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Submission #434957

# Submission time Handle Problem Language Result Execution time Memory
434957 2021-06-22T14:16:27 Z Lam_lai_cuoc_doi Boat (APIO16_boat) C++17
58 / 100
 2000 ms 8288 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()
{
    scanf("%d", &n); //cin >> n;

    block.reserve(n * 2);

    for (int i = 1; i <= n; ++i)
    {
        //cin >> s[i].first >> s[i].second;
        scanf("%d%d", &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();
    }
}

Compilation message

boat.cpp: In function 'void Read()':
boat.cpp:24:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   24 |     scanf("%d", &n); //cin >> n;
      |     ~~~~~^~~~~~~~~~
boat.cpp:31:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   31 |         scanf("%d%d", &s[i].first, &s[i].second);
      |         ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1079 ms 8176 KB Output is correct
2 Correct 1063 ms 8216 KB Output is correct
3 Correct 1057 ms 8148 KB Output is correct
4 Correct 1068 ms 8148 KB Output is correct
5 Correct 1116 ms 8288 KB Output is correct
6 Correct 912 ms 8284 KB Output is correct
7 Correct 900 ms 8156 KB Output is correct
8 Correct 937 ms 8108 KB Output is correct
9 Correct 968 ms 8120 KB Output is correct
10 Correct 970 ms 8188 KB Output is correct
11 Correct 970 ms 8272 KB Output is correct
12 Correct 970 ms 8140 KB Output is correct
13 Correct 994 ms 8188 KB Output is correct
14 Correct 929 ms 8216 KB Output is correct
15 Correct 989 ms 8212 KB Output is correct
16 Correct 193 ms 3576 KB Output is correct
17 Correct 196 ms 3704 KB Output is correct
18 Correct 204 ms 3696 KB Output is correct
19 Correct 205 ms 3712 KB Output is correct
20 Correct 220 ms 3764 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1079 ms 8176 KB Output is correct
2 Correct 1063 ms 8216 KB Output is correct
3 Correct 1057 ms 8148 KB Output is correct
4 Correct 1068 ms 8148 KB Output is correct
5 Correct 1116 ms 8288 KB Output is correct
6 Correct 912 ms 8284 KB Output is correct
7 Correct 900 ms 8156 KB Output is correct
8 Correct 937 ms 8108 KB Output is correct
9 Correct 968 ms 8120 KB Output is correct
10 Correct 970 ms 8188 KB Output is correct
11 Correct 970 ms 8272 KB Output is correct
12 Correct 970 ms 8140 KB Output is correct
13 Correct 994 ms 8188 KB Output is correct
14 Correct 929 ms 8216 KB Output is correct
15 Correct 989 ms 8212 KB Output is correct
16 Correct 193 ms 3576 KB Output is correct
17 Correct 196 ms 3704 KB Output is correct
18 Correct 204 ms 3696 KB Output is correct
19 Correct 205 ms 3712 KB Output is correct
20 Correct 220 ms 3764 KB Output is correct
21 Correct 455 ms 7868 KB Output is correct
22 Correct 437 ms 7872 KB Output is correct
23 Correct 457 ms 7828 KB Output is correct
24 Correct 438 ms 7748 KB Output is correct
25 Correct 492 ms 7692 KB Output is correct
26 Correct 527 ms 7700 KB Output is correct
27 Correct 630 ms 7748 KB Output is correct
28 Correct 556 ms 7680 KB Output is correct
29 Correct 551 ms 7688 KB Output is correct
30 Correct 919 ms 8116 KB Output is correct
31 Correct 964 ms 8084 KB Output is correct
32 Correct 909 ms 8132 KB Output is correct
33 Correct 867 ms 8136 KB Output is correct
34 Correct 865 ms 8136 KB Output is correct
35 Correct 983 ms 8168 KB Output is correct
36 Correct 992 ms 8184 KB Output is correct
37 Correct 1002 ms 8080 KB Output is correct
38 Correct 987 ms 8204 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 1612 KB Output is correct
2 Correct 17 ms 1628 KB Output is correct
3 Correct 18 ms 1592 KB Output is correct
