Submission #1081043

#	Time	Username	Problem	Language	Result	Execution time	Memory
1081043		Tymond	Boarding Passes (BOI22_passes)	C++17	100 / 100	420 ms	43440 KiB

passes

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define fi first
#define se second
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int, int>
#define pll pair<long long, long long>
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
inline int rand(int l,int r){return uniform_int_distribution<int>(l, r)(rng);}
inline ll rand(ll l,ll r){return uniform_int_distribution<ll>(l, r)(rng64);}
#ifdef DEBUG
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

const int MAXN = (1 << 15) + 7;
const int MAXM = 1e5 + 7;
int pref[MAXM];
ld dp[MAXN];
bool in[MAXN];
int n;
string s;
vi pos[20];
map<char, int> col;
int g;
ll cntPref[20][20][MAXM];
ll cntSuf[20][20][MAXM];

void preprocessing(){
    for(int i = 0; i < g; i++){
        for(int j = 1; j <= n; j++){
            pref[j] = pref[j - 1];
            if(col[s[j - 1]] == i){
                pref[j]++;
            }
        }

        for(int j = 0; j < g; j++){
            if(i == j){
                continue;
            }
            //for pref
            for(int y = 0; y < sz(pos[j]); y++){
                cntPref[i][j][y] = (ll)(y > 0 ? cntPref[i][j][y - 1] : 0) + pref[pos[j][y]];
            }
            //for suf
            for(int y = sz(pos[j]) - 1; y >= 0; y--){
                cntSuf[i][j][y] = (ll)(y < sz(pos[j]) - 1 ? cntSuf[i][j][y + 1] : 0) + pref[n] - pref[pos[j][y]];
            }
        }
    }
}

ld calc(int c, int k, int msk){
    int m = sz(pos[c]);
    ld ret = (ld)k * (k + 1) / 4 + (ld)(m - k - 1) * (m - k - 2) / 4;
    for(int i = 0; i < g; i++){
        if((1 << i) & msk){
            if(k >= 0){
                ret += cntPref[i][c][k];
            }

            if(k + 1 <= m - 1){
                ret += cntSuf[i][c][k + 1];
            }
        }  
    }

    return ret;
}

void bfs(){
    queue<int> q;
    q.push(0);
    in[0] = 1;
    while(sz(q)){
        int a = q.front();
        q.pop();

        for(int j = 0; j < g; j++){
            if((a & (1 << j)) != 0){
                continue;
            }
            ld add = calc(j, -1, a);
            int l = 0;
            int p = sz(pos[j]) - 1;
            while(p - l > 3){
                int q1 = l + (p - l) / 3;
                int q2 = p - (p - l) / 3;

                ld f1 = calc(j, q1, a);
                ld f2 = calc(j, q2, a);
                if(f1 < f2){
                    p = q2;
                }else{
                    l = q1;
                }
            }

            for(int i = l; i <= p; i++){
                add = min(add, calc(j, i, a));
            }

            if(!in[a + (1 << j)]){
                dp[a + (1 << j)] = dp[a] + add;
                in[a + (1 << j)] = 1;
                q.push(a + (1 << j));
            }else{
                dp[a + (1 << j)] = min(dp[a + (1 << j)], dp[a] + add);
            }
        }
    }
}


int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    
    cin >> s;
    n = sz(s);
    set<char> xd;
    for(auto ele : s){
        xd.insert(ele);
    }

    g = sz(xd);
    vector<char> vec;
    for(auto ele : xd){
        vec.pb(ele);
    }

    for(int i = 0; i < g; i++){
        col[vec[i]] = i;
    }

    for(int i = 0; i < n; i++){
        pos[col[s[i]]].pb(i);
    }

    if(g == 1){
        ld ans = (ld)(n / 2) * (n / 2 - 1) / 4 + (ld)(n - n / 2) * (n - n / 2 - 1) / 4;
        cout << fixed << setprecision(5) << ans << '\n';
        return 0;
    }

    preprocessing();
    bfs();

    cout << fixed << setprecision(9) << dp[(1 << g) - 1] << '\n';

    return 0;
}

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