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Submission #572573

# Submission time Handle Problem Language Result Execution time Memory
572573 2022-06-04T17:19:37 Z model_code Boarding Passes (BOI22_passes) C++17
100 / 100
 533 ms 57524 KB 
// DP approach with ternary search
// O(2^T * T^2 * log N + N * T)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

constexpr ll INF = numeric_limits<ll>::max() / 10;

int type_cnt;
int n;
vector<ll> cnt;
vector<vector<ll>> l, r; // t, pos -> number of passengers of type t left/right of pos
vector<vector<vector<ll>>> l2, r2; // A, B, i -> cost caused by group B boarding before A, to anyone up to the i-th member of group A and boarding from the left/right
vector<vector<int>> groups; // A -> positions of all members of group A, sorted

ll get_cost(size_t already_boarded, int next, int split)
{
    ll result = 0;
    for (int t = 0; t < type_cnt; ++t) {
        ll tmp = l2[next][t][split] + r2[next][t][split];
        if (already_boarded & (1ll << t)) {
            result += 2 * tmp;
        } else if (t == next) {
            result += tmp;
        }
    }
    return result;
}

// Cost of the next group boarding, if the given set of groups has already boarded before.
ll get_cost(size_t already_boarded, int next)
{
    int mini = 0, maxi = groups[next].size() + 1;
    while (maxi - mini > 1) {
        int m1 = (maxi + mini) / 2 - 1;
        int m2 = m1 + 1;
        ll c1 = get_cost(already_boarded, next, m1);
        ll c2 = get_cost(already_boarded, next, m2);
        if (c1 < c2) maxi = m2;
        else mini = m1 + 1;
    }

    ll result = get_cost(already_boarded, next, mini);
    return result;
}

ll calc_costs()
{
    vector<ll> dp(1ll << type_cnt, INF);
    dp[0] = 0;
    for (int i = 1; i < 1ll << type_cnt; ++i) {
        for (int t = 0; t < type_cnt; ++t) {
            if (!(i & (1ll << t))) continue;
            size_t parent = i & ~(1ll << t);
            dp[i] = min(dp[i], dp[parent] + get_cost(parent, t));
        }
    }
    return dp[(1ll << type_cnt) - 1];
}

int main()
{
    string s;
    cin >> s;
    n = s.size();
    map<char, char> types;
    for (char& c: s) {
        if (!types.count(c)) {
            char id = static_cast<char>(types.size());
            types[c] = id;
        }
        c = types[c];
    }

    type_cnt = types.size();
    cnt.assign(type_cnt, 0);
    for (char c: s) ++cnt[c];

    groups.resize(type_cnt);
    for (int i = 0; i < n; ++i) {
        groups[s[i]].push_back(i);
    }

    l = r = vector<vector<ll>>(type_cnt, vector<ll>(n));
    vector<ll> tmp_cnt(type_cnt, 0);
    for (size_t i = 0; i < n; ++i) {
        for (size_t j = 0; j < type_cnt; ++j) {
            l[j][i] = tmp_cnt[j];
            r[j][i] = cnt[j] - tmp_cnt[j];
        }
        ++tmp_cnt[s[i]];
        --r[s[i]][i];
    }

    vector<vector<ll>> tmp_costs_l, tmp_costs_r;
    tmp_costs_l = tmp_costs_r = vector<vector<ll>>(type_cnt, vector<ll>(type_cnt, 0));
    l2 = r2 = vector<vector<vector<ll>>>(type_cnt, vector<vector<ll>>(type_cnt, {0}));
    for (size_t i = 0; i < n; ++i) {
        for (int j = 0; j < type_cnt; ++j) {
            tmp_costs_l[s[i]][j] += l[j][i];
            tmp_costs_r[s[n - i - 1]][j] += r[j][n - i - 1];
        }
        for (int k = 0; k < type_cnt; ++k) {
            l2[s[i]][k].push_back(tmp_costs_l[s[i]][k]);
            r2[s[n - i - 1]][k].push_back(tmp_costs_r[s[n - i - 1]][k]);
        }
    }
    for (int i = 0; i < type_cnt; ++i) {
        for (int j = 0; j < type_cnt; ++j) {
            reverse(r2[i][j].begin(), r2[i][j].end());
        }
    }

    auto result = calc_costs();
    cout << result / 2 << ((result % 2) ? ".5" : "") << "\n";
}

Compilation message

passes.cpp: In function 'int main()':
passes.cpp:87:26: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   87 |     for (size_t i = 0; i < n; ++i) {
      |                        ~~^~~
passes.cpp:88:30: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   88 |         for (size_t j = 0; j < type_cnt; ++j) {
      |                            ~~^~~~~~~~~~
passes.cpp:99:26: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   99 |     for (size_t i = 0; i < n; ++i) {
      |                        ~~^~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 240 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 9 ms 4344 KB Output is correct
7 Correct 10 ms 4716 KB Output is correct
8 Correct 10 ms 5352 KB Output is correct
9 Correct 11 ms 5308 KB Output is correct

