Submission #1055270

#	Time	Username	Problem	Language	Result	Execution time	Memory
1055270		juicy	Ruins 3 (JOI20_ruins3)	C++17	100 / 100	544 ms	3164 KiB

ruins3

// https://www.cnblogs.com/legendstane/p/loj-3276-uoj-506-joisc-2020-day-2-ruins-2-solution-counting-dp.html

#include <bits/stdc++.h>

using namespace std;

#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif

const int N = 605, MD = 1e9 + 7;

int n;
int dp[N], f[N][N], C[N][N], fact[N];
bool spec[2 * N];

int add(int a, int b) {
  if ((a += b) >= MD) {
    a -= MD;
  }
  return a;
}

int bpow(int a, int b = MD - 2) {
  int res = 1;
  for (; b; a = (long long) a * a % MD, b /= 2) {
    if (b & 1) {
      res = (long long) res * a % MD;
    }
  }
  return res;
}

int main() {
  ios::sync_with_stdio(false); cin.tie(nullptr);

  cin >> n;
  for (int i = 1; i <= n; ++i) {
    int x; cin >> x;
    spec[x] = 1;
  }
  f[0][0] = 1;
  fact[0] = 1;
  for (int i = 0; i <= n; ++i) {
    fact[i + 1] = (long long) fact[i] * (i + 1) % MD;
    C[i][0] = 1;
    for (int j = 1; j <= i; ++j) {
      C[i][j] = add(C[i - 1][j], C[i - 1][j - 1]);
    }
    for (int j = i; j <= min(i * 2, n); ++j) {
      f[i + 1][j] = add(f[i + 1][j], f[i][j]);
      f[i + 1][j + 1] = add(f[i + 1][j + 1], 2 * f[i][j] % MD);
      f[i + 1][j + 2] = add(f[i + 1][j + 2], f[i][j]);
    }
  }
  int cnt = 0;
  dp[0] = 1;
  for (int i = 2 * n; i > 0; --i) {
    if (spec[i]) {
      for (int j = n - 1; j >= 0; --j) {
        if (dp[j]) {
          for (int k = 1; j + k <= n; ++k) {
            dp[j + k] = add(dp[j + k], (long long) dp[j] * C[cnt - j][k - 1] % MD * fact[k - 1] % MD * f[k - 1][k - 1] % MD * (k + 1) % MD);
          }
        }
      }
      ++cnt;
    } else {
      int x = 2 * n - i - cnt;
      for (int j = 0; j <= n; ++j) {
        dp[j] = (long long) dp[j] * (j - x) % MD;
      }
    }
  }
  cout << (long long) dp[n] * bpow(bpow(2, n)) % MD;
  return 0;
}

• Subtask 1: 6 / 6
• Subtask 2: 52 / 52
• Subtask 3: 42 / 42