oj.uz

Submission #434950

# Submission time Handle Problem Language Result Execution time Memory
434950 2021-06-22T13:39:30 Z Lam_lai_cuoc_doi Boat (APIO16_boat) C++17
58 / 100
 2000 ms 8276 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] = Pow(i, mod - 2) % 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 = c2 * ((block[i] - block[i - 1] - (t + 1) + 1) % mod) % mod * inv[t + 1] % mod;

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

                c1 = c1 * (j - 1 - (t + 1) + 1) % mod * inv[t + 1] % 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;
                    //cout << cnt << "+" << t << "-";
                    (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[i][j] << " ";
        }

        //cout << "\n";
    }

    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 1138 ms 8068 KB Output is correct
2 Correct 1144 ms 8140 KB Output is correct
3 Correct 1131 ms 8080 KB Output is correct
4 Correct 1153 ms 8244 KB Output is correct
5 Correct 1153 ms 8276 KB Output is correct
6 Correct 1014 ms 8120 KB Output is correct
7 Correct 1022 ms 8148 KB Output is correct
8 Correct 1022 ms 8152 KB Output is correct
9 Correct 1069 ms 8156 KB Output is correct
10 Correct 1055 ms 8244 KB Output is correct
11 Correct 1059 ms 8108 KB Output is correct
12 Correct 1051 ms 8128 KB Output is correct
13 Correct 1008 ms 8132 KB Output is correct
14 Correct 1067 ms 8076 KB Output is correct
15 Correct 1047 ms 8124 KB Output is correct
16 Correct 213 ms 3652 KB Output is correct
17 Correct 220 ms 3736 KB Output is correct
18 Correct 230 ms 3764 KB Output is correct
19 Correct 237 ms 3688 KB Output is correct
20 Correct 214 ms 3636 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1138 ms 8068 KB Output is correct
2 Correct 1144 ms 8140 KB Output is correct
3 Correct 1131 ms 8080 KB Output is correct
4 Correct 1153 ms 8244 KB Output is correct
5 Correct 1153 ms 8276 KB Output is correct
6 Correct 1014 ms 8120 KB Output is correct
7 Correct 1022 ms 8148 KB Output is correct
8 Correct 1022 ms 8152 KB Output is correct
9 Correct 1069 ms 8156 KB Output is correct
10 Correct 1055 ms 8244 KB Output is correct
11 Correct 1059 ms 8108 KB Output is correct
12 Correct 1051 ms 8128 KB Output is correct
13 Correct 1008 ms 8132 KB Output is correct
14 Correct 1067 ms 8076 KB Output is correct
15 Correct 1047 ms 8124 KB Output is correct
16 Correct 213 ms 3652 KB Output is correct
17 Correct 220 ms 3736 KB Output is correct
18 Correct 230 ms 3764 KB Output is correct
19 Correct 237 ms 3688 KB Output is correct
20 Correct 214 ms 3636 KB Output is correct
21 Correct 420 ms 8000 KB Output is correct
22 Correct 432 ms 7924 KB Output is correct
23 Correct 414 ms 7772 KB Output is correct
24 Correct 442 ms 7692 KB Output is correct
25 Correct 435 ms 7796 KB Output is correct
26 Correct 518 ms 7660 KB Output is correct
27 Correct 528 ms 7760 KB Output is correct
28 Correct 574 ms 7732 KB Output is correct
29 Correct 559 ms 7656 KB Output is correct
30 Correct 1125 ms 8224 KB Output is correct
31 Correct 1038 ms 8172 KB Output is correct
32 Correct 1066 ms 8132 KB Output is correct
33 Correct 1047 ms 8200 KB Output is correct
34 Correct 987 ms 8116 KB Output is correct
35 Correct 1090 ms 8088 KB Output is correct
36 Correct 1124 ms 8056 KB Output is correct
37 Correct 1138 ms 8136 KB Output is correct
38 Correct 1092 ms 8132 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 18 ms 1612 KB Output is correct
