Submission #599433

#	Time	Username	Problem	Language	Result	Execution time	Memory
599433		fvogel499	Boarding Passes (BOI22_passes)	C++17	0 / 100	1132 ms	28664 KiB

passes

/*
 * File created on 07/19/2022 at 15:24:35.
 * Link to problem: 
 * Description: 
 * Time complexity: O()
 * Space complexity: O()
 * Status: ---
 * Copyright: Ⓒ 2022 Francois Vogel
*/

#include <bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

#define pii pair<int, int>
#define f first
#define s second

#define vi vector<int>
#define all(x) x.begin(), x.end()
#define size(x) (int)((x).size())
#define pb push_back
#define ins insert
#define cls clear

#define int ll
#define ll long long
#define ld long double

typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

const int siz = 1e6+40;

ld fact [siz];

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

    fact[0] = 1;
    for (int i = 1; i < siz; i++) fact[i] = fact[i-1] * i;

    cout << fixed << setprecision(3);

    string b;
    cin >> b;
    const int n = size(b);
    ld bin [n+1][n+1]; // bin[i][j] = binomial coefficient (i, j) = i! / (j! * (i-j)!) = i * (i-1) * ... * (i-j+1) / j! = ways to choose j elements from i elements
    for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) {
        if (j > i) {
            bin[i][j] = 0;
            continue;
        }
        else if (i-j < j) {
            bin[i][j] = bin[i][i-j];
            continue;
        }
        bin[i][j] = 1;
        for (int k = i-j+1; k <= i; k++) bin[i][j] *= k;
        for (int k = 1; k <= j; k++) bin[i][j] /= k;
    }
    int gK = 0;
    for (char i : b) if (i-'A'+1 > gK) gK = i-'A'+1;
    vi toPermute;
    for (int i = 0; i < gK; i++) toPermute.pb(i);
    ld offMin = n*n;
    do {
        for (int i = 0; i < n; i++) {
            b[i] = char('A'+toPermute[b[i]-'A']);
        }
        ld res = 0;
        for (int i = 0; i < gK; i++) {
            vi pos;
            for (int j = 0; j < n; j++) if (b[j]-'A' == i) {
                pos.pb(j);
            }
            if (pos.empty()) continue;
            int pref [n];
            for (int j = 0; j < n; j++) pref[j] = (b[j]-'A' < i);
            for (int j = 1; j < n; j++) pref[j] += pref[j-1];
            int suf [n];
            for (int j = 0; j < n; j++) suf[j] = (b[j]-'A' < i);
            for (int j = n-2; j >= 0; j--) suf[j] += suf[j+1];
            for (int j = 0; j < size(pos); j++) {
                int dl = 0;
                if (pos[j]) dl = pref[pos[j]-1];
                int dr = 0;
                if (pos[j]+1 < n) dr = suf[pos[j]+1];
                int cl = j;
                int cr = size(pos)-1-j;
                for (int ul = 0; ul <= cl; ul++) for (int ur = 0; ur <= cr; ur++) {
                    ld loc = bin[cl][ul]*bin[cr][ur];
                    loc *= fact[ul+ur];
                    ld mul = min(dl+ul, dr+ur);
                    int lft = size(pos)-1-ul-ur;
                    res += loc*mul*fact[lft]/fact[size(pos)];
                }
            }
        }
        offMin = min(offMin, res);
        vi invToPermute(gK);
        for (int i = 0; i < gK; i++) invToPermute[toPermute[i]] = i;
        for (int i = 0; i < n; i++) {
            b[i] = char('A'+invToPermute[b[i]-'A']);
        }
    } while (next_permutation(all(toPermute)));
    cout << offMin;

    cout.flush();
    int d = 0;
    d++;
}

• Subtask 1: 0 / 5
• Subtask 2: 0 / 25
• Subtask 3: 0 / 30
• Subtask 4: 0 / 40