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Submission #938631

# Submission time Handle Problem Language Result Execution time Memory
938631 2024-03-05T11:28:36 Z LucaIlie Boarding Passes (BOI22_passes) C++17
5 / 100
 2 ms 1112 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 = mid1;
    }

    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 1 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 1 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 2 ms 856 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 2 ms 1088 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 2 ms 1112 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 2 ms 1112 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'

Subtask #2
0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 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 1020 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
4 Correct 1 ms 860 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 1 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 2 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Incorrect 2 ms 856 KB 1st numbers differ - expected: '703.0000000000', found: '713.0000000000', error = '0.0142247511'
8 Halted 0 ms 0 KB -

Subtask #3
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 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 1020 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
4 Correct 1 ms 860 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 1 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 2 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Incorrect 2 ms 856 KB 1st numbers differ - expected: '703.0000000000', found: '713.0000000000', error = '0.0142247511'
8 Halted 0 ms 0 KB -

Subtask #4
0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 1 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 2 ms 856 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 2 ms 1088 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 2 ms 1112 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 2 ms 1112 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
10 Correct 1 ms 344 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 1020 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
13 Correct 1 ms 860 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
14 Correct 1 ms 860 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
15 Correct 2 ms 860 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
16 Incorrect 2 ms 856 KB 1st numbers differ - expected: '703.0000000000', found: '713.0000000000', error = '0.0142247511'
17 Halted 0 ms 0 KB -