#include <iostream>
#include <deque>
using namespace std;
/*
dp[c][i] = min{dp[c-1][j] + (a_sum[i] - a_sum[j]) * a_sum[j] | 1 <= j < i}
= min{a_sum[j] * a_sum[i] + dp[c-1][j] - a_sum[j]^2 | 1 <= j < i}
A * X + B
*/
struct line
{
long long a;
long long b;
int i;
long long eval(long long x)
{
return a*x + b;
}
};
long long sq(long long x)
{
return x*x;
}
bool intersect_comp(line l1, line l2, line r1, line r2)
{
//intersect(l1, l2) <=> l1.a * x + l1.b == l2.a * x + l2.b
/*
xL = (l2.b - l1.b)/(l1.a - l2.a)
xR = (r2.b - r1.b)/(r1.a - r2.a)
xL < xR <=> ()
*/
return (l2.b - l1.b)*(r1.a - r2.a) < (r2.b - r1.b)*(l1.a - l2.a);
}
int main()
{
int n, k;
cin >> n >> k;
long long a[n+1], a_sum[n+1];
a_sum[0] = 0;
for(int i = 1; i <= n; i++)
{
cin >> a[i];
a_sum[i] = a[i] + a_sum[i-1];
}
long long* dp[k+1];
int* prev[k+1];
dp[0] = new long long[n+1];
dp[1] = new long long[n+1];
prev[0] = new int[n+1];
prev[1] = new int[n+1];
for(int x = 2; x <= k; x++)
{
dp[x] = dp[x-2];
prev[x] = new int[n+1];
}
for(int i = 0; i <= n; i++)
{
dp[0][i] = 0;
prev[0][i] = 0;
}
for(int c = 1; c <= k; c++)
{
prev[c][1] = 0;
dp[c][1] = 0;
deque<line> cht;
cht.push_back(line{a_sum[1], dp[c-1][1] - sq(a_sum[1]), 1});
for(int i = 2; i <= n; i++)
{
while(cht.size() > 1 && cht[0].eval(a_sum[i]) <= cht[1].eval(a_sum[i]))
cht.pop_front();
dp[c][i] = cht[0].eval(a_sum[i]);
prev[c][i] = cht[0].i;
line new_line = line{a_sum[i], dp[c-1][i] - sq(a_sum[i]), i};
while(cht.size() > 1 && !intersect_comp(cht[cht.size()-2], cht[cht.size()-1], cht.back(), new_line))
cht.pop_back();
cht.push_back(new_line);
}
}
cout << dp[k][n] << '\n';
int x = n, y = k;
for(y = k; y >= 1; y--)
{
cout << prev[y][x] << ' ';
x = prev[y][x];
}
cout << '\n';
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
1 ms |
288 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
2 ms |
460 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
2 ms |
344 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
2 ms |
332 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
2 ms |
460 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
1 ms |
332 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
1 ms |
332 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
332 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
1 ms |
332 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
7 ms |
1100 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
1 ms |
292 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
8 ms |
1132 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
7 ms |
1100 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
8 ms |
1132 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
6 ms |
1100 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
3 ms |
460 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
4 ms |
588 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
4 ms |
844 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
4 ms |
912 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
69 ms |
8516 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
5 ms |
844 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
53 ms |
5504 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
56 ms |
6192 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
62 ms |
6600 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
46 ms |
5552 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
54 ms |
6212 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
67 ms |
7812 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
34 ms |
5712 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
32 ms |
5624 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
716 ms |
82996 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
40 ms |
6092 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
870 ms |
82888 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
580 ms |
59180 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
648 ms |
63400 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
476 ms |
52132 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
518 ms |
59280 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
695 ms |
75000 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
