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Submission #969427

# Submission time Handle Problem Language Result Execution time Memory
969427 2024-04-25T06:51:05 Z aeg Boarding Passes (BOI22_passes) C++14
30 / 100
 21 ms 23644 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 - 10 ); i <= min( n, r + 10 ); i++ )
		bst = min( bst, queryCost( c, mask, i ) );

	return bst;
}

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 1 ms 348 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 0 ms 344 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 1 ms 348 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 1112 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 3 ms 1112 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 3 ms 1112 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 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 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 2 ms 1116 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 2 ms 856 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 2 ms 860 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 2 ms 868 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
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 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 2 ms 1116 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 2 ms 856 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 2 ms 860 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 2 ms 868 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 348 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 1 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
21 Correct 2 ms 992 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 2 ms 856 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 2 ms 860 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
29 Correct 2 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 868 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
32 Correct 2 ms 864 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
33 Correct 1 ms 868 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
34 Correct 2 ms 864 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
35 Correct 1 ms 356 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 Incorrect 21 ms 23644 KB 1st numbers differ - expected: '12223392.0000000000', found: '12223397.0000000000', error = '0.0000004091'
38 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 344 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 1 ms 348 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 1112 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 3 ms 1112 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 3 ms 1112 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
10 Correct 0 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 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 2 ms 1116 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
19 Correct 2 ms 856 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
20 Correct 2 ms 860 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
21 Correct 2 ms 868 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 348 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 1 ms 860 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
30 Correct 2 ms 992 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 2 ms 856 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 2 ms 860 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
38 Correct 2 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 868 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
41 Correct 2 ms 864 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
42 Correct 1 ms 868 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
43 Correct 2 ms 864 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
44 Correct 1 ms 356 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 Incorrect 21 ms 23644 KB 1st numbers differ - expected: '12223392.0000000000', found: '12223397.0000000000', error = '0.0000004091'
47 Halted 0 ms 0 KB -