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Submission #599831

# Submission time Handle Problem Language Result Execution time Memory
599831 2022-07-20T01:32:52 Z yanndev Boarding Passes (BOI22_passes) C++17
60 / 100
 2000 ms 2400 KB 
#include <bits/stdc++.h>
#define int long long
#define lgd long double
using namespace std;

lgd dp[(int)(1 << 15) + 42];
vector<int> vals[16];

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    
    string s;
    cin >> s;
    int n = (int)s.size();
    /*for (int i = 0; i < n; i++)
        s += 'A';*/
    int g = 0;
    vector<char> comp {};

    for (int i = 0; i < n; i++)
        comp.push_back(s[i]);

    sort(comp.begin(), comp.end());
    comp.resize(unique(comp.begin(), comp.end()) - comp.begin());

    for (int i = 0; i < n; i++)
        vals[lower_bound(comp.begin(), comp.end(), s[i]) - comp.begin()].push_back(i);

    g = (int)comp.size();
    //cout << g << '\n';
    dp[0] = 0;

    for (int mask = 1; mask < (1 << g); mask++) {
        dp[mask] = 1e18;

        vector<int> pref (n, 0);
        for (int group = 0; group < g; group++)
            if (mask & (1 << group))
                for (auto& x: vals[group])
                    pref[x]++;
        for (int pos = 1; pos < n; pos++)
            pref[pos] += pref[pos - 1];

        for (int lst = 0; lst < g; lst++) {
            if (mask & (1 << lst)) {
                // put everyone to the left 
                lgd esp = 0;
                for (int id = 0; id < (int)vals[lst].size(); id++) {
                    // inversions bcs of other groups, remove the ones from lst
                    esp += pref[vals[lst][id]] - (id + 1);
                }
                // add expected inversions from lst permutations
                lgd transi = esp + ((int)vals[lst].size() * ((int)vals[lst].size() - 1)) / 4.;
                
                // fix right limit
                for (int id = (int)vals[lst].size() - 1; id >= 0; id--) {
                    // remove from the left side
                    esp -= pref[vals[lst][id]];
                    esp += (id + 1);

                    // inversions bcs of other groups
                    esp += pref.back() - pref[vals[lst][id]];
                    // remove from lst
                    esp -= (int)vals[lst].size() - (id + 1);
                    transi = min(transi, esp + (((id) * (id - 1)) + ((int)vals[lst].size() - id) * ((int)vals[lst].size() - (id + 1))) / 4.);
                }

                dp[mask] = min(dp[mask], dp[mask ^ (1 << lst)] + transi);
            }
        }
    }
    
    cout << setprecision(42) << dp[(1 << g) - 1] << '\n';
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 4 ms 1864 KB Output is correct
7 Correct 4 ms 2120 KB Output is correct
8 Correct 4 ms 2248 KB Output is correct
9 Correct 4 ms 2248 KB Output is correct

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 0 ms 212 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 0 ms 212 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 0 ms 212 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 0 ms 212 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 0 ms 212 KB Output is correct
28 Correct 1 ms 212 KB Output is correct
29 Correct 0 ms 212 KB Output is correct
30 Correct 0 ms 212 KB Output is correct
31 Correct 0 ms 212 KB Output is correct
32 Correct 0 ms 212 KB Output is correct
33 Correct 0 ms 212 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 1 ms 468 KB Output is correct
36 Correct 1 ms 468 KB Output is correct
37 Correct 86 ms 468 KB Output is correct
38 Correct 85 ms 468 KB Output is correct
39 Correct 92 ms 580 KB Output is correct
40 Correct 85 ms 532 KB Output is correct
41 Correct 81 ms 472 KB Output is correct
42 Correct 82 ms 572 KB Output is correct
43 Correct 82 ms 576 KB Output is correct
44 Correct 87 ms 476 KB Output is correct
45 Correct 84 ms 556 KB Output is correct
46 Correct 83 ms 572 KB Output is correct

