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Submission #855913

# Submission time Handle Problem Language Result Execution time Memory
855913 2023-10-02T08:56:41 Z wakandaaa Magneti (COCI21_magneti) C++17
110 / 110
 105 ms 121876 KB 
#include <bits/stdc++.h>

using namespace std;

#define mp make_pair
#define fi first
#define se second
#define all(x) x.begin(), x.end()

#define getbit(x, i) (((x) >> (i)) & 1)
#define bit(x) (1 << (x))
#define popcount __builtin_popcountll

mt19937_64 rd(chrono::steady_clock::now().time_since_epoch().count());
long long rand(long long l, long long r) {
    return l + rd() % (r - l + 1);
}

const int N = 1e6 + 5;
const int mod = 1e9 + 7; // 998244353;
const int lg = 25; // lg + 1
const int inf = 1e9; // INT_MAX;
const long long llinf = 1e18; // LLONG_MAX;

template<class X, class Y>
bool minimize(X &a, Y b) {
    return a > b ? (a = b, true) : false;
}

template<class X, class Y>
bool maximize(X &a, Y b) {
    return a < b ? (a = b, true) : false;
}

template<class X, class Y>
bool add(X &a, Y b) {
    a += b;
    while (a >= mod) a -= mod;
    while (a < 0) a += mod;
    return true;
}

const int MAX_N = 50 + 5;
const int MAX_L = 1e4 + 5;

int n, l;
int a[N];
int f[MAX_N][MAX_N][MAX_L];

int pw(int x, int y) {
    int res = 1;
    while (y) {
        if (y & 1) res = 1LL * res * x % mod;
        x = 1LL * x * x % mod;
        y >>= 1;
    }
    return res % mod;
}
int fac[N], inv[N];
void pre() {
    int n = 1e6;
    fac[0] = 1;
    for (int i = 1; i <= n; ++i) fac[i] = 1LL * fac[i - 1] * i % mod;
    inv[n] = pw(fac[n], mod - 2);
    for (int i = n; i >= 1; --i) inv[i - 1] = 1LL * inv[i] * i % mod;
}
int nCk(int n, int k) {
    if (k > n || k < 0) return 0;
    return 1LL * fac[n] * inv[k] % mod * inv[n - k] % mod;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    pre();

    cin >> n >> l;
    for (int i = 1; i <= n; ++i)
        cin >> a[i];

    sort(a + 1, a + n + 1);

    f[0][0][0] = 1;

    for (int i = 1; i <= n; ++i)
        for (int j = 1; j <= i; ++j)
            for (int k = 1; k <= l; ++k) {
                int r = a[i];
                // new component
                f[i][j][k] = f[i - 1][j - 1][k - 1];

                // append
                if (k - r >= 0)
                    add(f[i][j][k], 1LL * f[i - 1][j][k - r] * 2 * j % mod);
                
                // join
                // (r - 1) + (r - 1) + 1 = 2r - 1
                if (k - 2 * r + 1 >= 0)
                    add(f[i][j][k], 1LL * f[i - 1][j + 1][k - 2 * r + 1] * j * (j + 1) % mod);
            }

    int res = 0;
    for (int i = 1; i <= l; ++i)
        add(res, 1LL * f[n][1][i] * nCk(n + l - i, n) % mod);

    cout << res;

