Submission #1028217

# Submission time Handle Problem Language Result Execution time Memory
1028217 2024-07-19T15:21:10 Z anango Boarding Passes (BOI22_passes) C++17
60 / 100
923 ms 251140 KB
#include <bits/stdc++.h>
#define int long long
using namespace std;
int INF = 1LL<<62;

void solve() {

    string S; cin >> S;
    int n = S.size();
    vector<int> ar(n); for (int i=0; i<n; i++) ar[i] = (S[i]-'A');
    int G = *max_element(ar.begin(), ar.end()); G++;
    int pref[n+1][G]; //count of character c, before index i
    int suff[n+1][G]; //count of character c, after or equal to index i
    for (int i=0; i<=n; i++) {
        for (int j=0; j<G; j++) {
            pref[i][j] = suff[i][j] = 0;
        }
    }
    for (int i=0; i<n; i++) {
        for (int j=0; j<=G; j++) {
            if (j==ar[i]) {
                pref[i+1][j] = pref[i][j]+1;
            }
            else {
                pref[i+1][j] = pref[i][j];
            }
        }
    }
    
    for (int i=n-1; i>=0; i--) {
        for (int j=0; j<G; j++) {
            if (j==ar[i]) {
                suff[i][j] = suff[i+1][j]+1;
            }
            else {
                suff[i][j] = suff[i+1][j];
            }
        }
    }
    //everyone before L boards from the front, everyone after or equal to it boards from the back. 
    vector<vector<int>> counts(G,vector<int>(G,0));     //counts[i][j] = sum of subsequences of (i,j) before l, and subsequences of (j,i) after L
    //counts[i][j] = sum of pref[k][j] for k<=L and ar[k]=i, and analogous expression for the suffix
    //first, get initial count values (for everyone boarding from the back)
    //and assuming that these are already boarded since the back breaker may not be the same for each group - that was false assumption
    //so precomp counts then ternary search on the breakpoint
    for (int j=0; j<G; j++) {
        for (int k=0; k<n; k++) {
            int i = ar[k];
            //cout << "adding " << i <<" " << j <<" " << k <<" " << j << " " << suff[k][j] << endl;
            counts[i][j] += suff[k+1][j];
        }
    }
    vector<vector<vector<int>>> acounts;
    acounts.push_back(counts);
    for (int L=0; L<n; L++) {

        //counts[i][j] = number of swaps required if i goes after j



        //transfer L to the right
        int cur = ar[L];
        for (int j=0; j<G; j++) {
            int delta = suff[L+1][j];
            int delta2 = pref[L][j];
            counts[cur][j] -= delta-delta2;
        }
        acounts.push_back(counts);
        
        /*cout << "TRANSFERRED TO " << L+1 << endl;
        for (int i=0; i<G; i++) {
            for (int j=0; j<G; j++) {
                cout << i <<" " << j <<" " << counts[i][j] << endl;
            }
        }
        cout << endl;*/
    }
    vector<int> dp;
    dp=vector<int>(1<<G,INF); //dp[mask] = min cost if this mask is at the beginning of the ordering
    dp[0] = 0;
    for (int mask=0; mask<1<<G; mask++) {
        for (int addon=0; addon<G; addon++) {
            if (mask&(1<<addon)) continue;
            int l = 0; int r = n;
            while (l<r) {
                int m1 = l+(r-l)/6;
                int m2 = r-(r-l)/6;
                int am1 = 0;
                for (int j=0; j<G; j++) {
                    if (mask&(1<<j)) {
                        am1+=2*acounts[m1][addon][j];
                    }
                    if (j==addon) {
                        am1+=acounts[m1][addon][j];
                    }
                }
                int am2 = 0;
                for (int j=0; j<G; j++) {
                    if (mask&(1<<j)) {
                        am2+=2*acounts[m2][addon][j];
                    }
                    if (j==addon) {
                        am2+=acounts[m2][addon][j];
                    }
                }
                //cout << "adding " << mask <<" " << addon <<" " << l <<" " << r <<" " << m1 <<" " << m2 <<" " << am1 <<" " << am2 << endl;
                if (am1>am2) {
                    l=m1+1; r=r;
                }
                else if (am1<am2) {
                    l=l; r=m2-1;
                }
                else {
                    l=m1+1; r=m2;
                }
                //cout << mask <<" " << addon <<" " << al <<endl;
            }
            int al = 0;
            for (int j=0; j<G; j++) {
                if (mask&(1<<j)) {
                    al+=2*acounts[l][addon][j];
                }
                if (j==addon) {
                    al+=acounts[l][addon][j];
                }
            }
            dp[mask | (1<<addon)] = min(dp[mask | (1<<addon)],dp[mask]+al);
        }
    }
    int ans=dp[(1<<G)-1];

    long double a2 = ans;
    a2/=(long double)2;
    cout << setprecision(100) << a2 << endl;
}

signed main() {
    int local=0;
    if (local) {
        // for getting input from input.txt
        freopen("input.txt", "r", stdin);
        // for writing output to output.txt
        freopen("output.txt", "w", stdout);
    }
    /*#ifdef ONLINE_JUDGE
    	ios_base::sync_with_stdio(false);
    	cin.tie(NULL);
    #endif*/ //fast IO
    solve();
    
