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Submission #465071

# Submission time Handle Problem Language Result Execution time Memory
465071 2021-08-15T06:51:30 Z arminatarod Boat (APIO16_boat) C++17
100 / 100
 1851 ms 8352 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;
            }
 
            d[i][j] %= 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
                }
 
            dp[i][j] %= mod;
        }
    }
 
    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 998 ms 8160 KB Output is correct
2 Correct 1018 ms 8148 KB Output is correct
3 Correct 984 ms 8196 KB Output is correct
4 Correct 991 ms 8180 KB Output is correct
5 Correct 991 ms 8140 KB Output is correct
6 Correct 892 ms 8176 KB Output is correct
7 Correct 895 ms 8104 KB Output is correct
8 Correct 900 ms 8224 KB Output is correct
9 Correct 906 ms 8208 KB Output is correct
10 Correct 901 ms 8296 KB Output is correct
11 Correct 899 ms 8152 KB Output is correct
12 Correct 900 ms 8144 KB Output is correct
13 Correct 896 ms 8224 KB Output is correct
14 Correct 889 ms 8268 KB Output is correct
15 Correct 896 ms 8184 KB Output is correct
16 Correct 179 ms 3592 KB Output is correct
17 Correct 195 ms 3776 KB Output is correct
18 Correct 186 ms 3692 KB Output is correct
19 Correct 194 ms 3736 KB Output is correct
20 Correct 199 ms 3680 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 998 ms 8160 KB Output is correct
2 Correct 1018 ms 8148 KB Output is correct
3 Correct 984 ms 8196 KB Output is correct
4 Correct 991 ms 8180 KB Output is correct
5 Correct 991 ms 8140 KB Output is correct
6 Correct 892 ms 8176 KB Output is correct
7 Correct 895 ms 8104 KB Output is correct
8 Correct 900 ms 8224 KB Output is correct
9 Correct 906 ms 8208 KB Output is correct
10 Correct 901 ms 8296 KB Output is correct
11 Correct 899 ms 8152 KB Output is correct
12 Correct 900 ms 8144 KB Output is correct
13 Correct 896 ms 8224 KB Output is correct
14 Correct 889 ms 8268 KB Output is correct
15 Correct 896 ms 8184 KB Output is correct
16 Correct 179 ms 3592 KB Output is correct
17 Correct 195 ms 3776 KB Output is correct
18 Correct 186 ms 3692 KB Output is correct
19 Correct 194 ms 3736 KB Output is correct
20 Correct 199 ms 3680 KB Output is correct
21 Correct 340 ms 7856 KB Output is correct
22 Correct 353 ms 7844 KB Output is correct
23 Correct 327 ms 7800 KB Output is correct
24 Correct 332 ms 7748 KB Output is correct
25 Correct 341 ms 7792 KB Output is correct
26 Correct 296 ms 7620 KB Output is correct
27 Correct 310 ms 7736 KB Output is correct
28 Correct 297 ms 7676 KB Output is correct
29 Correct 308 ms 7688 KB Output is correct
30 Correct 867 ms 8156 KB Output is correct
31 Correct 856 ms 8132 KB Output is correct
32 Correct 865 ms 8260 KB Output is correct
33 Correct 864 ms 8128 KB Output is correct
34 Correct 853 ms 8220 KB Output is correct
35 Correct 972 ms 8220 KB Output is correct
36 Correct 977 ms 8084 KB Output is correct
37 Correct 973 ms 8116 KB Output is correct
38 Correct 961 ms 8232 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 1612 KB Output is correct
2 Correct 15 ms 1652 KB Output is correct
3 Correct 16 ms 1616 KB Output is correct
4 Correct 15 ms 1600 KB Output is correct
5 Correct 16 ms 1660 KB Output is correct
6 Correct 16 ms 1576 KB Output is correct
7 Correct 16 ms 1640 KB Output is correct
8 Correct 17 ms 1656 KB Output is correct
9 Correct 16 ms 1612 KB Output is correct
10 Correct 16 ms 1612 KB Output is correct
11 Correct 16 ms 1612 KB Output is correct
12 Correct 17 ms 1560 KB Output is correct
13 Correct 16 ms 1636 KB Output is correct
14 Correct 15 ms 1672 KB Output is correct
