Submission #629572

#	Time	Username	Problem	Language	Result	Execution time	Memory
629572		_martynas	Boarding Passes (BOI22_passes)	C++11	100 / 100	286 ms	25548 KiB

passes

#include <bits/stdc++.h>
 
using namespace std;
using namespace std::chrono;
 
using ll = long long;
 
const int MXG = 15;
const ll INF = 1e17;
 
string s;
int n;
vector<ll> A[MXG];
// pref[i][j][k] -> i after j cost from left at k
vector<ll> pref[MXG][MXG];
// suff[i][j][k] -> i after j cost from right at k
vector<ll> suff[MXG][MXG];
ll dp[1 << MXG];
bool visited[1 << MXG];
 
// vector.insert(vector.begin(), x) 100x slower than vector.push_back(x)...
void init()
{
    // pref
    for(int i = 0; i < MXG; i++) {
        for(int j = 0; j < MXG; j++) {
            if(i == j || A[i].empty() || A[j].empty()) continue;
            int r = 0;
            int cost = 0;
            for(int k = 0; k < A[i].size(); k++) {
                while(r < A[j].size() && A[j][r] < A[i][k]) {
                    r++;
                }
                cost += r;
                pref[i][j].push_back(4*cost);
            }
        }
    }
    // suff
    for(int i = 0; i < MXG; i++) {
        for(int j = 0; j < MXG; j++) {
            if(i == j || A[i].empty() || A[j].empty()) continue;
            int r = A[j].size()-1;
            int cost = 0;
            for(int k = A[i].size()-1; k >= 0; k--) {
                while(r >= 0 && A[j][r] > A[i][k]) {
                    r--;
                }
                cost += A[j].size()-1-r;
                suff[i][j].push_back(4*cost);
            }
            reverse(suff[i][j].begin(), suff[i][j].end());
        }
    }
}
 
ll cost(int group, int bitmask, int split)
{
    ll sum = 0;
    for(int g = 0; g < MXG; g++) {
        if(((bitmask >> g) & 1) == 0 || A[g].empty() || g == group) continue;
        //cerr << "left: " << (split > -1 ? pref[group][g][split] : 0) << "\n";
        sum += split > -1 ? pref[group][g][split] : 0;
        //cerr << "right: " << (split+1 < A[group].size() ? suff[group][g][split+1] : 0) << "\n";
        sum += split+1 < A[group].size() ? suff[group][g][split+1] : 0;
    }
    if(split > 0) {
        //cerr << "left chance: " << split*(split+1) << "\n";
        // int*int overflow LET'S GO!
        sum += 1LL*split*(split+1); // chance to collide between on the left
    }
    ll cnt = A[group].size() - (split+1);
    if(cnt > 1) {
        //cerr << "right chance: " << cnt*(cnt-1) << "\n";
        sum += cnt*(cnt-1); // chance to collide between on the right
    }
    return sum;
}
 
ll recur(int bitmask)
{
    if(bitmask == 0) {
        return 0;
    }
    if(visited[bitmask]) {
        return dp[bitmask];
    }
    visited[bitmask] = true;
    ll mn = INF;
    for(int g = 0; g < MXG; g++) {
        if(((bitmask >> g) & 1) == 0) continue;
        int bits = bitmask - (1 << g);
        ll initial = recur(bits);
        if(A[g].empty()) {
            mn = min(mn, initial);
            continue;
        }
        int l = -1, r = A[g].size()-1;
        while(l < r) {
            int mid = l == -1 && r == 0 ? -1 : (l + r) / 2;
            ll a = cost(g, bits, mid);
            ll b = cost(g, bits, mid+1);
            if(a < b) {
                r = mid;
            }
            else {
                l = mid+1;
            }
        }
        mn = min(mn, initial + cost(g, bits, l));
    }
    dp[bitmask] = mn;
    return dp[bitmask];
}
 
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(0);
 
    getline(cin, s);
    n = s.size();
 
    for(int i = 0; i < n; i++) {
        A[s[i]-'A'].push_back(i);
    }
    init();
    double ans = recur(0x7fff);
    cout << fixed << setprecision(2) << ans / 4;
 
    return 0;
}
/*
AACCAA
HEHEHEHIHILOL
ONMLKJIHGFEDCBAABCDEFGHIJKLMNO
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
 
*/

Compilation message (stderr)

passes.cpp: In function 'void init()':
passes.cpp:30:30: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   30 |             for(int k = 0; k < A[i].size(); k++) {
      |                            ~~^~~~~~~~~~~~~
passes.cpp:31:25: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   31 |                 while(r < A[j].size() && A[j][r] < A[i][k]) {
      |                       ~~^~~~~~~~~~~~~
passes.cpp: In function 'll cost(int, int, int)':
passes.cpp:65:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   65 |         sum += split+1 < A[group].size() ? suff[group][g][split+1] : 0;
      |                ~~~~~~~~^~~~~~~~~~~~~~~~~

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