Submission #969427

#	Time	Username	Problem	Language	Result	Execution time	Memory
969427		aeg	Boarding Passes (BOI22_passes)	C++14	30 / 100	21 ms	23644 KiB

passes

#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 / 5
• Subtask 2: 25 / 25
• Subtask 3: 0 / 30
• Subtask 4: 0 / 40