4 Correct 17 ms 1588 KB Output is correct
5 Correct 17 ms 1612 KB Output is correct
6 Correct 18 ms 1556 KB Output is correct
7 Correct 19 ms 1604 KB Output is correct
8 Correct 18 ms 1612 KB Output is correct
9 Correct 17 ms 1612 KB Output is correct
10 Correct 21 ms 1672 KB Output is correct
11 Correct 20 ms 1612 KB Output is correct
12 Correct 16 ms 1660 KB Output is correct
13 Correct 19 ms 1584 KB Output is correct
14 Correct 17 ms 1624 KB Output is correct
15 Correct 17 ms 1616 KB Output is correct
16 Correct 8 ms 1228 KB Output is correct
17 Correct 8 ms 1228 KB Output is correct
18 Correct 8 ms 1244 KB Output is correct
19 Correct 9 ms 1228 KB Output is correct
20 Correct 10 ms 1172 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1079 ms 8176 KB Output is correct
2 Correct 1063 ms 8216 KB Output is correct
3 Correct 1057 ms 8148 KB Output is correct
4 Correct 1068 ms 8148 KB Output is correct
5 Correct 1116 ms 8288 KB Output is correct
6 Correct 912 ms 8284 KB Output is correct
7 Correct 900 ms 8156 KB Output is correct
8 Correct 937 ms 8108 KB Output is correct
9 Correct 968 ms 8120 KB Output is correct
10 Correct 970 ms 8188 KB Output is correct
11 Correct 970 ms 8272 KB Output is correct
12 Correct 970 ms 8140 KB Output is correct
13 Correct 994 ms 8188 KB Output is correct
14 Correct 929 ms 8216 KB Output is correct
15 Correct 989 ms 8212 KB Output is correct
16 Correct 193 ms 3576 KB Output is correct
17 Correct 196 ms 3704 KB Output is correct
18 Correct 204 ms 3696 KB Output is correct
19 Correct 205 ms 3712 KB Output is correct
20 Correct 220 ms 3764 KB Output is correct
21 Correct 455 ms 7868 KB Output is correct
22 Correct 437 ms 7872 KB Output is correct
23 Correct 457 ms 7828 KB Output is correct
24 Correct 438 ms 7748 KB Output is correct
25 Correct 492 ms 7692 KB Output is correct
26 Correct 527 ms 7700 KB Output is correct
27 Correct 630 ms 7748 KB Output is correct
28 Correct 556 ms 7680 KB Output is correct
29 Correct 551 ms 7688 KB Output is correct
30 Correct 919 ms 8116 KB Output is correct
31 Correct 964 ms 8084 KB Output is correct
32 Correct 909 ms 8132 KB Output is correct
33 Correct 867 ms 8136 KB Output is correct
34 Correct 865 ms 8136 KB Output is correct
35 Correct 983 ms 8168 KB Output is correct
36 Correct 992 ms 8184 KB Output is correct
37 Correct 1002 ms 8080 KB Output is correct
38 Correct 987 ms 8204 KB Output is correct
39 Correct 19 ms 1612 KB Output is correct
40 Correct 17 ms 1628 KB Output is correct
41 Correct 18 ms 1592 KB Output is correct
42 Correct 17 ms 1588 KB Output is correct
43 Correct 17 ms 1612 KB Output is correct
44 Correct 18 ms 1556 KB Output is correct
45 Correct 19 ms 1604 KB Output is correct
46 Correct 18 ms 1612 KB Output is correct
47 Correct 17 ms 1612 KB Output is correct
48 Correct 21 ms 1672 KB Output is correct
49 Correct 20 ms 1612 KB Output is correct
50 Correct 16 ms 1660 KB Output is correct
51 Correct 19 ms 1584 KB Output is correct
52 Correct 17 ms 1624 KB Output is correct
53 Correct 17 ms 1616 KB Output is correct
54 Correct 8 ms 1228 KB Output is correct
55 Correct 8 ms 1228 KB Output is correct
56 Correct 8 ms 1244 KB Output is correct
57 Correct 9 ms 1228 KB Output is correct
58 Correct 10 ms 1172 KB Output is correct
59 Correct 1891 ms 8156 KB Output is correct
60 Correct 1907 ms 8156 KB Output is correct
61 Correct 1908 ms 8164 KB Output is correct
62 Correct 1935 ms 8120 KB Output is correct
63 Correct 1903 ms 8140 KB Output is correct
64 Execution timed out 2060 ms 8192 KB Time limit exceeded
65 Halted 0 ms 0 KB -