답안 #220626

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
220626	2020-04-08T10:01:52 Z	rama_pang	Asceticism (JOI18_asceticism)	C++14	100 / 100	51 ms	1152 KB

asceticism

#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

#	결과	실행 시간	메모리	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

#	결과	실행 시간	메모리	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

#	결과	실행 시간	메모리	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

#	결과	실행 시간	메모리	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

답안 #220626

Compilation message

Subtask #1 4.0 / 4.0

Subtask #2 20.0 / 20.0

Subtask #3 25.0 / 25.0

Subtask #4 51.0 / 51.0

Subtask #1
4.0 / 4.0

Subtask #2
20.0 / 20.0

Subtask #3
25.0 / 25.0

Subtask #4
51.0 / 51.0