oj.uz

Submission #434952

# Submission time Handle Problem Language Result Execution time Memory
434952 2021-06-22T13:53:08 Z Lam_lai_cuoc_doi Boat (APIO16_boat) C++17
58 / 100
 2000 ms 8336 KB 
#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;

constexpr bool typetest = 0;
constexpr int N = 5e2 + 2;
constexpr ll mod = 1e9 + 7;

/* https://codeforces.com/blog/entry/57324?#comment-409800 */

int n;

/// dp[i][j]: choose i first elements in j first blocks
ll dp[N][N * 2], d[N * 2][N], inv[N];

pair<int, int> s[N];
vector<int> block;

void Read()
{
    cin >> n;

    block.reserve(n * 2);

    for (int i = 1; i <= n; ++i)
    {
        cin >> s[i].first >> s[i].second;
        block.emplace_back(s[i].first - 1);
        block.emplace_back(s[i].second);
    }

    sort(block.begin(), block.end());
    block.resize(unique(block.begin(), block.end()) - block.begin());
}

ll Pow(ll a, ll b)
{
    ll ans(1);

    for (; b > 0; b >>= 1)
    {
        if (b & 1)
            ans = ans * a % mod;
        a = a * a % mod;
    }

    return ans;
}

void Solve()
{
    inv[0] = 1;
    for (int i = 1; i <= n; ++i)
        inv[i] = inv[i - 1] * i % mod;

    ll tmp = Pow(inv[n], mod - 2);

    for (int i = n; i; --i)
    {
        inv[i] = tmp * inv[i - 1] % mod;
        (tmp *= i) %= mod;
    }

    /// Pre-calculate d[], I'll define d[] below

    for (int i = 1; i < (int)block.size(); ++i)
    {
        d[i][0] = 1;
        for (int j = 1; j <= n; ++j)
        {
            ll c1(1), c2(1);
            for (int t = 0; t < j && t + 1 <= block[i] - block[i - 1]; ++t)
            {
                (c2 *= inv[t + 1] * (block[i] - block[i - 1] - (t + 1) + 1) % mod) %= mod;

                (d[i][j] += c1 * c2) %= mod;

                (c1 *= inv[t + 1] * (j - 1 - (t + 1) + 1) % mod) %= mod;
            }
        }
    }

    for (int i = 0; i < (int)block.size(); ++i)
        dp[0][i] = 1;

    for (int i = 1; i <= n; ++i)
    {
        dp[i][0] = 1;
        for (int j = 1; j < (int)block.size(); ++j)
        {
            /// no element in j block
            dp[i][j] = dp[i][j - 1];

            /// there're some elements in j block
            for (int t = i, cnt(0); t; --t)
                if (s[t].first <= block[j - 1] + 1 && s[t].second >= block[j])
                {
                    ++cnt;
                    (dp[i][j] += dp[t - 1][j - 1] * d[j][cnt]) %= mod;
                    /// d[j][i] : number of ways to make array that have less or equal i element only from block j
                    /// to prevent overlap counting, we need to change sthg about definition
                }
        }
    }

