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Submission #585311

# Submission time Handle Problem Language Result Execution time Memory
585311 2022-06-28T15:25:24 Z _martynas Boarding Passes (BOI22_passes) C++11
100 / 100
 244 ms 25528 KB 
#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];

// Ok but, why is vector.insert(vector.begin(), x) is 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();
    // the hell is this grader?
    ll ans = recur(0x7fff);
    cout << ans / 4;
    if(ans % 4 == 1) {
        cout << ".25";
    }
    else if(ans % 4 == 2) {
        cout << ".5";
    }
    else if(ans % 4 == 3) {
        cout << ".75";
    }

    return 0;
}
/*
AACCAA
HEHEHEHIHILOL
ONMLKJIHGFEDCBAABCDEFGHIJKLMNO
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

*/

Compilation message

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
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 596 KB Output is correct
2 Correct 4 ms 596 KB Output is correct
3 Correct 5 ms 596 KB Output is correct
4 Correct 5 ms 596 KB Output is correct
5 Correct 9 ms 596 KB Output is correct
6 Correct 16 ms 1680 KB Output is correct
7 Correct 15 ms 1680 KB Output is correct
8 Correct 16 ms 1680 KB Output is correct
9 Correct 15 ms 1680 KB Output is correct

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 596 KB Output is correct
2 Correct 7 ms 620 KB Output is correct
3 Correct 32 ms 596 KB Output is correct
4 Correct 35 ms 596 KB Output is correct
5 Correct 20 ms 636 KB Output is correct
6 Correct 18 ms 596 KB Output is correct
7 Correct 31 ms 596 KB Output is correct
8 Correct 26 ms 620 KB Output is correct
9 Correct 28 ms 596 KB Output is correct
10 Correct 25 ms 596 KB Output is correct
11 Correct 24 ms 624 KB Output is correct
12 Correct 26 ms 596 KB Output is correct
13 Correct 28 ms 624 KB Output is correct
14 Correct 27 ms 596 KB Output is correct
15 Correct 25 ms 596 KB Output is correct
16 Correct 27 ms 596 KB Output is correct
17 Correct 26 ms 596 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 596 KB Output is correct
2 Correct 7 ms 620 KB Output is correct
3 Correct 32 ms 596 KB Output is correct
4 Correct 35 ms 596 KB Output is correct
5 Correct 20 ms 636 KB Output is correct
6 Correct 18 ms 596 KB Output is correct
7 Correct 31 ms 596 KB Output is correct
8 Correct 26 ms 620 KB Output is correct
9 Correct 28 ms 596 KB Output is correct
10 Correct 25 ms 596 KB Output is correct
11 Correct 24 ms 624 KB Output is correct
12 Correct 26 ms 596 KB Output is correct
13 Correct 28 ms 624 KB Output is correct
14 Correct 27 ms 596 KB Output is correct
15 Correct 25 ms 596 KB Output is correct
16 Correct 27 ms 596 KB Output is correct
17 Correct 26 ms 596 KB Output is correct
18 Correct 8 ms 596 KB Output is correct
19 Correct 8 ms 596 KB Output is correct
20 Correct 34 ms 724 KB Output is correct
21 Correct 37 ms 596 KB Output is correct
22 Correct 20 ms 632 KB Output is correct
23 Correct 21 ms 596 KB Output is correct
24 Correct 29 ms 612 KB Output is correct
25 Correct 24 ms 596 KB Output is correct
26 Correct 27 ms 596 KB Output is correct
27 Correct 25 ms 628 KB Output is correct
28 Correct 24 ms 628 KB Output is correct
29 Correct 25 ms 596 KB Output is correct
30 Correct 27 ms 620 KB Output is correct
31 Correct 28 ms 596 KB Output is correct
32 Correct 24 ms 596 KB Output is correct
33 Correct 28 ms 620 KB Output is correct
34 Correct 30 ms 608 KB Output is correct
35 Correct 14 ms 748 KB Output is correct
36 Correct 12 ms 852 KB Output is correct
37 Correct 95 ms 2388 KB Output is correct
38 Correct 111 ms 2132 KB Output is correct
39 Correct 35 ms 2260 KB Output is correct
40 Correct 86 ms 2132 KB Output is correct
41 Correct 99 ms 2596 KB Output is correct
42 Correct 91 ms 2616 KB Output is correct
43 Correct 98 ms 2560 KB Output is correct
44 Correct 93 ms 2516 KB Output is correct
45 Correct 94 ms 2612 KB Output is correct
46 Correct 92 ms 2648 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 596 KB Output is correct
2 Correct 4 ms 596 KB Output is correct
3 Correct 5 ms 596 KB Output is correct
4 Correct 5 ms 596 KB Output is correct
5 Correct 9 ms 596 KB Output is correct
6 Correct 16 ms 1680 KB Output is correct
7 Correct 15 ms 1680 KB Output is correct
8 Correct 16 ms 1680 KB Output is correct
