Submission #949831

#	Time	Username	Problem	Language	Result	Execution time	Memory
949831		sysia	Boarding Passes (BOI22_passes)	C++17	100 / 100	231 ms	91308 KiB

passes

//Sylwia Sapkowska
#include <bits/stdc++.h>
#pragma GCC optimize("O3", "unroll-loops")
using namespace std;

void __print(int x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << "'" << x << "'";}
void __print(const char *x) {cerr << '"' << x << '"';}
void __print(const string &x) {cerr << '"' << x << '"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef LOCAL
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif

#define int long long
typedef pair<int, int> T;
const int oo = 1e18, oo2 = 1e9+7, K = 30;
const int mod = 998244353;
typedef long double ld;

void solve(){
    string s; cin >> s;
    int n = (int)s.size();
    vector<int>used(K);
    for (auto c: s) used[c-'A']++;
    vector<int>scale(K);
    int G = 0;
    for (int i = 0; i<K; i++) if (used[i]) scale[i] = G++;
    debug(G); //grupy [0, G-1]
    vector<vector<int>>what(G);
    for (int i = 0; i<n; i++) {
        what[scale[s[i]-'A']].emplace_back(i);
    }
    vector<ld>dp((1<<G), oo);
    dp[0] = 0;
    vector left(n, vector<int>(G)), right(n, vector<int>(G)); //dla i-tego indeksu grupa g doklada left[i] elementow z lewej
    for (int i = 0; i<n; i++){
        for (int g = 0; g < G; g++){
            if (scale[s[i]-'A'] == g) continue;
            int t = (int)(lower_bound(what[g].begin(), what[g].end(), i)-what[g].begin());
            left[i][g] = t;
            right[i][g] = (int)what[g].size()-t;
        }
    }
    vector<int>prev(G, -1);
    vector pref(n, vector<int>(G)), suf(n, vector<int>(G));
    vector lewo(n, vector<int>(G)), prawo(n, vector<int>(G));
    for (int i = 0; i<n; i++){
        int c = scale[s[i]-'A'];
        if (prev[c] != -1) pref[i] = pref[prev[c]];
        //pref[i][g] -> suma po left[j][g] po wszystkich j<=i, ze j jest w tej samej grupie co i
        for (int g = 0; g < G; g++){
            pref[i][g] += left[i][g];
        }
        prev[c] = i;
        lewo[i] = prev;
    }
    prev.assign(G, -1);
    for (int i = n-1; i>=0; i--){
        int c = scale[s[i]-'A'];
        if (prev[c] != -1) suf[i] = suf[prev[c]];
        for (int g = 0; g < G; g++) suf[i][g] += right[i][g];
        prev[c] = i;
        prawo[i] = prev;
    }
    //2^{G-1} * G * (GlogN)
    for (int mask = 0; mask < (1<<G); mask++){
        for (int i = 0; i<G; i++){
            if (mask&(1<<i)) continue;
            //dokladam grupe i --> to sie wydarzy 2^{G-1} razy
            int k = (int)what[i].size();
            auto check = [&](int p){
                ld L = (ld)p/2.0;
                ld R = (ld)(k-p-1)/2.0;
                for (int rep = 0; rep < G; rep++){
                    if (mask&(1<<rep)){
                        L += left[what[i][p]][rep];
                        R += right[what[i][p]][rep];
                    }
                }
                return L <= R;
            };
            auto total = [&](int p) -> ld {
                //jesli osoba p jest ostatnia osoba ktora idzie z lewej strony, to koszt to?
                //L = (0 + 1 + .. + p)/2        R = (0 + 1 + ... + (k-(p+1)-1))/2
                ld L = (ld)(p*(p+1))/4.0;
                ld R = (ld)(k-p-2)*(k-p-1)/4.0;
                for (int rep = 0; rep < G; rep++){
                    if (mask&(1<<rep)){
                        if (p >= 0) {
                            L += pref[what[i][p]][rep];
                            debug(pref[what[i][p]][rep]);
                        }
                        if (p+1 < k){
                            R += suf[what[i][p+1]][rep];
                            debug(suf[what[i][p+1]][rep]);
                        }   
                    }
                }
                return L+R;
            };
            //pewien prefiks przyjdzie z lewej, pewien sufiks z prawej
            int l = 0, r = k-1, curr = -1;
            while (r >= l){
                int m = (l+r)/2;
                if (check(m)){
                    curr = m;
                    l = m+1;
                } else {
                    r = m-1;
                }
            }
            dp[mask^(1<<i)] = min(dp[mask^(1<<i)], dp[mask] + total(curr));
        }
    }
    cout << fixed << setprecision(10) << dp.back() << "\n";
}

int32_t main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    int t = 1;
    //cin >> t;
    while (t--) solve();

    return 0;
}

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