oj.uz

Submission #220626

# Submission time Handle Problem Language Result Execution time Memory
220626 2020-04-08T10:01:52 Z rama_pang Asceticism (JOI18_asceticism) C++14
100 / 100
 51 ms 1152 KB 
#include <bits/stdc++.h>
using namespace std;

const int MOD = 1e9 + 7;

void RADD(int &a, int b) {
  if ((a += b) >= MOD) a -= MOD;
  if (a < 0) a += MOD;
}

int MUL(int a, int b) {
  return 1ll * a * b % MOD;
}

int PushDP(int N, int K) { // O(N^2) DP solution
  vector<vector<int>> dp(N + 1, vector<int>(K + 2, 0));
  dp[0][0] = 1; // dp[i][j] = answer for N = i and K = j
  for (int i = 0; i < N; i++) {
    for (int j = 0; j <= K; j++) {
      // There are j positions where we insert at back, K doesn't increase
      RADD(dp[i + 1][j], MUL(dp[i][j], j)); 

      // Among i+1 possible places to be inserted, inserting other than the back increases K, 
      // of which there are (i + 1 - j) positions.
      RADD(dp[i + 1][j + 1], MUL(dp[i][j], i + 1 - j)); 
    }
  }
  return dp[N][K];
}

int PullDP(int N, int K) { // O(N^2) DP solution
  vector<vector<int>> dp(N + 1, vector<int>(K + 2, 0));
  dp[0][0] = 1; // dp[i][j] = answer for N = i and K = j
  for (int i = 1; i <= N; i++) {
    for (int j = 1; j <= K; j++) {
      RADD(dp[i][j], MUL(dp[i - 1][j], j));
      RADD(dp[i][j], MUL(dp[i - 1][j - 1], i + 1 - j));
    }
  }
  return dp[N][K];
}

int Power(int n, int x) {
  if (x == 0) return 1;
  int res = Power(n, x / 2);
  res = MUL(res, res);
  if (x & 1) res = MUL(res, n);
  return res;
}

int Solve(int N, int K) { // O(N log N) combinatorial solution
  vector<int> fact(N + 2);
  vector<int> invfact(N + 2);

  invfact[0] = fact[0] = 1;
  for (int i = 1; i <= N + 1; i++) {
    fact[i] = MUL(i, fact[i - 1]);
    invfact[i] = Power(fact[i], MOD - 2); // by Fermat's Little Theorem
  }

  auto C = [&](int n, int k) { // binomial
    if (k < 0 || k > n) return 0;
    return MUL(fact[n], MUL(invfact[k], invfact[n - k]));
  };

  int ans = 0;

  // sum_{k = 0}^{K}((-1)^k * C(N + 1, k) * (K - k + 1)^N)
  for (int k = 0, sgn = 1; k < K; k++, sgn *= -1) {
    RADD(ans, sgn * MUL(C(N + 1, k), Power(K - k, N)));
  }

  return ans;
}

int main() {
  int N, K;
  cin >> N >> K;
  cout << Solve(N, K) << "\n";
  return 0;
}

Subtask #1
4.0 / 4.0

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

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB Output is correct
2 Correct 5 ms 256 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 256 KB Output is correct
7 Correct 4 ms 256 KB Output is correct
8 Correct 4 ms 256 KB Output is correct
9 Correct 5 ms 256 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 372 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 256 KB Output is correct
14 Correct 4 ms 256 KB Output is correct
15 Correct 5 ms 256 KB Output is correct
16 Correct 5 ms 256 KB Output is correct
17 Correct 5 ms 256 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
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB Output is correct
2 Correct 5 ms 256 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 256 KB Output is correct
7 Correct 4 ms 256 KB Output is correct
8 Correct 4 ms 256 KB Output is correct
9 Correct 5 ms 256 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 372 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 256 KB Output is correct
14 Correct 4 ms 256 KB Output is correct
15 Correct 5 ms 256 KB Output is correct
16 Correct 5 ms 256 KB Output is correct
17 Correct 5 ms 256 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 5 ms 384 KB Output is correct
22 Correct 5 ms 384 KB Output is correct
23 Correct 5 ms 256 KB Output is correct
24 Correct 5 ms 256 KB Output is correct
25 Correct 5 ms 256 KB Output is correct
26 Correct 5 ms 384 KB Output is correct
27 Correct 5 ms 256 KB Output is correct
28 Correct 5 ms 256 KB Output is correct
29 Correct 5 ms 384 KB Output is correct
30 Correct 5 ms 256 KB Output is correct

Subtask #4
51.0 / 51.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB Output is correct
2 Correct 5 ms 256 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 256 KB Output is correct
7 Correct 4 ms 256 KB Output is correct
8 Correct 4 ms 256 KB Output is correct
9 Correct 5 ms 256 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 372 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 256 KB Output is correct
14 Correct 4 ms 256 KB Output is correct
15 Correct 5 ms 256 KB Output is correct
16 Correct 5 ms 256 KB Output is correct
17 Correct 5 ms 256 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 5 ms 384 KB Output is correct
22 Correct 5 ms 384 KB Output is correct
23 Correct 5 ms 256 KB Output is correct
24 Correct 5 ms 256 KB Output is correct
25 Correct 5 ms 256 KB Output is correct
26 Correct 5 ms 384 KB Output is correct
27 Correct 5 ms 256 KB Output is correct
28 Correct 5 ms 256 KB Output is correct
29 Correct 5 ms 384 KB Output is correct
30 Correct 5 ms 256 KB Output is correct
31 Correct 37 ms 1152 KB Output is correct
32 Correct 36 ms 1152 KB Output is correct
33 Correct 37 ms 1152 KB Output is correct
34 Correct 40 ms 1152 KB Output is correct
35 Correct 50 ms 1152 KB Output is correct
36 Correct 50 ms 1152 KB Output is correct
37 Correct 51 ms 1152 KB Output is correct
38 Correct 12 ms 384 KB Output is correct
39 Correct 32 ms 896 KB Output is correct
40 Correct 42 ms 1152 KB Output is correct