#include <bits/stdc++.h>
using namespace std;
#define int long long
int inf = 5e18;
int n,k,a[100005];
int dp[205][100005];
int f[100005];
int 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:140:28: warning: 'cine' may be used uninitialized in this function [-Wmaybe-uninitialized]
140 | lol.push_back(cine - 1);
| ~~~~~^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
344 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
0 ms |
344 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 |
348 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
0 ms |
464 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 |
0 ms |
348 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
0 ms |
464 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 |
| # |
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 |
348 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 |
604 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
1 ms |
348 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
0 ms |
604 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
0 ms |
348 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
3 ms |
3416 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
0 ms |
344 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
2 ms |
2364 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
3 ms |
2908 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
3 ms |
3164 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
1 ms |
1116 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
1 ms |
768 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
1 ms |
1116 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
1 ms |
604 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
13 ms |
5784 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
1 ms |
344 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
14 ms |
5724 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
12 ms |
5012 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
14 ms |
5608 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
12 ms |
5724 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
3 ms |
1544 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
5 ms |
2652 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
1116 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
3 ms |
1372 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
135 ms |
34132 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
3 ms |
1116 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
89 ms |
20816 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
103 ms |
24144 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
103 ms |
25684 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
82 ms |
21024 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
94 ms |
24084 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
118 ms |
30844 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
24 ms |
8256 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
22 ms |
8352 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Runtime error |
515 ms |
131072 KB |
Execution killed with signal 9 |
| 4 |
Halted |
0 ms |
0 KB |
- |
