oj.uz

Submission #581240

# Submission time Handle Problem Language Result Execution time Memory
581240 2022-06-22T12:13:43 Z Josia Boarding Passes (BOI22_passes) C++14
100 / 100
 274 ms 30968 KB 
#include <bits/stdc++.h>

using namespace std;

#define int int64_t


vector<vector<int>> groups;
int n, g;


vector<vector<int>> groupPFS;


void generateGroupPFS() {
    for (auto i: groups) {
        vector<int> pfs = {0};

        for (int j = 0; j<n; j++) {
            pfs.push_back(pfs.back() + binary_search(i.begin(), i.end(), j));
        }

        groupPFS.push_back(pfs);
    }
}



vector<vector<vector<int>>> prefixsum;

void init() {
    generateGroupPFS();

    prefixsum.assign(g, vector<vector<int>>(g));

    for (int i = 0; i<g; i++) {
        for (int j = 0; j<g; j++) {
            // if (i == j) continue;
            vector<pair<int, int>> costPerElem;
            for (int k = 0; k<groups[i].size(); k++) {
                int l = groupPFS[j][groups[i][k]] - groupPFS[j][0];
                int r = groupPFS[j][n] - groupPFS[j][groups[i][k]];
                costPerElem.push_back({l, r});
            }

            // for (auto i: costPerElem) {
            //     cerr << i.first << " ";
            // }
            // cerr << "\n";
            // for (auto i: costPerElem) {
            //     cerr << i.second << " ";
            // }
            // cerr << "\n\n";


            vector<pair<int, int>> pfs(groups[i].size()+1, {0, 0});

            for (int k = 1; k<=groups[i].size(); k++) {
                pfs[k].first = pfs[k-1].first + costPerElem[k-1].first;
            }

            reverse(pfs.begin(), pfs.end());
            reverse(costPerElem.begin(), costPerElem.end());
            for (int k = 1; k<=groups[i].size(); k++) {
                pfs[k].second = pfs[k-1].second + costPerElem[k-1].second;
            }
            reverse(costPerElem.begin(), costPerElem.end());
            reverse(pfs.begin(), pfs.end());

            // for (auto i: pfs) {
            //     cerr << i.first << " ";
            // }
            // cerr << "\n";
            // for (auto i: pfs) {
            //     cerr << i.second << " ";
            // }
            // cerr << "\n\n";

            vector<int> costForSplit;

            for (int k = 0; k<=groups[i].size(); k++) {
                costForSplit.push_back(pfs[k].first + pfs[k].second);
            }


            prefixsum[i][j] = costForSplit;
        }
    }

    // for (int i = 0; i<g; i++) {
    //     for (int j = 0; j<g; j++) {
    //         for (int k: prefixsum[i][j]) {
    //             cerr << k << " ";
    //         }
    //         cerr << "\n";
    //     }
    //     cerr << "\n";
    // }
}



struct binarySearch {
    int getCostOneToOne(int from, int to, int pos) {
        return prefixsum[from][to][pos];
    }

    double getSelfintersections(int from, int pos) {
        int n1 = pos;
        int n2 = groups[from].size()-pos;
        return ((n1-1)*n1 + (n2-1)*n2)/4.0;
    }

    double getTotalCost(int from, int bm, int pos) {
        double res = getSelfintersections(from, pos);

        for (int j = 0; j<g; j++) {
            if ((1<<j) & bm) {
                res += getCostOneToOne(from, j, pos);
            }
        }
        return res;
    }


    bool check(int from, int bm, int pos) {
        if (pos + 1 > groups[from].size()) return 0 || check(from, bm, pos-1);
        return getTotalCost(from, bm, pos) < getTotalCost(from, bm, pos+1);
    }


    double bs(int from, int bm) {
        int l = 0; int r = groups[from].size();

        for (int i = l; i<=r; i++) {
            // cerr << getTotalCost(from, bm, i) << " ";
        }

        while (l<r) {
            int m = (l + r) / 2;
            if (check(from, bm, m)) r = m;
            else l = m+1;
        }