    cout << dp[n][block.size() - 1] - 1;
}

int32_t main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int t(1);
    if (typetest)
        cin >> t;
    for (int _ = 1; _ <= t; ++_)
    {
        Read();
        Solve();
    }
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1031 ms 8124 KB Output is correct
2 Correct 1114 ms 8272 KB Output is correct
3 Correct 1055 ms 8132 KB Output is correct
4 Correct 1120 ms 8172 KB Output is correct
5 Correct 1016 ms 8180 KB Output is correct
6 Correct 900 ms 8164 KB Output is correct
7 Correct 904 ms 8080 KB Output is correct
8 Correct 906 ms 8216 KB Output is correct
9 Correct 908 ms 8140 KB Output is correct
10 Correct 900 ms 8264 KB Output is correct
11 Correct 896 ms 8244 KB Output is correct
12 Correct 901 ms 8080 KB Output is correct
13 Correct 988 ms 8232 KB Output is correct
14 Correct 906 ms 8132 KB Output is correct
15 Correct 916 ms 8196 KB Output is correct
16 Correct 214 ms 3860 KB Output is correct
17 Correct 200 ms 3800 KB Output is correct
18 Correct 191 ms 3632 KB Output is correct
19 Correct 199 ms 3776 KB Output is correct
20 Correct 200 ms 3744 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1031 ms 8124 KB Output is correct
2 Correct 1114 ms 8272 KB Output is correct
3 Correct 1055 ms 8132 KB Output is correct
4 Correct 1120 ms 8172 KB Output is correct
5 Correct 1016 ms 8180 KB Output is correct
6 Correct 900 ms 8164 KB Output is correct
7 Correct 904 ms 8080 KB Output is correct
8 Correct 906 ms 8216 KB Output is correct
9 Correct 908 ms 8140 KB Output is correct
10 Correct 900 ms 8264 KB Output is correct
11 Correct 896 ms 8244 KB Output is correct
12 Correct 901 ms 8080 KB Output is correct
13 Correct 988 ms 8232 KB Output is correct
14 Correct 906 ms 8132 KB Output is correct
15 Correct 916 ms 8196 KB Output is correct
16 Correct 214 ms 3860 KB Output is correct
17 Correct 200 ms 3800 KB Output is correct
18 Correct 191 ms 3632 KB Output is correct
19 Correct 199 ms 3776 KB Output is correct
20 Correct 200 ms 3744 KB Output is correct
21 Correct 440 ms 7868 KB Output is correct
22 Correct 478 ms 7832 KB Output is correct
23 Correct 399 ms 7760 KB Output is correct
24 Correct 464 ms 7876 KB Output is correct
25 Correct 443 ms 7780 KB Output is correct
26 Correct 593 ms 7616 KB Output is correct
27 Correct 555 ms 7780 KB Output is correct
28 Correct 569 ms 7644 KB Output is correct
29 Correct 576 ms 7640 KB Output is correct
30 Correct 891 ms 8136 KB Output is correct
31 Correct 917 ms 8260 KB Output is correct
32 Correct 904 ms 8104 KB Output is correct
33 Correct 896 ms 8252 KB Output is correct
34 Correct 866 ms 8336 KB Output is correct
35 Correct 1014 ms 8172 KB Output is correct
36 Correct 1042 ms 8172 KB Output is correct
37 Correct 1077 ms 8240 KB Output is correct
38 Correct 1031 ms 8152 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 1604 KB Output is correct
2 Correct 17 ms 1612 KB Output is correct
3 Correct 16 ms 1596 KB Output is correct
4 Correct 16 ms 1604 KB Output is correct
5 Correct 22 ms 1552 KB Output is correct
6 Correct 17 ms 1636 KB Output is correct
7 Correct 19 ms 1604 KB Output is correct
8 Correct 18 ms 1620 KB Output is correct
9 Correct 18 ms 1612 KB Output is correct
10 Correct 20 ms 1652 KB Output is correct
11 Correct 20 ms 1568 KB Output is correct
12 Correct 19 ms 1604 KB Output is correct
13 Correct 17 ms 1612 KB Output is correct
14 Correct 18 ms 1576 KB Output is correct
15 Correct 18 ms 1552 KB Output is correct
16 Correct 8 ms 1228 KB Output is correct
17 Correct 9 ms 1164 KB Output is correct
18 Correct 8 ms 1228 KB Output is correct
19 Correct 8 ms 1180 KB Output is correct
20 Correct 8 ms 1172 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1031 ms 8124 KB Output is correct
2 Correct 1114 ms 8272 KB Output is correct
3 Correct 1055 ms 8132 KB Output is correct
4 Correct 1120 ms 8172 KB Output is correct
5 Correct 1016 ms 8180 KB Output is correct
6 Correct 900 ms 8164 KB Output is correct
7 Correct 904 ms 8080 KB Output is correct
8 Correct 906 ms 8216 KB Output is correct
9 Correct 908 ms 8140 KB Output is correct
10 Correct 900 ms 8264 KB Output is correct
11 Correct 896 ms 8244 KB Output is correct
12 Correct 901 ms 8080 KB Output is correct
13 Correct 988 ms 8232 KB Output is correct
14 Correct 906 ms 8132 KB Output is correct
15 Correct 916 ms 8196 KB Output is correct
16 Correct 214 ms 3860 KB Output is correct
17 Correct 200 ms 3800 KB Output is correct
18 Correct 191 ms 3632 KB Output is correct
19 Correct 199 ms 3776 KB Output is correct
20 Correct 200 ms 3744 KB Output is correct
21 Correct 440 ms 7868 KB Output is correct
22 Correct 478 ms 7832 KB Output is correct
23 Correct 399 ms 7760 KB Output is correct
24 Correct 464 ms 7876 KB Output is correct
25 Correct 443 ms 7780 KB Output is correct
26 Correct 593 ms 7616 KB Output is correct
27 Correct 555 ms 7780 KB Output is correct
28 Correct 569 ms 7644 KB Output is correct
29 Correct 576 ms 7640 KB Output is correct
30 Correct 891 ms 8136 KB Output is correct
31 Correct 917 ms 8260 KB Output is correct
32 Correct 904 ms 8104 KB Output is correct
33 Correct 896 ms 8252 KB Output is correct
34 Correct 866 ms 8336 KB Output is correct
35 Correct 1014 ms 8172 KB Output is correct
36 Correct 1042 ms 8172 KB Output is correct
37 Correct 1077 ms 8240 KB Output is correct
38 Correct 1031 ms 8152 KB Output is correct
39 Correct 19 ms 1604 KB Output is correct
40 Correct 17 ms 1612 KB Output is correct
41 Correct 16 ms 1596 KB Output is correct
42 Correct 16 ms 1604 KB Output is correct
43 Correct 22 ms 1552 KB Output is correct
44 Correct 17 ms 1636 KB Output is correct
45 Correct 19 ms 1604 KB Output is correct
46 Correct 18 ms 1620 KB Output is correct
47 Correct 18 ms 1612 KB Output is correct
48 Correct 20 ms 1652 KB Output is correct
49 Correct 20 ms 1568 KB Output is correct
50 Correct 19 ms 1604 KB Output is correct
51 Correct 17 ms 1612 KB Output is correct
52 Correct 18 ms 1576 KB Output is correct
53 Correct 18 ms 1552 KB Output is correct
54 Correct 8 ms 1228 KB Output is correct
55 Correct 9 ms 1164 KB Output is correct
56 Correct 8 ms 1228 KB Output is correct
57 Correct 8 ms 1180 KB Output is correct
58 Correct 8 ms 1172 KB Output is correct
59 Execution timed out 2029 ms 8180 KB Time limit exceeded
60 Halted 0 ms 0 KB -