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Submission #1012706

# Submission time Handle Problem Language Result Execution time Memory
1012706 2024-07-02T14:03:05 Z andrei_iorgulescu Split the sequence (APIO14_sequence) C++14
71 / 100
 638 ms 131072 KB 
#include <bits/stdc++.h>

using namespace std;

using integer = int;

#define int long long

int inf = 5e18;

int n,k,a[100005];
int dp[205][100005];
int f[100005];
integer ant[205][100005];

struct dreapta
{
    int offset, panta;

    int eval(int x)
    {
        return offset + panta * x;
    }
};

deque<pair<dreapta,int>> dq;

long double inters(dreapta d1, dreapta d2)
{
    long double numarator = d2.offset - d1.offset,numitor = d1.panta - d2.panta;
    return numarator / numitor;
}

void update(dreapta d,int pos)
{
    dq.push_back({d,pos});
    while (dq.size() >= 2)
    {
        dreapta d1 = dq.back().first;
        int pos1 = dq.back().second;
        dq.pop_back();
        dreapta d2 = dq.back().first;
        if (d1.panta != d2.panta)
        {
            dq.push_back({d1,pos1});
            break;
        }
        else
        {
            int pos2 = dq.back().second;
            dq.pop_back();
            if (d1.offset > d2.offset)
                dq.push_back({d1,pos1});
            else
                dq.push_back({d2,pos2});
        }
    }
    while (dq.size() >= 3)
    {
        dreapta d1 = dq.back().first;
        int pos1 = dq.back().second;
        dq.pop_back();
        dreapta d2 = dq.back().first;
        int pos2 = dq.back().second;
        dq.pop_back();
        dreapta d3 = dq.back().first;
        int pos3 = dq.back().second;
        dq.pop_back();
        if (inters(d1,d2) >= inters(d2,d3))
        {
            dq.push_back({d3,pos3});
            dq.push_back({d1,pos1});
        }
        else
        {
            dq.push_back({d3,pos3});
            dq.push_back({d2,pos2});
            dq.push_back({d1,pos1});
            break;
        }
    }
}

int query(int x)
{
    if (dq.empty())
        return -inf;
    while (dq.size() >= 2)
    {
        dreapta d1 = dq.front().first;
        int pos1 = dq.front().second;
        dq.pop_front();
        dreapta d2 = dq.front().first;
        if (d1.eval(x) > d2.eval(x))
        {
            dq.push_front({d1,pos1});
            break;
        }
    }
    return dq.front().first.eval(x);
}

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    cin >> n >> k;
    for (int i = 1; i <= n; i++)
        cin >> a[i];
    f[n] = a[n];
    for (int i = n - 1; i >= 1; i--)
        f[i] = f[i + 1] + a[i];
    dp[0][1] = 0;
    for (int i = 2; i <= n; i++)
        dp[0][i] = -inf;
    for (int j = 1; j <= k; j++)
    {
        dq.clear();
        for (int i = 1; i <= n; i++)
        {
            dp[j][i] = query(f[i]) - f[i] * f[i];
            if (!dq.empty())
                ant[j][i] = dq.front().second;
            dreapta aux;
            aux.offset = dp[j - 1][i];
            aux.panta = f[i];
            update(aux,i);
        }
    }
    int ans = 0;
    for (int i = k + 1; i <= n; i++)
        ans = max(ans,dp[k][i]);
    cout << ans << '\n';
    int cine;
    for (int i = k + 1; i <= n; i++)
        if (dp[k][i] == ans)
            cine = i;
    vector<int> lol;
    for (int i = k; i >= 1; i--)
    {
        lol.push_back(cine - 1);
        cine = ant[i][cine];
    }
    reverse(lol.begin(),lol.end());
    for (auto it : lol)
        cout << it << ' ';
    return 0;
}

/*
7 3
4 1 3 4 0 2 3
*/

/**
Nu conteaza ordinea operatiilor, so dp[j][i] = facand j splituri pe locuri pana inainte de i (ultimul pe i), care e suma maxima pe care o pot obtine
dp[j][i] = max(dp[j - 1][q < i] + f[i] * (f[q] - f[i]))
f[i] = suma pe sufix de la i incolo

deci am -f[i] * f[i] mereu, vreau maximul din dp[j - 1][q < i] + f[i] * f[q]
Asta e evident CHT, cu update: dreapta dp[j - 1][i] cu panta f[i] si query in f[i]
Query-urile sunt sortate descrescator si update-urile sunt tot descrescator dupa panta
**/

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:142:28: warning: 'cine' may be used uninitialized in this function [-Wmaybe-uninitialized]
  142 |         lol.push_back(cine - 1);
      |                       ~~~~~^~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 600 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 348 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 348 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 348 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 348 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 348 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 344 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 424 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 348 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 348 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 348 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 348 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 348 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 348 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 348 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 348 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 348 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 348 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 860 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 348 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 344 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 348 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 604 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 348 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 348 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 600 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 348 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 2740 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 348 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 2140 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 2652 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 2908 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 860 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 604 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 1116 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 348 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 14 ms 4740 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 344 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 17 ms 4700 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 15 ms 4184 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 18 ms 4696 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 15 ms 4700 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 1372 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 7 ms 2140 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1116 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 1168 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 120 ms 26052 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 1116 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 78 ms 15932 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 98 ms 18520 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 94 ms 19788 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 80 ms 16212 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 94 ms 18628 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 118 ms 23516 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 24 ms 7224 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 23 ms 7212 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Runtime error 638 ms 131072 KB Execution killed with signal 9
4 Halted 0 ms 0 KB -