    return 0;
}

/*

*/

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 89 ms 121640 KB Output is correct
2 Correct 21 ms 121656 KB Output is correct
3 Correct 16 ms 35472 KB Output is correct
4 Correct 13 ms 21204 KB Output is correct
5 Correct 19 ms 58072 KB Output is correct
6 Correct 38 ms 72424 KB Output is correct
7 Correct 32 ms 117520 KB Output is correct
8 Correct 11 ms 12892 KB Output is correct
9 Correct 21 ms 90816 KB Output is correct
10 Correct 11 ms 12764 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 33368 KB Output is correct
2 Correct 11 ms 16988 KB Output is correct
3 Correct 15 ms 33440 KB Output is correct
4 Correct 13 ms 21136 KB Output is correct
5 Correct 16 ms 33624 KB Output is correct
6 Correct 13 ms 25180 KB Output is correct
7 Correct 15 ms 33244 KB Output is correct
8 Correct 13 ms 33416 KB Output is correct
9 Correct 12 ms 23132 KB Output is correct
10 Correct 11 ms 12892 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 76380 KB Output is correct
2 Correct 15 ms 55956 KB Output is correct
3 Correct 17 ms 76380 KB Output is correct
4 Correct 16 ms 57948 KB Output is correct
5 Correct 17 ms 76496 KB Output is correct
6 Correct 14 ms 53852 KB Output is correct
7 Correct 17 ms 76508 KB Output is correct
8 Correct 13 ms 33372 KB Output is correct
9 Correct 16 ms 58076 KB Output is correct
10 Correct 13 ms 33248 KB Output is correct

Subtask #4
50.0 / 50.0

# Verdict Execution time Memory Grader output
1 Correct 89 ms 121640 KB Output is correct
2 Correct 21 ms 121656 KB Output is correct
3 Correct 16 ms 35472 KB Output is correct
4 Correct 13 ms 21204 KB Output is correct
5 Correct 19 ms 58072 KB Output is correct
6 Correct 38 ms 72424 KB Output is correct
7 Correct 32 ms 117520 KB Output is correct
8 Correct 11 ms 12892 KB Output is correct
9 Correct 21 ms 90816 KB Output is correct
10 Correct 11 ms 12764 KB Output is correct
11 Correct 15 ms 33368 KB Output is correct
12 Correct 11 ms 16988 KB Output is correct
13 Correct 15 ms 33440 KB Output is correct
14 Correct 13 ms 21136 KB Output is correct
15 Correct 16 ms 33624 KB Output is correct
16 Correct 13 ms 25180 KB Output is correct
17 Correct 15 ms 33244 KB Output is correct
18 Correct 13 ms 33416 KB Output is correct
19 Correct 12 ms 23132 KB Output is correct
20 Correct 11 ms 12892 KB Output is correct
21 Correct 19 ms 76380 KB Output is correct
22 Correct 15 ms 55956 KB Output is correct
23 Correct 17 ms 76380 KB Output is correct
24 Correct 16 ms 57948 KB Output is correct
25 Correct 17 ms 76496 KB Output is correct
26 Correct 14 ms 53852 KB Output is correct
27 Correct 17 ms 76508 KB Output is correct
28 Correct 13 ms 33372 KB Output is correct
29 Correct 16 ms 58076 KB Output is correct
30 Correct 13 ms 33248 KB Output is correct
31 Correct 103 ms 121876 KB Output is correct
32 Correct 69 ms 111184 KB Output is correct
33 Correct 101 ms 121684 KB Output is correct
34 Correct 35 ms 70328 KB Output is correct
35 Correct 105 ms 121560 KB Output is correct
36 Correct 19 ms 41820 KB Output is correct
37 Correct 101 ms 121640 KB Output is correct
38 Correct 33 ms 117584 KB Output is correct
39 Correct 94 ms 121656 KB Output is correct
40 Correct 35 ms 72272 KB Output is correct
41 Correct 97 ms 121572 KB Output is correct
42 Correct 13 ms 29276 KB Output is correct
43 Correct 86 ms 121584 KB Output is correct
44 Correct 21 ms 53848 KB Output is correct
45 Correct 88 ms 121592 KB Output is correct
46 Correct 11 ms 14936 KB Output is correct
47 Correct 22 ms 78608 KB Output is correct
48 Correct 20 ms 94812 KB Output is correct
49 Correct 13 ms 27244 KB Output is correct
50 Correct 13 ms 35420 KB Output is correct