Submission #898226

# Submission time Handle Problem Language Result Execution time Memory
898226 2024-01-04T11:46:41 Z GrindMachine Boarding Passes (BOI22_passes) C++17
100 / 100
207 ms 27480 KB
#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;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*



*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

vector<ll> add_pref[15][15], add_suff[15][15];

void solve(int test_case)
{
    string s; cin >> s;
    ll n = sz(s);
    s = "$" + s;

    ll siz = 0;
    rep1(i,n){
        amax(siz,(ll)s[i]-'A'+1);
    }

    vector<ll> pos[siz];
    rep1(i,n) pos[s[i]-'A'].pb(i);

    vector<ll> pref(n+5);

    rep(x,siz){
        fill(all(pref),0);
        trav(i,pos[x]){
            pref[i]++;
        }

        rep1(i,n) pref[i] += pref[i-1];
        
        rep(y,siz){
            if(x == y) conts;

            ll sum1 = 0, sum2 = 0;            
            add_pref[x][y].pb(0);
            add_suff[x][y].pb(0);

            trav(i,pos[y]){
                sum1 += pref[i];
                sum2 += pref[n]-pref[i];
                add_pref[x][y].pb(sum1);
                add_suff[x][y].pb(sum2);
            }
        }
    }

    vector<ll> dp(1<<siz,inf2);
    dp[0] = 0;

    rep(mask,1<<siz){
        vector<ll> seated;
        rep(c,siz){
            if(mask&(1<<c)){
                seated.pb(c);
            }
        }

        rep(c,siz){
            if(mask&(1<<c)) conts;

            ll sizp = sz(pos[c]);
            
            auto f = [&](ll i){
                ll s1 = i, s2 = sizp-i;
                ll cost1 = 0, cost2 = 0;
                trav(d,seated){
                    cost1 += add_pref[d][c][i];
                    cost2 += add_suff[d][c].back()-add_suff[d][c][i];
                }

                ll cost = s1*(s1-1)+s2*(s2-1)+cost1*4+cost2*4;
                return cost;
            };

            ll l = 0, r = sizp;
            ll p = sizp;

            while(l <= r){
                ll mid = (l+r) >> 1;
                if(f(mid) <= f(mid+1)){
                    p = mid;
                    r = mid-1;
                }
                else{
                    l = mid+1;
                }
            }

            ll mn_cost = inf2;

            for(int i = max(p-5,0ll); i <= min(p+5,sizp); ++i){
                amin(mn_cost,f(i));
            }