2 Correct 18 ms 1668 KB Output is correct
3 Correct 19 ms 1588 KB Output is correct
4 Correct 18 ms 1612 KB Output is correct
5 Correct 18 ms 1596 KB Output is correct
6 Correct 20 ms 1644 KB Output is correct
7 Correct 21 ms 1612 KB Output is correct
8 Correct 20 ms 1596 KB Output is correct
9 Correct 19 ms 1612 KB Output is correct
10 Correct 20 ms 1612 KB Output is correct
11 Correct 19 ms 1612 KB Output is correct
12 Correct 24 ms 1612 KB Output is correct
13 Correct 19 ms 1612 KB Output is correct
14 Correct 18 ms 1612 KB Output is correct
15 Correct 20 ms 1640 KB Output is correct
16 Correct 9 ms 1228 KB Output is correct
17 Correct 10 ms 1228 KB Output is correct
18 Correct 10 ms 1228 KB Output is correct
19 Correct 9 ms 1248 KB Output is correct
20 Correct 10 ms 1216 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1138 ms 8068 KB Output is correct
2 Correct 1144 ms 8140 KB Output is correct
3 Correct 1131 ms 8080 KB Output is correct
4 Correct 1153 ms 8244 KB Output is correct
5 Correct 1153 ms 8276 KB Output is correct
6 Correct 1014 ms 8120 KB Output is correct
7 Correct 1022 ms 8148 KB Output is correct
8 Correct 1022 ms 8152 KB Output is correct
9 Correct 1069 ms 8156 KB Output is correct
10 Correct 1055 ms 8244 KB Output is correct
11 Correct 1059 ms 8108 KB Output is correct
12 Correct 1051 ms 8128 KB Output is correct
13 Correct 1008 ms 8132 KB Output is correct
14 Correct 1067 ms 8076 KB Output is correct
15 Correct 1047 ms 8124 KB Output is correct
16 Correct 213 ms 3652 KB Output is correct
17 Correct 220 ms 3736 KB Output is correct
18 Correct 230 ms 3764 KB Output is correct
19 Correct 237 ms 3688 KB Output is correct
20 Correct 214 ms 3636 KB Output is correct
21 Correct 420 ms 8000 KB Output is correct
22 Correct 432 ms 7924 KB Output is correct
23 Correct 414 ms 7772 KB Output is correct
24 Correct 442 ms 7692 KB Output is correct
25 Correct 435 ms 7796 KB Output is correct
26 Correct 518 ms 7660 KB Output is correct
27 Correct 528 ms 7760 KB Output is correct
28 Correct 574 ms 7732 KB Output is correct
29 Correct 559 ms 7656 KB Output is correct
30 Correct 1125 ms 8224 KB Output is correct
31 Correct 1038 ms 8172 KB Output is correct
32 Correct 1066 ms 8132 KB Output is correct
33 Correct 1047 ms 8200 KB Output is correct
34 Correct 987 ms 8116 KB Output is correct
35 Correct 1090 ms 8088 KB Output is correct
36 Correct 1124 ms 8056 KB Output is correct
37 Correct 1138 ms 8136 KB Output is correct
38 Correct 1092 ms 8132 KB Output is correct
39 Correct 18 ms 1612 KB Output is correct
40 Correct 18 ms 1668 KB Output is correct
41 Correct 19 ms 1588 KB Output is correct
42 Correct 18 ms 1612 KB Output is correct
43 Correct 18 ms 1596 KB Output is correct
44 Correct 20 ms 1644 KB Output is correct
45 Correct 21 ms 1612 KB Output is correct
46 Correct 20 ms 1596 KB Output is correct
47 Correct 19 ms 1612 KB Output is correct
48 Correct 20 ms 1612 KB Output is correct
49 Correct 19 ms 1612 KB Output is correct
50 Correct 24 ms 1612 KB Output is correct
51 Correct 19 ms 1612 KB Output is correct
52 Correct 18 ms 1612 KB Output is correct
53 Correct 20 ms 1640 KB Output is correct
54 Correct 9 ms 1228 KB Output is correct
55 Correct 10 ms 1228 KB Output is correct
56 Correct 10 ms 1228 KB Output is correct
57 Correct 9 ms 1248 KB Output is correct
58 Correct 10 ms 1216 KB Output is correct
59 Execution timed out 2055 ms 7404 KB Time limit exceeded
60 Halted 0 ms 0 KB -