Submission #1028228

# Submission time Handle Problem Language Result Execution time Memory
1028228 2024-07-19T15:25:23 Z anango Boarding Passes (BOI22_passes) C++17
60 / 100
2000 ms 251348 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,m2;
                if (r-l>100) {
                    m1 = l+(r-l)/9;
                    m2 = r-(r-l)/9;
                }
                else {
                    m1 = l;
                    m2 = r;
                }
                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];

    int a2 = ans/2;
    cout << a2;
    if (ans%2==1) cout << ".50";
    cout << 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:149:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  149 |         freopen("input.txt", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
passes.cpp:151:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  151 |         freopen("output.txt", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
# 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 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 1 ms 344 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 13 ms 9520 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 14 ms 10764 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 15 ms 11532 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 15 ms 11532 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 1 ms 344 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 1 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 1 ms 348 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 0 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 1 ms 348 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 0 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 1 ms 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 1 ms 348 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 1 ms 440 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 1 ms 600 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
16 Correct 1 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 1 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 1 ms 344 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 1 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 1 ms 348 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 0 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 1 ms 348 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 0 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 1 ms 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 1 ms 348 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 1 ms 440 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 1 ms 600 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
16 Correct 1 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 344 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 1 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
22 Correct 1 ms 348 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 596 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 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
29 Correct 1 ms 432 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 1 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 10 ms 10136 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
36 Correct 10 ms 10388 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
37 Correct 32 ms 14232 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
38 Correct 24 ms 14128 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
39 Correct 24 ms 14232 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
40 Correct 26 ms 13976 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
41 Correct 34 ms 13716 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
42 Correct 27 ms 13720 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
43 Correct 29 ms 13940 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
44 Correct 29 ms 13720 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
45 Correct 29 ms 13720 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
46 Correct 29 ms 13720 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 0 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 1 ms 344 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 13 ms 9520 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 14 ms 10764 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 15 ms 11532 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 15 ms 11532 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
10 Correct 1 ms 344 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
11 Correct 1 ms 344 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 1 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
14 Correct 1 ms 348 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 0 ms 348 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
18 Correct 1 ms 348 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
19 Correct 0 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
20 Correct 1 ms 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
21 Correct 1 ms 348 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
22 Correct 1 ms 440 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 1 ms 600 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
25 Correct 1 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 344 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 1 ms 348 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
31 Correct 1 ms 348 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 596 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 348 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
38 Correct 1 ms 432 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 1 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 10 ms 10136 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
45 Correct 10 ms 10388 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
46 Correct 32 ms 14232 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
47 Correct 24 ms 14128 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
48 Correct 24 ms 14232 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
49 Correct 26 ms 13976 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
50 Correct 34 ms 13716 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
51 Correct 27 ms 13720 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
52 Correct 29 ms 13940 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
53 Correct 29 ms 13720 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
54 Correct 29 ms 13720 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
55 Correct 29 ms 13720 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
56 Correct 172 ms 600 KB found '7.5000000000', expected '7.5000000000', error '0.0000000000'
57 Correct 276 ms 600 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
58 Correct 1 ms 348 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
59 Correct 1 ms 416 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 0 ms 348 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
63 Correct 12 ms 9632 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
64 Correct 14 ms 10872 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
65 Correct 14 ms 11532 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
66 Correct 14 ms 11372 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
67 Correct 1 ms 348 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
68 Correct 1 ms 348 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
69 Correct 1 ms 436 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 432 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 344 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 1 ms 348 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
77 Correct 1 ms 344 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 0 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 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 10 ms 10228 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 37 ms 14232 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
87 Correct 25 ms 14232 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
88 Correct 22 ms 14232 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
89 Correct 24 ms 13972 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
90 Correct 28 ms 13720 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
91 Correct 29 ms 13716 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
92 Correct 28 ms 13972 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
93 Correct 29 ms 13976 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
94 Correct 31 ms 13720 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
95 Correct 30 ms 13820 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
96 Execution timed out 2071 ms 251348 KB Time limit exceeded
97 Halted 0 ms 0 KB -