            amin(dp[mask|(1<<c)],dp[mask]+mn_cost);
        }
    }

    ld ans = (ld)dp[(1<<siz)-1]/4;
    cout << fixed << setprecision(11);
    cout << ans << endl;
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}
# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
3 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
4 Correct 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 0 ms 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 3 ms 1996 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 2 ms 2252 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 3 ms 2128 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 3 ms 2252 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
3 Correct 1 ms 468 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
4 Correct 0 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 1 ms 344 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 1 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 1 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
8 Correct 1 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 1 ms 344 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 1 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 1 ms 344 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 1 ms 344 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 1 ms 344 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
14 Correct 1 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
15 Correct 0 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
16 Correct 0 ms 348 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
17 Correct 1 ms 348 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
3 Correct 1 ms 468 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
4 Correct 0 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 1 ms 344 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 1 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 1 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
8 Correct 1 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 1 ms 344 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 1 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 1 ms 344 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 1 ms 344 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 1 ms 344 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
14 Correct 1 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
15 Correct 0 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
16 Correct 0 ms 348 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
17 Correct 1 ms 348 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
18 Correct 1 ms 468 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
19 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
20 Correct 1 ms 348 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
21 Correct 1 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
22 Correct 1 ms 344 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
23 Correct 1 ms 604 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
24 Correct 1 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
25 Correct 1 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
26 Correct 1 ms 348 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
27 Correct 0 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
28 Correct 1 ms 344 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
29 Correct 1 ms 344 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
30 Correct 1 ms 348 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
31 Correct 0 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
32 Correct 1 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
33 Correct 1 ms 348 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
34 Correct 1 ms 348 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
35 Correct 2 ms 1884 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
36 Correct 2 ms 1884 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
37 Correct 4 ms 2140 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
38 Correct 5 ms 1884 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
39 Correct 3 ms 2140 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
40 Correct 3 ms 1884 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
41 Correct 5 ms 2396 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
42 Correct 4 ms 2396 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
43 Correct 4 ms 2396 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
44 Correct 5 ms 2392 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
45 Correct 4 ms 2396 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
46 Correct 4 ms 2396 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
3 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
4 Correct 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 0 ms 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 3 ms 1996 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 2 ms 2252 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 3 ms 2128 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 3 ms 2252 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
10 Correct 0 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
11 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
12 Correct 1 ms 468 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
13 Correct 0 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
14 Correct 1 ms 344 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
15 Correct 1 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
16 Correct 1 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
17 Correct 1 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
18 Correct 1 ms 344 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
19 Correct 1 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
20 Correct 1 ms 344 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
21 Correct 1 ms 344 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
22 Correct 1 ms 344 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
23 Correct 1 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
24 Correct 0 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
25 Correct 0 ms 348 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
26 Correct 1 ms 348 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
27 Correct 1 ms 468 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
28 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
29 Correct 1 ms 348 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
30 Correct 1 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
31 Correct 1 ms 344 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
32 Correct 1 ms 604 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
33 Correct 1 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
34 Correct 1 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
35 Correct 1 ms 348 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
36 Correct 0 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
37 Correct 1 ms 344 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
38 Correct 1 ms 344 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
39 Correct 1 ms 348 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
40 Correct 0 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
41 Correct 1 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
42 Correct 1 ms 348 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
43 Correct 1 ms 348 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
44 Correct 2 ms 1884 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
45 Correct 2 ms 1884 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
46 Correct 4 ms 2140 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
47 Correct 5 ms 1884 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
48 Correct 3 ms 2140 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
49 Correct 3 ms 1884 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
50 Correct 5 ms 2396 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
51 Correct 4 ms 2396 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
52 Correct 4 ms 2396 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
53 Correct 5 ms 2392 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
54 Correct 4 ms 2396 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
55 Correct 4 ms 2396 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
56 Correct 23 ms 604 KB found '7.5000000000', expected '7.5000000000', error '0.0000000000'
57 Correct 30 ms 604 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
58 Correct 1 ms 344 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
59 Correct 0 ms 344 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
60 Correct 1 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
61 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
62 Correct 0 ms 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
63 Correct 2 ms 2248 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
64 Correct 2 ms 2252 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
65 Correct 2 ms 2128 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
66 Correct 2 ms 2252 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
67 Correct 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
68 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
69 Correct 0 ms 468 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
70 Correct 1 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
71 Correct 1 ms 348 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
72 Correct 1 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
73 Correct 1 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
74 Correct 1 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
75 Correct 1 ms 344 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
76 Correct 1 ms 404 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
77 Correct 1 ms 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
78 Correct 1 ms 344 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
79 Correct 1 ms 348 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
80 Correct 1 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
81 Correct 1 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
82 Correct 0 ms 464 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
83 Correct 0 ms 348 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
84 Correct 2 ms 1884 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
85 Correct 2 ms 1884 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
86 Correct 4 ms 2136 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
87 Correct 3 ms 1884 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
88 Correct 3 ms 2140 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
89 Correct 4 ms 1884 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
90 Correct 4 ms 2396 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
91 Correct 4 ms 2596 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
92 Correct 4 ms 2396 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
93 Correct 4 ms 2396 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
94 Correct 4 ms 2396 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
95 Correct 4 ms 2396 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
96 Correct 179 ms 26332 KB found '1239972790.0000000000', expected '1239972790.0000000000', error '0.0000000000'
97 Correct 17 ms 600 KB found '128.0000000000', expected '128.0000000000', error '0.0000000000'
98 Correct 191 ms 26284 KB found '161053893.0000000000', expected '161053893.0000000000', error '0.0000000000'
99 Correct 72 ms 24896 KB found '1249625032.0000000000', expected '1249625032.0000000000', error '0.0000000000'
100 Correct 28 ms 600 KB found '10.5000000000', expected '10.5000000000', error '0.0000000000'
101 Correct 179 ms 26340 KB found '1095334900.0000000000', expected '1095334900.0000000000', error '0.0000000000'
102 Correct 188 ms 26960 KB found '1249723731.0000000000', expected '1249723731.0000000000', error '0.0000000000'
103 Correct 184 ms 26712 KB found '1239994164.5000000000', expected '1239994164.5000000000', error '0.0000000000'
104 Correct 203 ms 26900 KB found '1239994234.5000000000', expected '1239994234.5000000000', error '0.0000000000'
105 Correct 183 ms 26840 KB found '1239994121.0000000000', expected '1239994121.0000000000', error '0.0000000000'
106 Correct 179 ms 26740 KB found '1239994009.0000000000', expected '1239994009.0000000000', error '0.0000000000'
107 Correct 196 ms 26844 KB found '1239993860.5000000000', expected '1239993860.5000000000', error '0.0000000000'
108 Correct 100 ms 24616 KB found '1237107336.5000000000', expected '1237107336.5000000000', error '0.0000000000'
109 Correct 207 ms 27480 KB found '1239994062.5000000000', expected '1239994062.5000000000', error '0.0000000000'