL_DEFINE
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
  return 0;
}