        // cerr << " --" << l << "-- ";

        return getTotalCost(from, bm, l);
    }
};



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

    string s; cin >> s;

    n = s.size();

    vector<vector<int>> groupsAlph(26);

    for (int i = 0; i<n; i++) {
        groupsAlph[s[i]-'A'].push_back(i);
    }

    for (auto i: groupsAlph) {
        if (i.size()) groups.push_back(i);
    }

    g = groups.size();

    init();

    vector<int> order(g);
    iota(order.begin(), order.end(), 0);




    vector<double> dp(1<<g, 1e18);
    dp[0] = 0;

    for (int i = 1; i<1<<g; i++) {
        for (int j = 0; j<g; j++) {
            if (1<<j & i) {
                binarySearch bs;
                dp[i] = min(dp[i], bs.bs(j, i^(1<<j)) + dp[i^(1<<j)]);
            }
        }
    }

    cout << setprecision(100) << dp[(1<<g)-1] << "\n";






    // double res = 1e18;
    // do {
    //     // for (int i: order) cerr << i << " ";
    //     // cerr << "\n";


    //     double tmpres = 0;

    //     int bm = 0;

    //     for (int i: order) {
    //         binarySearch bs;
    //         tmpres += bs.bs(i, bm);

    //         // cerr << "\n";

    //         bm += 1<<i;
    //     }
    //     // cerr << "\n";


    //     // cerr << tmpres << "\n";
    //     res = min(tmpres, res);
    // } while (next_permutation(order.begin(), order.end()));

    
    // // cerr << "\n\n";
    // cout << setprecision(100) << res << "\n";

    return 0;
}

Compilation message

passes.cpp: In function 'void init()':
passes.cpp:40:30: warning: comparison of integer expressions of different signedness: 'int64_t' {aka 'long int'} and 'std::vector<long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   40 |             for (int k = 0; k<groups[i].size(); k++) {
      |                             ~^~~~~~~~~~~~~~~~~
passes.cpp:58:30: warning: comparison of integer expressions of different signedness: 'int64_t' {aka 'long int'} and 'std::vector<long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   58 |             for (int k = 1; k<=groups[i].size(); k++) {
      |                             ~^~~~~~~~~~~~~~~~~~
passes.cpp:64:30: warning: comparison of integer expressions of different signedness: 'int64_t' {aka 'long int'} and 'std::vector<long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   64 |             for (int k = 1; k<=groups[i].size(); k++) {
      |                             ~^~~~~~~~~~~~~~~~~~
passes.cpp:81:30: warning: comparison of integer expressions of different signedness: 'int64_t' {aka 'long int'} and 'std::vector<long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   81 |             for (int k = 0; k<=groups[i].size(); k++) {
      |                             ~^~~~~~~~~~~~~~~~~~
passes.cpp: In member function 'bool binarySearch::check(int64_t, int64_t, int64_t)':
passes.cpp:127:21: warning: comparison of integer expressions of different signedness: 'int64_t' {aka 'long int'} and 'std::vector<long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  127 |         if (pos + 1 > groups[from].size()) return 0 || check(from, bm, pos-1);
      |             ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 0 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 10 ms 6588 KB Output is correct
7 Correct 12 ms 8280 KB Output is correct
8 Correct 14 ms 8828 KB Output is correct
9 Correct 12 ms 8044 KB Output is correct