}

Compilation message

passes.cpp: In function 'int main()':
passes.cpp:141:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  141 |         freopen("input.txt", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
passes.cpp:143:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  143 |         freopen("output.txt", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 0 ms 344 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
3 Correct 1 ms 344 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
4 Correct 0 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 1 ms 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 11 ms 10524 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 15 ms 10736 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 14 ms 11920 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 15 ms 11788 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
3 Correct 1 ms 348 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 0 ms 348 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 0 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 0 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
8 Correct 1 ms 344 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 0 ms 348 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 0 ms 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 0 ms 348 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 1 ms 604 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 1 ms 344 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 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
3 Correct 1 ms 348 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 0 ms 348 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 0 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 0 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
8 Correct 1 ms 344 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 0 ms 348 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 0 ms 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 0 ms 348 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 1 ms 604 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 1 ms 344 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 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
19 Correct 0 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 0 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 0 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
24 Correct 1 ms 344 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
25 Correct 1 ms 344 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 0 ms 432 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 0 ms 348 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
31 Correct 1 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
32 Correct 0 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
33 Correct 1 ms 600 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
34 Correct 1 ms 600 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
35 Correct 8 ms 10304 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
36 Correct 10 ms 10336 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
37 Correct 18 ms 14112 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
38 Correct 14 ms 14268 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
39 Correct 13 ms 14232 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
40 Correct 15 ms 13976 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
41 Correct 17 ms 13976 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
42 Correct 17 ms 13720 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
43 Correct 16 ms 13752 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
44 Correct 22 ms 13972 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
45 Correct 17 ms 13976 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
46 Correct 16 ms 13972 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 0 ms 344 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
3 Correct 1 ms 344 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
4 Correct 0 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 1 ms 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 11 ms 10524 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 15 ms 10736 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 14 ms 11920 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 15 ms 11788 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
10 Correct 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
11 Correct 0 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
12 Correct 1 ms 348 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 0 ms 348 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
15 Correct 0 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
16 Correct 0 ms 348 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
17 Correct 1 ms 344 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
18 Correct 0 ms 348 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 0 ms 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
21 Correct 0 ms 348 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
22 Correct 1 ms 604 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 1 ms 344 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 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
28 Correct 0 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 0 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 0 ms 348 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
33 Correct 1 ms 344 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
34 Correct 1 ms 344 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 0 ms 432 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 0 ms 348 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
40 Correct 1 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
41 Correct 0 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
42 Correct 1 ms 600 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
43 Correct 1 ms 600 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
44 Correct 8 ms 10304 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
45 Correct 10 ms 10336 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
46 Correct 18 ms 14112 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
47 Correct 14 ms 14268 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
48 Correct 13 ms 14232 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
49 Correct 15 ms 13976 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
50 Correct 17 ms 13976 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
51 Correct 17 ms 13720 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
52 Correct 16 ms 13752 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
53 Correct 22 ms 13972 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
54 Correct 17 ms 13976 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
55 Correct 16 ms 13972 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
56 Correct 106 ms 604 KB found '7.5000000000', expected '7.5000000000', error '0.0000000000'
57 Correct 123 ms 756 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
58 Correct 0 ms 344 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
59 Correct 0 ms 348 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
60 Correct 0 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 1 ms 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
63 Correct 11 ms 10508 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
64 Correct 13 ms 11276 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
65 Correct 14 ms 11784 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
66 Correct 16 ms 11560 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
67 Correct 0 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
68 Correct 0 ms 344 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
69 Correct 1 ms 348 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
70 Correct 0 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 0 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 348 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
76 Correct 0 ms 348 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 0 ms 348 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
79 Correct 0 ms 348 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
80 Correct 0 ms 348 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
81 Correct 0 ms 348 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
82 Correct 1 ms 348 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
83 Correct 1 ms 348 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
84 Correct 9 ms 10136 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
85 Correct 9 ms 10136 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
86 Correct 17 ms 14232 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
87 Correct 14 ms 14232 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
88 Correct 13 ms 14076 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
89 Correct 15 ms 13972 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
90 Correct 16 ms 13720 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
91 Correct 16 ms 13972 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
92 Correct 16 ms 13720 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
93 Correct 16 ms 13720 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
94 Correct 16 ms 13876 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
95 Correct 17 ms 13744 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
96 Incorrect 923 ms 251140 KB 1st numbers differ - expected: '1239972790.0000000000', found: '1239972795.0000000000', error = '0.0000000040'
97 Halted 0 ms 0 KB -