oj.uz

Submission #938624

# Submission time Handle Problem Language Result Execution time Memory
938624 2024-03-05T11:26:15 Z LucaIlie Boarding Passes (BOI22_passes) C++17
60 / 100
 1278 ms 343108 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 ) {
    int l = 0, r = n;
    while ( r - l > 2 ) {
        int mid1 = (l * 2 + r) / 3;
        int mid2 = (l + r * 2) / 3;

        if ( queryCost( c, mask, mid1 ) > queryCost( c, mask, mid2 ) )
            l = mid1;
        else if ( queryCost( c, mask, mid1 ) < queryCost( c, mask, mid2 ) )
            r = mid2;
        else {
            l++;
            r--;
        }
    }

    double bst = (double)n * n;
    for ( int i = max( 0, l - 20 ); i <= min( n, r + 50 ); i++ )
        bst = min( bst, queryCost( c, mask, i ) );

    return bst;
}

int main() {
    cin.tie( NULL );
    cout.tie( NULL );
    ios_base::sync_with_stdio( false );
    
    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 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 1 ms 856 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 2 ms 856 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 2 ms 856 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 2 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 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 1 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 856 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 2 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 856 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 1 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 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 1 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 856 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 2 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 856 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 1 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 1 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
19 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
20 Correct 2 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
21 Correct 2 ms 860 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 2 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 872 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 860 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
34 Correct 1 ms 860 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
35 Correct 0 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 23 ms 23712 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
38 Correct 497 ms 23648 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
39 Correct 552 ms 23688 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
40 Correct 277 ms 23644 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
41 Correct 22 ms 23384 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
42 Correct 24 ms 23296 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
43 Correct 22 ms 23388 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
44 Correct 23 ms 23388 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
45 Correct 22 ms 23380 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
46 Correct 23 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 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 1 ms 856 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 2 ms 856 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 2 ms 856 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 2 ms 856 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
10 Correct 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
11 Correct 1 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 856 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
16 Correct 2 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 856 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 1 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 1 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
28 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
29 Correct 2 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
30 Correct 2 ms 860 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 2 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 872 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 860 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
43 Correct 1 ms 860 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
44 Correct 0 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 23 ms 23712 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
47 Correct 497 ms 23648 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
48 Correct 552 ms 23688 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
49 Correct 277 ms 23644 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
50 Correct 22 ms 23384 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
51 Correct 24 ms 23296 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
52 Correct 22 ms 23388 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
53 Correct 23 ms 23388 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
54 Correct 22 ms 23380 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
55 Correct 23 ms 23388 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
56 Correct 1 ms 604 KB found '7.5000000000', expected '7.5000000000', error '0.0000000000'
57 Correct 297 ms 3216 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 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
60 Correct 1 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 1 ms 856 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
64 Correct 2 ms 856 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
65 Correct 2 ms 856 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
66 Correct 2 ms 856 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
67 Correct 0 ms 344 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 856 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 2 ms 860 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
74 Correct 1 ms 860 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
75 Correct 1 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 856 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
78 Correct 1 ms 860 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 860 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
84 Correct 0 ms 348 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
85 Correct 1 ms 348 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
86 Correct 22 ms 23708 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
87 Correct 489 ms 23692 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
88 Correct 536 ms 23640 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
89 Correct 278 ms 23644 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
90 Correct 22 ms 23384 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
91 Correct 24 ms 23384 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
92 Correct 22 ms 23436 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
93 Correct 23 ms 23388 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
94 Correct 23 ms 23388 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
95 Correct 22 ms 23388 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
96 Incorrect 1278 ms 343108 KB 1st numbers differ - expected: '1239972790.0000000000', found: '1239972800.0000000000', error = '0.0000000081'
97 Halted 0 ms 0 KB -