oj.uz

Submission #938602

# Submission time Handle Problem Language Result Execution time Memory
938602 2024-03-05T11:01:52 Z LucaIlie Boarding Passes (BOI22_passes) C++17
60 / 100
 2000 ms 342612 KB 
#include <bits/stdc++.h>

using namespace std;

const int MAX_G = 15;
const int MAX_N = 1e5;
int n, g;
string s;
double dp[1 << MAX_G];
int frecv[MAX_G][MAX_N + 1];
long long costPref[MAX_G][MAX_G][MAX_N + 2], costSuf[MAX_G][MAX_G][MAX_N + 2];
unordered_map<char, int> lit;

double expectedInversions( int n ) {
    return (double)n * (n - 1) / 4;
}

double queryCost( int c, int mask, int i ) {
    double cost = expectedInversions( frecv[c][i] ) + expectedInversions( frecv[c][n] - frecv[c][i] );

    for ( int d = 0; d < g; d++ ) {
        if ( (mask >> d) & 1 )
            cost += costPref[c][d][i] + costSuf[c][d][i + 1];
    }

    return cost;
}

double solve( int c, int mask ) {
    double best = (double)n * n;

    for ( int i = 0; i <= n; i++ ) {
        double cost = queryCost( c, mask, i );
        best = min( best, cost );
    }

    return best;
}

int main() {
    cin >> s;
    n = s.size();
    s = " " + s;

    g = 0;
    for ( int i = 1; i <= n; i++ ) {
        if ( lit[s[i]] == 0 )
            lit[s[i]] = ++g;
        s[i] = lit[s[i]] - 1;
    }

    for ( int c = 0; c < g; c++ ) {
        for ( int i = 1; i <= n; i++ )
            frecv[c][i] = frecv[c][i - 1] + (s[i] == c);
    }
    for ( int c = 0; c < g; c++ ) {
        for ( int d = 0; d < g; d++ ) {
            if ( c == d )
                continue;

            int cnt;

            cnt = 0;
            for ( int i = 1; i <= n; i++ ) {
                costPref[c][d][i] = costPref[c][d][i - 1];
                if ( s[i] == c )
                    costPref[c][d][i] += cnt;
                if ( s[i] == d )
                    cnt++;
            }
            cnt = 0;
            for ( int i = n; i >= 1; i-- ) {
                costSuf[c][d][i] = costSuf[c][d][i + 1];
                if ( s[i] == c )
                    costSuf[c][d][i] += cnt;
                if ( s[i] == d )
                    cnt++;
            }
        }
    }

    cout << fixed << setprecision( 1 );
    for ( int mask = 1; mask < (1 << g); mask++ ) {
        dp[mask] = (double)n * n;
        for ( int c = 0; c < g; c++ ) {
            if ( (mask >> c) & 1 )
                dp[mask] = min( dp[mask], dp[mask - (1 << c)] + solve( c, mask - (1 << c) ) );
        }
    }

    cout << dp[(1 << g) - 1];

    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
3 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
4 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 0 ms 344 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 3 ms 856 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 3 ms 856 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 5 ms 852 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 4 ms 856 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
3 Correct 2 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
4 Correct 2 ms 860 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 2 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 1 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 1 ms 860 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
8 Correct 1 ms 860 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 1 ms 860 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 1 ms 860 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 1 ms 1112 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 1 ms 860 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 1 ms 860 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
14 Correct 1 ms 860 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
15 Correct 2 ms 860 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
16 Correct 1 ms 860 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
17 Correct 1 ms 860 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
3 Correct 2 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
4 Correct 2 ms 860 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 2 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 1 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 1 ms 860 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
8 Correct 1 ms 860 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 1 ms 860 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 1 ms 860 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 1 ms 1112 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 1 ms 860 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 1 ms 860 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
14 Correct 1 ms 860 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
15 Correct 2 ms 860 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
16 Correct 1 ms 860 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
17 Correct 1 ms 860 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
18 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
19 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
20 Correct 1 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
21 Correct 2 ms 856 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
22 Correct 2 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
23 Correct 1 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
24 Correct 1 ms 860 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
25 Correct 1 ms 860 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
26 Correct 1 ms 860 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
27 Correct 1 ms 860 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
28 Correct 1 ms 860 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
29 Correct 1 ms 860 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
30 Correct 1 ms 860 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
31 Correct 1 ms 860 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
32 Correct 1 ms 860 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
33 Correct 1 ms 856 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
34 Correct 1 ms 856 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
35 Correct 1 ms 348 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
36 Correct 1 ms 348 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
37 Correct 702 ms 23680 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
38 Correct 697 ms 23644 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
39 Correct 694 ms 23668 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
40 Correct 702 ms 23624 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
41 Correct 693 ms 23640 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
42 Correct 690 ms 23636 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
43 Correct 739 ms 23632 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
44 Correct 698 ms 23264 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
45 Correct 712 ms 23384 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
46 Correct 719 ms 23388 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'