15 Correct 15 ms 1612 KB Output is correct
16 Correct 8 ms 1228 KB Output is correct
17 Correct 8 ms 1228 KB Output is correct
18 Correct 7 ms 1228 KB Output is correct
19 Correct 8 ms 1228 KB Output is correct
20 Correct 8 ms 1224 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 998 ms 8160 KB Output is correct
2 Correct 1018 ms 8148 KB Output is correct
3 Correct 984 ms 8196 KB Output is correct
4 Correct 991 ms 8180 KB Output is correct
5 Correct 991 ms 8140 KB Output is correct
6 Correct 892 ms 8176 KB Output is correct
7 Correct 895 ms 8104 KB Output is correct
8 Correct 900 ms 8224 KB Output is correct
9 Correct 906 ms 8208 KB Output is correct
10 Correct 901 ms 8296 KB Output is correct
11 Correct 899 ms 8152 KB Output is correct
12 Correct 900 ms 8144 KB Output is correct
13 Correct 896 ms 8224 KB Output is correct
14 Correct 889 ms 8268 KB Output is correct
15 Correct 896 ms 8184 KB Output is correct
16 Correct 179 ms 3592 KB Output is correct
17 Correct 195 ms 3776 KB Output is correct
18 Correct 186 ms 3692 KB Output is correct
19 Correct 194 ms 3736 KB Output is correct
20 Correct 199 ms 3680 KB Output is correct
21 Correct 340 ms 7856 KB Output is correct
22 Correct 353 ms 7844 KB Output is correct
23 Correct 327 ms 7800 KB Output is correct
24 Correct 332 ms 7748 KB Output is correct
25 Correct 341 ms 7792 KB Output is correct
26 Correct 296 ms 7620 KB Output is correct
27 Correct 310 ms 7736 KB Output is correct
28 Correct 297 ms 7676 KB Output is correct
29 Correct 308 ms 7688 KB Output is correct
30 Correct 867 ms 8156 KB Output is correct
31 Correct 856 ms 8132 KB Output is correct
32 Correct 865 ms 8260 KB Output is correct
33 Correct 864 ms 8128 KB Output is correct
34 Correct 853 ms 8220 KB Output is correct
35 Correct 972 ms 8220 KB Output is correct
36 Correct 977 ms 8084 KB Output is correct
37 Correct 973 ms 8116 KB Output is correct
38 Correct 961 ms 8232 KB Output is correct
39 Correct 16 ms 1612 KB Output is correct
40 Correct 15 ms 1652 KB Output is correct
41 Correct 16 ms 1616 KB Output is correct
42 Correct 15 ms 1600 KB Output is correct
43 Correct 16 ms 1660 KB Output is correct
44 Correct 16 ms 1576 KB Output is correct
45 Correct 16 ms 1640 KB Output is correct
46 Correct 17 ms 1656 KB Output is correct
47 Correct 16 ms 1612 KB Output is correct
48 Correct 16 ms 1612 KB Output is correct
49 Correct 16 ms 1612 KB Output is correct
50 Correct 17 ms 1560 KB Output is correct
51 Correct 16 ms 1636 KB Output is correct
52 Correct 15 ms 1672 KB Output is correct
53 Correct 15 ms 1612 KB Output is correct
54 Correct 8 ms 1228 KB Output is correct
55 Correct 8 ms 1228 KB Output is correct
56 Correct 7 ms 1228 KB Output is correct
57 Correct 8 ms 1228 KB Output is correct
58 Correct 8 ms 1224 KB Output is correct
59 Correct 1851 ms 8224 KB Output is correct
60 Correct 1794 ms 8180 KB Output is correct
61 Correct 1776 ms 8156 KB Output is correct
62 Correct 1813 ms 8276 KB Output is correct
63 Correct 1821 ms 8352 KB Output is correct
64 Correct 1799 ms 8264 KB Output is correct
65 Correct 1770 ms 8216 KB Output is correct
66 Correct 1794 ms 8252 KB Output is correct
67 Correct 1758 ms 8300 KB Output is correct
68 Correct 1790 ms 8252 KB Output is correct
69 Correct 1779 ms 8288 KB Output is correct
70 Correct 1778 ms 8284 KB Output is correct
71 Correct 1772 ms 8252 KB Output is correct
72 Correct 1784 ms 8340 KB Output is correct
73 Correct 1796 ms 8224 KB Output is correct
74 Correct 227 ms 3700 KB Output is correct
75 Correct 227 ms 3676 KB Output is correct
76 Correct 224 ms 3752 KB Output is correct
77 Correct 245 ms 3704 KB Output is correct
78 Correct 226 ms 3676 KB Output is correct