9 Correct 15 ms 1680 KB Output is correct
10 Correct 7 ms 596 KB Output is correct
11 Correct 7 ms 620 KB Output is correct
12 Correct 32 ms 596 KB Output is correct
13 Correct 35 ms 596 KB Output is correct
14 Correct 20 ms 636 KB Output is correct
15 Correct 18 ms 596 KB Output is correct
16 Correct 31 ms 596 KB Output is correct
17 Correct 26 ms 620 KB Output is correct
18 Correct 28 ms 596 KB Output is correct
19 Correct 25 ms 596 KB Output is correct
20 Correct 24 ms 624 KB Output is correct
21 Correct 26 ms 596 KB Output is correct
22 Correct 28 ms 624 KB Output is correct
23 Correct 27 ms 596 KB Output is correct
24 Correct 25 ms 596 KB Output is correct
25 Correct 27 ms 596 KB Output is correct
26 Correct 26 ms 596 KB Output is correct
27 Correct 8 ms 596 KB Output is correct
28 Correct 8 ms 596 KB Output is correct
29 Correct 34 ms 724 KB Output is correct
30 Correct 37 ms 596 KB Output is correct
31 Correct 20 ms 632 KB Output is correct
32 Correct 21 ms 596 KB Output is correct
33 Correct 29 ms 612 KB Output is correct
34 Correct 24 ms 596 KB Output is correct
35 Correct 27 ms 596 KB Output is correct
36 Correct 25 ms 628 KB Output is correct
37 Correct 24 ms 628 KB Output is correct
38 Correct 25 ms 596 KB Output is correct
39 Correct 27 ms 620 KB Output is correct
40 Correct 28 ms 596 KB Output is correct
41 Correct 24 ms 596 KB Output is correct
42 Correct 28 ms 620 KB Output is correct
43 Correct 30 ms 608 KB Output is correct
44 Correct 14 ms 748 KB Output is correct
45 Correct 12 ms 852 KB Output is correct
46 Correct 95 ms 2388 KB Output is correct
47 Correct 111 ms 2132 KB Output is correct
48 Correct 35 ms 2260 KB Output is correct
49 Correct 86 ms 2132 KB Output is correct
50 Correct 99 ms 2596 KB Output is correct
51 Correct 91 ms 2616 KB Output is correct
52 Correct 98 ms 2560 KB Output is correct
53 Correct 93 ms 2516 KB Output is correct
54 Correct 94 ms 2612 KB Output is correct
55 Correct 92 ms 2648 KB Output is correct
56 Correct 20 ms 628 KB Output is correct
57 Correct 64 ms 612 KB Output is correct
58 Correct 10 ms 632 KB Output is correct
59 Correct 4 ms 616 KB Output is correct
60 Correct 5 ms 616 KB Output is correct
61 Correct 6 ms 596 KB Output is correct
62 Correct 10 ms 632 KB Output is correct
63 Correct 15 ms 1680 KB Output is correct
64 Correct 15 ms 1680 KB Output is correct
65 Correct 15 ms 1680 KB Output is correct
66 Correct 15 ms 1680 KB Output is correct
67 Correct 8 ms 596 KB Output is correct
68 Correct 7 ms 628 KB Output is correct
69 Correct 33 ms 620 KB Output is correct
70 Correct 37 ms 608 KB Output is correct
71 Correct 21 ms 596 KB Output is correct
72 Correct 20 ms 620 KB Output is correct
73 Correct 29 ms 596 KB Output is correct
74 Correct 25 ms 620 KB Output is correct
75 Correct 29 ms 596 KB Output is correct
76 Correct 26 ms 596 KB Output is correct
77 Correct 26 ms 624 KB Output is correct
78 Correct 26 ms 620 KB Output is correct
79 Correct 27 ms 596 KB Output is correct
80 Correct 28 ms 596 KB Output is correct
81 Correct 25 ms 596 KB Output is correct
82 Correct 27 ms 596 KB Output is correct
83 Correct 27 ms 596 KB Output is correct
84 Correct 12 ms 752 KB Output is correct
85 Correct 14 ms 752 KB Output is correct
86 Correct 95 ms 2428 KB Output is correct
87 Correct 112 ms 2152 KB Output is correct
88 Correct 36 ms 2260 KB Output is correct
89 Correct 87 ms 2168 KB Output is correct
90 Correct 93 ms 2600 KB Output is correct
91 Correct 96 ms 2516 KB Output is correct
92 Correct 98 ms 2516 KB Output is correct
93 Correct 92 ms 2516 KB Output is correct
94 Correct 92 ms 2516 KB Output is correct
95 Correct 97 ms 2644 KB Output is correct
96 Correct 244 ms 25240 KB Output is correct
97 Correct 68 ms 596 KB Output is correct
98 Correct 235 ms 25216 KB Output is correct
99 Correct 85 ms 23944 KB Output is correct
100 Correct 40 ms 716 KB Output is correct
101 Correct 229 ms 25264 KB Output is correct
102 Correct 219 ms 25352 KB Output is correct
103 Correct 223 ms 25228 KB Output is correct
104 Correct 225 ms 25332 KB Output is correct
105 Correct 230 ms 25376 KB Output is correct
106 Correct 222 ms 25204 KB Output is correct
107 Correct 225 ms 25528 KB Output is correct
108 Correct 211 ms 23452 KB Output is correct
109 Correct 234 ms 25460 KB Output is correct