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 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 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 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 0 ms 212 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 212 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 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 1 ms 212 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 0 ms 212 KB Output is correct
35 Correct 2 ms 1028 KB Output is correct
36 Correct 1 ms 1028 KB Output is correct
37 Correct 8 ms 2144 KB Output is correct
38 Correct 8 ms 2016 KB Output is correct
39 Correct 7 ms 2524 KB Output is correct
40 Correct 9 ms 2000 KB Output is correct
41 Correct 8 ms 2016 KB Output is correct
42 Correct 9 ms 2144 KB Output is correct
43 Correct 7 ms 2144 KB Output is correct
44 Correct 8 ms 2144 KB Output is correct
45 Correct 8 ms 2144 KB Output is correct
46 Correct 7 ms 2148 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 0 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 10 ms 6588 KB Output is correct
7 Correct 12 ms 8280 KB Output is correct
8 Correct 14 ms 8828 KB Output is correct
9 Correct 12 ms 8044 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 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 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 0 ms 212 KB Output is correct
22 Correct 1 ms 212 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 0 ms 212 KB Output is correct
28 Correct 0 ms 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 1 ms 340 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 1 ms 212 KB Output is correct
36 Correct 1 ms 212 KB Output is correct
37 Correct 1 ms 212 KB Output is correct
38 Correct 1 ms 212 KB Output is correct
39 Correct 1 ms 212 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 0 ms 212 KB Output is correct
44 Correct 2 ms 1028 KB Output is correct
45 Correct 1 ms 1028 KB Output is correct
46 Correct 8 ms 2144 KB Output is correct
47 Correct 8 ms 2016 KB Output is correct
48 Correct 7 ms 2524 KB Output is correct
49 Correct 9 ms 2000 KB Output is correct
50 Correct 8 ms 2016 KB Output is correct
51 Correct 9 ms 2144 KB Output is correct
52 Correct 7 ms 2144 KB Output is correct
53 Correct 8 ms 2144 KB Output is correct
54 Correct 8 ms 2144 KB Output is correct
55 Correct 7 ms 2148 KB Output is correct
56 Correct 0 ms 212 KB Output is correct
57 Correct 74 ms 596 KB Output is correct
58 Correct 1 ms 340 KB Output is correct
59 Correct 1 ms 212 KB Output is correct
60 Correct 1 ms 212 KB Output is correct
61 Correct 0 ms 212 KB Output is correct
62 Correct 1 ms 340 KB Output is correct
63 Correct 11 ms 6588 KB Output is correct
64 Correct 12 ms 8396 KB Output is correct
65 Correct 13 ms 8812 KB Output is correct
66 Correct 13 ms 8052 KB Output is correct
67 Correct 0 ms 212 KB Output is correct
68 Correct 1 ms 212 KB Output is correct
69 Correct 1 ms 212 KB Output is correct
70 Correct 1 ms 212 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 0 ms 212 KB Output is correct
75 Correct 1 ms 212 KB Output is correct
76 Correct 0 ms 212 KB Output is correct
77 Correct 0 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 212 KB Output is correct
81 Correct 1 ms 212 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 1028 KB Output is correct
85 Correct 2 ms 1028 KB Output is correct
86 Correct 8 ms 2144 KB Output is correct
87 Correct 8 ms 2016 KB Output is correct
88 Correct 6 ms 2524 KB Output is correct
89 Correct 7 ms 2016 KB Output is correct
90 Correct 8 ms 2016 KB Output is correct
91 Correct 8 ms 2144 KB Output is correct
92 Correct 8 ms 2016 KB Output is correct
93 Correct 7 ms 2140 KB Output is correct
94 Correct 8 ms 2144 KB Output is correct
95 Correct 8 ms 2196 KB Output is correct
96 Correct 262 ms 26292 KB Output is correct
97 Correct 30 ms 468 KB Output is correct
98 Correct 271 ms 26192 KB Output is correct
99 Correct 113 ms 30968 KB Output is correct
100 Correct 47 ms 596 KB Output is correct
101 Correct 250 ms 26112 KB Output is correct
102 Correct 270 ms 26352 KB Output is correct
103 Correct 261 ms 26412 KB Output is correct
104 Correct 262 ms 26244 KB Output is correct
105 Correct 264 ms 26480 KB Output is correct
106 Correct 264 ms 26380 KB Output is correct
107 Correct 274 ms 26368 KB Output is correct
108 Correct 156 ms 24524 KB Output is correct
109 Correct 260 ms 26424 KB Output is correct