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Submission #498649

# Submission time Handle Problem Language Result Execution time Memory
498649 2021-12-26T04:43:17 Z model_code NoM (RMI21_nom) C++17
100 / 100
 173 ms 63524 KB 
// nom_100_popovici.cpp
#include <iostream>
#include <fstream>
#include <cassert>
 
/*
     Time       O(M * N + N ^ 2)
     Memory     O(M * N + N ^ 2)
*/
 
 
constexpr int MOD = (int)1e9 + 7;
constexpr int MAXN = 3000;
constexpr int MAXM = 3000;
 
int comb[2 * MAXN + 1][2 * MAXN + 1];
int pow2[2 * MAXN + 1], fact[2 * MAXN + 1];
int counter[MAXM];
 
inline void add(int& x, int y) {
    x += y;
    if (x >= MOD)
        x -= MOD;
}
 
void prec(int N, int M) {
    for (int i = 0; i <= 2 * N; i++) {
        comb[i][0] = 1;
        for (int j = 1; j <= i; j++) {
            add(comb[i][j], comb[i - 1][j]);
            add(comb[i][j], comb[i - 1][j - 1]);
        }
    }
 
    for (int i = 0; i < 2 * N; i++) {
        counter[i % M]++;
    }
 
    pow2[0] = fact[0] = 1;
    for (int i = 1; i <= 2 * N; i++) {
        pow2[i] = (2LL * pow2[i - 1]) % MOD;
        fact[i] = (1LL * i * fact[i - 1]) % MOD;
    }
}
 
 
int dp[MAXM + 1][MAXN + 1];
int ways[MAXN + 1];
 
 
int main() {
    std::istream& fin = std::cin;
    std::ostream& fout = std::cout;
 
    int N, M;
    fin >> N >> M;
 
    prec(N, M);
 
    dp[M][0] = 1;
    for (int rem = M; rem > 0; rem--) {
        for (int i = 0; i <= N; i++) {
            if (dp[rem][i] == 0) 
                continue;
 
            for (int j = 0; 2 * j <= counter[rem - 1]; j++) {
                if (i + j > N)
                    assert(0);
 
                int current = (1LL * comb[N - i][j] * comb[counter[rem - 1]][2 * j]) % MOD;
                current = (1LL * current * fact[2 * j]) % MOD;
                current = (1LL * current * dp[rem][i]) % MOD;
                add(dp[rem - 1][i + j], current);
            }
        }
    }
 
    for (int i = N; i >= 0; i--) {
        ways[i] = (1LL * dp[0][i] * fact[2 * N - 2 * i]) % MOD;
        for (int j = i + 1; j <= N; j++) {
            int current = MOD - (1LL * ways[j] * comb[j][i]) % MOD;
            add(ways[i], current);
        }
    }
 
    fout << ways[0] << "\n";
 
    return 0;
}
 
/*
{1}
        dp[rem][i] * coef -> dp[rem - 1][i + j],    coef = C(N - i, j) * A(counter[rem - 1], 2 * j)
{1}
        ways[i] = dp[0][i] * (2 * N - 2 * i)!
{1}
        ways[i] = ways[i] - sum(ways[j] * C(j, i))
*/

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 1356 KB Output is correct
12 Correct 1 ms 1100 KB Output is correct
13 Correct 1 ms 844 KB Output is correct
14 Correct 1 ms 972 KB Output is correct
15 Correct 1 ms 1100 KB Output is correct
16 Correct 1 ms 1100 KB Output is correct
17 Correct 1 ms 972 KB Output is correct
18 Correct 1 ms 1100 KB Output is correct
19 Correct 1 ms 972 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 1356 KB Output is correct
12 Correct 1 ms 1100 KB Output is correct
13 Correct 1 ms 844 KB Output is correct
14 Correct 1 ms 972 KB Output is correct
15 Correct 1 ms 1100 KB Output is correct
16 Correct 1 ms 1100 KB Output is correct
17 Correct 1 ms 972 KB Output is correct
18 Correct 1 ms 1100 KB Output is correct
19 Correct 1 ms 972 KB Output is correct
20 Correct 2 ms 1868 KB Output is correct
21 Correct 2 ms 1996 KB Output is correct
22 Correct 4 ms 4172 KB Output is correct
23 Correct 3 ms 2764 KB Output is correct
24 Correct 5 ms 4044 KB Output is correct
25 Correct 4 ms 3916 KB Output is correct
26 Correct 2 ms 2892 KB Output is correct
27 Correct 6 ms 4812 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 1356 KB Output is correct
12 Correct 1 ms 1100 KB Output is correct
13 Correct 1 ms 844 KB Output is correct
14 Correct 1 ms 972 KB Output is correct
15 Correct 1 ms 1100 KB Output is correct
16 Correct 1 ms 1100 KB Output is correct
17 Correct 1 ms 972 KB Output is correct
18 Correct 1 ms 1100 KB Output is correct
19 Correct 1 ms 972 KB Output is correct
20 Correct 2 ms 1868 KB Output is correct
21 Correct 2 ms 1996 KB Output is correct
22 Correct 4 ms 4172 KB Output is correct
23 Correct 3 ms 2764 KB Output is correct
24 Correct 5 ms 4044 KB Output is correct
25 Correct 4 ms 3916 KB Output is correct
26 Correct 2 ms 2892 KB Output is correct
27 Correct 6 ms 4812 KB Output is correct
28 Correct 9 ms 8524 KB Output is correct
29 Correct 14 ms 10752 KB Output is correct
30 Correct 15 ms 11728 KB Output is correct
31 Correct 11 ms 8660 KB Output is correct
32 Correct 13 ms 11260 KB Output is correct
33 Correct 16 ms 13392 KB Output is correct
34 Correct 32 ms 19096 KB Output is correct

Subtask #5
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 1356 KB Output is correct
12 Correct 1 ms 1100 KB Output is correct
13 Correct 1 ms 844 KB Output is correct
14 Correct 1 ms 972 KB Output is correct
15 Correct 1 ms 1100 KB Output is correct
16 Correct 1 ms 1100 KB Output is correct
17 Correct 1 ms 972 KB Output is correct
18 Correct 1 ms 1100 KB Output is correct
19 Correct 1 ms 972 KB Output is correct
20 Correct 2 ms 1868 KB Output is correct
21 Correct 2 ms 1996 KB Output is correct
22 Correct 4 ms 4172 KB Output is correct
23 Correct 3 ms 2764 KB Output is correct
24 Correct 5 ms 4044 KB Output is correct
25 Correct 4 ms 3916 KB Output is correct
26 Correct 2 ms 2892 KB Output is correct
27 Correct 6 ms 4812 KB Output is correct
28 Correct 9 ms 8524 KB Output is correct
29 Correct 14 ms 10752 KB Output is correct
30 Correct 15 ms 11728 KB Output is correct
31 Correct 11 ms 8660 KB Output is correct
32 Correct 13 ms 11260 KB Output is correct
33 Correct 16 ms 13392 KB Output is correct
34 Correct 32 ms 19096 KB Output is correct
35 Correct 57 ms 34220 KB Output is correct
36 Correct 98 ms 51768 KB Output is correct
37 Correct 50 ms 33484 KB Output is correct
38 Correct 96 ms 40868 KB Output is correct
39 Correct 89 ms 42980 KB Output is correct
40 Correct 173 ms 63524 KB Output is correct