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 244 KB Output is correct
2 Correct 1 ms 236 KB Output is correct
3 Correct 1 ms 360 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 1 ms 376 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 252 KB Output is correct
9 Correct 1 ms 256 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 256 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 244 KB Output is correct
2 Correct 1 ms 236 KB Output is correct
3 Correct 1 ms 360 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 1 ms 376 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 252 KB Output is correct
9 Correct 1 ms 256 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 256 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 256 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 360 KB Output is correct
22 Correct 1 ms 384 KB Output is correct
23 Correct 1 ms 256 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 0 ms 212 KB Output is correct
26 Correct 1 ms 216 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 1 ms 216 KB Output is correct
29 Correct 1 ms 256 KB Output is correct
30 Correct 1 ms 224 KB Output is correct
31 Correct 1 ms 212 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 1 ms 212 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 2 ms 852 KB Output is correct
36 Correct 2 ms 852 KB Output is correct
37 Correct 10 ms 4084 KB Output is correct
38 Correct 10 ms 3572 KB Output is correct
39 Correct 8 ms 4320 KB Output is correct
40 Correct 9 ms 3540 KB Output is correct
41 Correct 8 ms 4288 KB Output is correct
42 Correct 11 ms 4164 KB Output is correct
43 Correct 10 ms 3964 KB Output is correct
44 Correct 10 ms 3924 KB Output is correct
45 Correct 8 ms 4180 KB Output is correct
46 Correct 13 ms 4192 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 240 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 9 ms 4344 KB Output is correct
7 Correct 10 ms 4716 KB Output is correct
8 Correct 10 ms 5352 KB Output is correct
9 Correct 11 ms 5308 KB Output is correct
10 Correct 1 ms 244 KB Output is correct
11 Correct 1 ms 236 KB Output is correct
12 Correct 1 ms 360 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 376 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 252 KB Output is correct
18 Correct 1 ms 256 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 1 ms 256 KB Output is correct
23 Correct 1 ms 212 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 1 ms 212 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 1 ms 256 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 ms 360 KB Output is correct
31 Correct 1 ms 384 KB Output is correct
32 Correct 1 ms 256 KB Output is correct
33 Correct 1 ms 340 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 1 ms 216 KB Output is correct
36 Correct 1 ms 212 KB Output is correct
37 Correct 1 ms 216 KB Output is correct
38 Correct 1 ms 256 KB Output is correct
39 Correct 1 ms 224 KB Output is correct
40 Correct 1 ms 212 KB Output is correct
41 Correct 1 ms 212 KB Output is correct
42 Correct 1 ms 212 KB Output is correct
43 Correct 1 ms 212 KB Output is correct
44 Correct 2 ms 852 KB Output is correct
45 Correct 2 ms 852 KB Output is correct
46 Correct 10 ms 4084 KB Output is correct
47 Correct 10 ms 3572 KB Output is correct
48 Correct 8 ms 4320 KB Output is correct
49 Correct 9 ms 3540 KB Output is correct
50 Correct 8 ms 4288 KB Output is correct
51 Correct 11 ms 4164 KB Output is correct
52 Correct 10 ms 3964 KB Output is correct
53 Correct 10 ms 3924 KB Output is correct
54 Correct 8 ms 4180 KB Output is correct
55 Correct 13 ms 4192 KB Output is correct
56 Correct 1 ms 224 KB Output is correct
57 Correct 73 ms 608 KB Output is correct
58 Correct 1 ms 340 KB Output is correct
59 Correct 0 ms 212 KB Output is correct
60 Correct 0 ms 212 KB Output is correct
61 Correct 1 ms 212 KB Output is correct
62 Correct 1 ms 344 KB Output is correct
63 Correct 9 ms 4384 KB Output is correct
64 Correct 11 ms 4752 KB Output is correct
65 Correct 11 ms 5308 KB Output is correct
66 Correct 12 ms 5392 KB Output is correct
67 Correct 1 ms 212 KB Output is correct
68 Correct 1 ms 256 KB Output is correct
69 Correct 1 ms 340 KB Output is correct
70 Correct 1 ms 340 KB Output is correct
71 Correct 1 ms 340 KB Output is correct
72 Correct 1 ms 212 KB Output is correct
73 Correct 1 ms 212 KB Output is correct
74 Correct 1 ms 256 KB Output is correct
75 Correct 1 ms 212 KB Output is correct
76 Correct 1 ms 256 KB Output is correct
77 Correct 1 ms 212 KB Output is correct
78 Correct 1 ms 212 KB Output is correct
79 Correct 1 ms 212 KB Output is correct
80 Correct 1 ms 256 KB Output is correct
81 Correct 1 ms 308 KB Output is correct
82 Correct 1 ms 212 KB Output is correct
83 Correct 1 ms 212 KB Output is correct
84 Correct 2 ms 852 KB Output is correct
85 Correct 2 ms 852 KB Output is correct
86 Correct 10 ms 4096 KB Output is correct
87 Correct 9 ms 3620 KB Output is correct
88 Correct 8 ms 4412 KB Output is correct
89 Correct 10 ms 3536 KB Output is correct
90 Correct 10 ms 4316 KB Output is correct
91 Correct 9 ms 4180 KB Output is correct
92 Correct 11 ms 4096 KB Output is correct
93 Correct 10 ms 3976 KB Output is correct
94 Correct 10 ms 4200 KB Output is correct
95 Correct 9 ms 4180 KB Output is correct
96 Correct 500 ms 52956 KB Output is correct
97 Correct 31 ms 468 KB Output is correct
98 Correct 503 ms 51824 KB Output is correct
99 Correct 153 ms 53988 KB Output is correct
100 Correct 37 ms 640 KB Output is correct
101 Correct 407 ms 52512 KB Output is correct
102 Correct 412 ms 54148 KB Output is correct
103 Correct 352 ms 54396 KB Output is correct
104 Correct 409 ms 55704 KB Output is correct
105 Correct 384 ms 54304 KB Output is correct
106 Correct 378 ms 54504 KB Output is correct
107 Correct 533 ms 54368 KB Output is correct
108 Correct 248 ms 49712 KB Output is correct
109 Correct 460 ms 57524 KB Output is correct