Submission #1036854

#	Time	Username	Problem	Language	Result	Execution time	Memory
1036854		anango	Boarding Passes (BOI22_passes)	C++17	60 / 100	2078 ms	252332 KiB

passes

#include <bits/stdc++.h>
#define int long long
using namespace std;
#define o 0
#define push_front push_back
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;*/
    }
    //acounts[breakpoint][group_1][group_2]
    //ABCABCAA

    vector<int> dp;
    vector<vector<int>> indices(G);
    for (int i=0; i<n; i++) {
        indices[ar[i]].push_back(i);
    }
    for (int i=0; i<G; i++) {
        if (indices[i].size()==0) continue;
        if (indices[i].front()!=0) indices[i].push_front(0);
        if (indices[i].back()!=n-1) {
            indices[i].push_back(n-1);
        }
    }
    for (int i=0; i<G; i++) {
        sort(indices[i].begin(), indices[i].end());
    }
    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;
            if (indices[addon].size()==0) { 
                dp[mask | (1<<addon)] = min(dp[mask | (1<<addon)],dp[mask]+o);
                continue;
            }
            int l = 0; int r = indices[addon].size(); r--;
            int mi = 1LL<<62;
            while (l<r-1) {
                //cout << l << " " << r << endl;
                //cout << indices[addon][l] <<" " << indices[addon][r] << endl;
                int m1,m2;
                if (r-l>10) {
                    m1 = l+(r-l)/9;
                    m2 = r-(r-l)/9;
                }
                else {
                    m1 = l;
                    m2 = r;
                }
                m1=l; m2=r;
                int am1 = 0;
                for (int j=0; j<G; j++) {
                    if (mask&(1<<j)) {
                        am1+=2*acounts[indices[addon][m1]][addon][j];
                    }
                    if (j==addon) {
                        am1+=acounts[indices[addon][m1]][addon][j];
                    }
                }
                int am2 = 0;
                for (int j=0; j<G; j++) {
                    if (mask&(1<<j)) {
                        am2+=2*acounts[indices[addon][m2]][addon][j];
                    }
                    if (j==addon) {
                        am2+=acounts[indices[addon][m2]][addon][j];
                    }
                }
                mi = min(mi,min(am1,am2));
                //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[indices[addon][l]][addon][j];
                }
                if (j==addon) {
                    al+=acounts[indices[addon][l]][addon][j];
                }
            }
            dp[mask | (1<<addon)] = min(dp[mask | (1<<addon)],dp[mask]+al);
            if (l+1==indices[addon].size()) {
                continue;
            }
            al = 0;
            for (int j=0; j<G; j++) {
                if (mask&(1<<j)) {
                    al+=2*acounts[indices[addon][l+1]][addon][j];
                }
                if (j==addon) {
                    al+=acounts[indices[addon][l+1]][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 (stderr)

passes.cpp: In function 'void solve()':
passes.cpp:163:20: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  163 |             if (l+1==indices[addon].size()) {
      |                 ~~~^~~~~~~~~~~~~~~~~~~~~~~
passes.cpp: In function 'int main()':
passes.cpp:190:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  190 |         freopen("input.txt", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
passes.cpp:192:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  192 |         freopen("output.txt", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 25 / 25
• Subtask 3: 30 / 30
• Subtask 4: 0 / 40