Subtask #4
0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
3 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
4 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 0 ms 344 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 3 ms 856 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 3 ms 856 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 5 ms 852 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 4 ms 856 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
10 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
11 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
12 Correct 2 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
13 Correct 2 ms 860 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
14 Correct 2 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
15 Correct 1 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
16 Correct 1 ms 860 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
17 Correct 1 ms 860 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
18 Correct 1 ms 860 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
19 Correct 1 ms 860 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
20 Correct 1 ms 1112 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
21 Correct 1 ms 860 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
22 Correct 1 ms 860 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
23 Correct 1 ms 860 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
24 Correct 2 ms 860 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
25 Correct 1 ms 860 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
26 Correct 1 ms 860 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
27 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
28 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
29 Correct 1 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
30 Correct 2 ms 856 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
31 Correct 2 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
32 Correct 1 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
33 Correct 1 ms 860 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
34 Correct 1 ms 860 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
35 Correct 1 ms 860 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
36 Correct 1 ms 860 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
37 Correct 1 ms 860 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
38 Correct 1 ms 860 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
39 Correct 1 ms 860 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
40 Correct 1 ms 860 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
41 Correct 1 ms 860 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
42 Correct 1 ms 856 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
43 Correct 1 ms 856 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
44 Correct 1 ms 348 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
45 Correct 1 ms 348 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
46 Correct 702 ms 23680 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
47 Correct 697 ms 23644 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
48 Correct 694 ms 23668 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
49 Correct 702 ms 23624 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
50 Correct 693 ms 23640 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
51 Correct 690 ms 23636 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
52 Correct 739 ms 23632 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
53 Correct 698 ms 23264 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
54 Correct 712 ms 23384 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
55 Correct 719 ms 23388 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
56 Correct 1 ms 600 KB found '7.5000000000', expected '7.5000000000', error '0.0000000000'
57 Correct 195 ms 3108 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
58 Correct 0 ms 348 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
59 Correct 0 ms 344 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
60 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
61 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
62 Correct 0 ms 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
63 Correct 3 ms 856 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
64 Correct 3 ms 856 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
65 Correct 4 ms 852 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
66 Correct 4 ms 856 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
67 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
68 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
69 Correct 2 ms 872 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
70 Correct 2 ms 860 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
71 Correct 2 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
72 Correct 1 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
73 Correct 1 ms 860 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
74 Correct 1 ms 604 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
75 Correct 2 ms 860 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
76 Correct 1 ms 860 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
77 Correct 1 ms 860 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
78 Correct 1 ms 856 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
79 Correct 1 ms 860 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
80 Correct 1 ms 860 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
81 Correct 1 ms 860 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
82 Correct 1 ms 860 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
83 Correct 1 ms 856 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
84 Correct 1 ms 348 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
85 Correct 1 ms 344 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
86 Correct 728 ms 23664 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
87 Correct 693 ms 23656 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
88 Correct 708 ms 24144 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
89 Correct 704 ms 23620 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
90 Correct 690 ms 23632 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
91 Correct 706 ms 23392 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
92 Correct 721 ms 23396 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
93 Correct 698 ms 23384 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
94 Correct 706 ms 23400 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
95 Correct 686 ms 23392 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
96 Execution timed out 2064 ms 342612 KB Time limit exceeded
97 Halted 0 ms 0 KB -