Submission #1054189

#	Time	Username	Problem	Language	Result	Execution time	Memory
1054189		sofijavelkovska	Boarding Passes (BOI22_passes)	C++17	100 / 100	170 ms	141148 KiB

passes

#include <bits/stdc++.h>
using namespace std;

const int MAXN=1e5, MAXK=15;
const long long INF=1e18;

string s;
int n, k;
vector<vector<int> > groups;
double geninv[MAXN+1], inv[MAXK][MAXK][MAXN+1];
double memo[(1<<MAXK)];

double dp(int mask)
{
    if (memo[mask]!=-1)
        return memo[mask];
    if (mask==(1<<k)-1)
        return memo[mask]=0;
    double mintotal=INF;
    for (int i=0; i<k; i++)
    {
        if (mask&(1<<i))
            continue;
        int l=0;
        int r=groups[i].size();
        int g=groups[i].size();
        double minsum=INF;
        while ((r-l)/3>0)
        {
            int t1=l+(r-l)/3;
            int t2=r-(r-l)/3;
            double sum1=0;
            for (int j=0; j<k; j++)
                if (mask&(1<<j))
                    sum1=sum1+inv[i][j][t1];
            sum1=sum1+geninv[t1]+geninv[g-t1];
            double sum2=0;
            for (int j=0; j<k; j++)
                if (mask&(1<<j))
                    sum2=sum2+inv[i][j][t2];
            sum2=sum2+geninv[t2]+geninv[g-t2];
            if (sum1<sum2)
            {
                minsum=min(minsum, sum1);
                r=t2;
            }
            else
                l=t1;
        }
        for (int t=l; t<=r; t++)
        {
            double sum=0;
            for (int j=0; j<k; j++)
                if (mask&(1<<j))
                    sum=sum+inv[i][j][t];
            sum=sum+geninv[t]+geninv[g-t];
            minsum=min(minsum, sum);
        }
        mintotal=min(mintotal, minsum+dp(mask|(1<<i)));
    }

    return memo[mask]=mintotal;
}

void calcinv(int a, int b)
{
    int prefix[n]={0};
    for (auto x : groups[b])
        prefix[x]=1;
    for (int i=1; i<n; i++)
        prefix[i]=prefix[i-1]+prefix[i];
    int m=prefix[n-1];
    long long maininv=0;
    int g=groups[a].size();
    for (auto x : groups[a])
        if (x!=0)
            maininv=maininv+prefix[x-1];
    inv[a][b][g]=maininv;
    for (int j=g-1; j>=0; j--)
    {
        int x=groups[a][j];
        if (x!=0)
            maininv=maininv-prefix[x-1];
        maininv=maininv+(m-prefix[x]);
        inv[a][b][j]=maininv;
    }

    return;
}

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    cin >> s;
    n=s.size();
    map<char, vector<int> > groupsbychar;
    for (int i=0; i<n; i++)
        groupsbychar[s[i]].push_back(i);
    for (auto t : groupsbychar)
        groups.push_back(t.second);
    k=groups.size();
    for (int i=0; i<=n; i++)
        geninv[i]=(double)i*(i-1)/4;
    for (int i=0; i<k; i++)
        for (int j=0; j<k; j++)
            if (i!=j)
                calcinv(i, j);
    for (int i=0; i<(1<<k); i++)
        memo[i]=-1;
    cout << fixed << setprecision(5) << dp(0);

    return 0;
}

• Subtask 1: 5 / 5
• Subtask 2: 25 / 25
• Subtask 3: 30 / 30
• Subtask 4: 40 / 40