Subtask #4
0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 4 ms 1864 KB Output is correct
7 Correct 4 ms 2120 KB Output is correct
8 Correct 4 ms 2248 KB Output is correct
9 Correct 4 ms 2248 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 0 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 0 ms 212 KB Output is correct
26 Correct 0 ms 212 KB Output is correct
27 Correct 0 ms 212 KB Output is correct
28 Correct 0 ms 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 1 ms 212 KB Output is correct
31 Correct 0 ms 212 KB Output is correct
32 Correct 0 ms 212 KB Output is correct
33 Correct 1 ms 212 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 0 ms 212 KB Output is correct
37 Correct 1 ms 212 KB Output is correct
38 Correct 0 ms 212 KB Output is correct
39 Correct 0 ms 212 KB Output is correct
40 Correct 0 ms 212 KB Output is correct
41 Correct 0 ms 212 KB Output is correct
42 Correct 0 ms 212 KB Output is correct
43 Correct 0 ms 212 KB Output is correct
44 Correct 1 ms 468 KB Output is correct
45 Correct 1 ms 468 KB Output is correct
46 Correct 86 ms 468 KB Output is correct
47 Correct 85 ms 468 KB Output is correct
48 Correct 92 ms 580 KB Output is correct
49 Correct 85 ms 532 KB Output is correct
50 Correct 81 ms 472 KB Output is correct
51 Correct 82 ms 572 KB Output is correct
52 Correct 82 ms 576 KB Output is correct
53 Correct 87 ms 476 KB Output is correct
54 Correct 84 ms 556 KB Output is correct
55 Correct 83 ms 572 KB Output is correct
56 Correct 1 ms 212 KB Output is correct
57 Correct 12 ms 724 KB Output is correct
58 Correct 0 ms 340 KB Output is correct
59 Correct 0 ms 212 KB Output is correct
60 Correct 0 ms 212 KB Output is correct
61 Correct 0 ms 212 KB Output is correct
62 Correct 1 ms 340 KB Output is correct
63 Correct 5 ms 1864 KB Output is correct
64 Correct 5 ms 2120 KB Output is correct
65 Correct 5 ms 2244 KB Output is correct
66 Correct 5 ms 2248 KB Output is correct
67 Correct 0 ms 212 KB Output is correct
68 Correct 1 ms 212 KB Output is correct
69 Correct 1 ms 212 KB Output is correct
70 Correct 1 ms 212 KB Output is correct
71 Correct 1 ms 212 KB Output is correct
72 Correct 1 ms 212 KB Output is correct
73 Correct 0 ms 212 KB Output is correct
74 Correct 1 ms 212 KB Output is correct
75 Correct 0 ms 212 KB Output is correct
76 Correct 1 ms 212 KB Output is correct
77 Correct 0 ms 212 KB Output is correct
78 Correct 1 ms 212 KB Output is correct
79 Correct 1 ms 212 KB Output is correct
80 Correct 1 ms 212 KB Output is correct
81 Correct 0 ms 212 KB Output is correct
82 Correct 0 ms 212 KB Output is correct
83 Correct 1 ms 212 KB Output is correct
84 Correct 1 ms 468 KB Output is correct
85 Correct 1 ms 468 KB Output is correct
86 Correct 87 ms 572 KB Output is correct
87 Correct 93 ms 524 KB Output is correct
88 Correct 86 ms 572 KB Output is correct
89 Correct 84 ms 648 KB Output is correct
90 Correct 83 ms 580 KB Output is correct
91 Correct 85 ms 468 KB Output is correct
92 Correct 89 ms 576 KB Output is correct
93 Correct 88 ms 548 KB Output is correct
94 Correct 81 ms 572 KB Output is correct
95 Correct 82 ms 468 KB Output is correct
96 Execution timed out 2057 ms 2400 KB Time limit exceeded
97 Halted 0 ms 0 KB -