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Submission #212789

# Submission time Handle Problem Language Result Execution time Memory
212789 2020-03-24T10:02:10 Z IOrtroiii Ruins 3 (JOI20_ruins3) C++14
100 / 100
 202 ms 1920 KB 
#include <bits/stdc++.h>

using namespace std;

const int MOD = 1e9 + 7;
using ll = long long;

int mult(int x, int y) {
   return (long long) x * y % MOD;
}

void add(int &x, int y) {
   x += y;
   if (x >= MOD) x -= MOD;
}

int main() {
   ios_base::sync_with_stdio(false);
   int N;
   cin >> N;
   vector<bool> alive(2 * N);
   for (int i = 0; i < N; ++i) {
      int x;
      cin >> x;
      alive[--x] = true;
   }
   vector<int> ways(N + 1);
   {
      vector<vector<int>> dp(N + 1, vector<int>(N + 1));
      dp[0][0] = 1;
      for (int i = 1; i <= N; ++i) {
         for (int j = 0; j <= i; ++j) {
            dp[i][j] = dp[i - 1][j];
            if (j > 0) add(dp[i][j], mult(2 * j, dp[i - 1][j - 1]));
            if (j > 1) add(dp[i][j], mult(j * (j - 1), dp[i - 1][j - 2]));
         }
      }
      for (int i = 1; i <= N; ++i) {
         ways[i] = mult(dp[i - 1][i - 1], i + 1);
      }
   }
   vector<vector<int>> C(N + 1, vector<int>(N + 1));
   for (int i = 0; i <= N; ++i) {
      C[i][0] = 1;
      for (int j = 1; j <= i; ++j) {
         C[i][j] = C[i - 1][j] + C[i - 1][j - 1];
         if (C[i][j] >= MOD) C[i][j] -= MOD;
      }
   }
   vector<int> dp(N + 1);
   dp[0] = 1;
   int cnt0 = 0;
   int cnt1 = 0;
   for (int i = 2 * N - 1; i >= 0; --i) {
      vector<int> ndp(N + 1);
      if (alive[i]) {
         for (int j = cnt0; j <= cnt1; ++j) {
            if (!dp[j]) continue;
            add(ndp[j], dp[j]);
            for (int k = j + 1; k <= cnt1 + 1; ++k) {
               add(ndp[k], mult(mult(C[cnt1 - j][k - j - 1], ways[k - j]), dp[j]));
            }
         }
         ++cnt1;
      } else {
         for (int j = cnt0; j <= cnt1; ++j) {
            add(ndp[j], mult(j - cnt0, dp[j]));
         }
         ++cnt0;
      }
      dp = ndp;
   }
   int ans = dp[N];
   for (int i = 0; i < N; ++i) ans = mult(ans, (MOD + 1) >> 1);
   cout << ans << "\n";
   return 0;
}

Subtask #1
6.0 / 6.0

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

Subtask #2
52.0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 384 KB Output is correct
2 Correct 4 ms 384 KB Output is correct
3 Correct 4 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 4 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 4 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 4 ms 384 KB Output is correct
15 Correct 5 ms 392 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 384 KB Output is correct
19 Correct 5 ms 384 KB Output is correct
20 Correct 5 ms 384 KB Output is correct

Subtask #3
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 384 KB Output is correct
2 Correct 4 ms 384 KB Output is correct
3 Correct 4 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 4 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 4 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 4 ms 384 KB Output is correct
15 Correct 5 ms 392 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 384 KB Output is correct
19 Correct 5 ms 384 KB Output is correct
20 Correct 5 ms 384 KB Output is correct
21 Correct 9 ms 1792 KB Output is correct
22 Correct 10 ms 1920 KB Output is correct
23 Correct 8 ms 1792 KB Output is correct
24 Correct 10 ms 1792 KB Output is correct
25 Correct 8 ms 1792 KB Output is correct
26 Correct 9 ms 1792 KB Output is correct
27 Correct 12 ms 1792 KB Output is correct
28 Correct 8 ms 1792 KB Output is correct
29 Correct 8 ms 1792 KB Output is correct
30 Correct 202 ms 1792 KB Output is correct
31 Correct 108 ms 1792 KB Output is correct
32 Correct 152 ms 1792 KB Output is correct
33 Correct 188 ms 1792 KB Output is correct
34 Correct 124 ms 1792 KB Output is correct
35 Correct 158 ms 1792 KB Output is correct
36 Correct 193 ms 1792 KB Output is correct