#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")
#include <iostream>
#include <vector>
#include <algorithm>
#include <deque>
#include <set>
#include <string>
#include <numeric>
#include <cmath>
#include <cassert>
#include <array>
#include <numeric>
using namespace std;
using ll = long long;
const ll INF = 1e18;
struct Line
{
ll k, b;
int who;
Line(ll k = 0, ll b = 0, int who = 0) : k(k), b(b), who(who)
{}
ll operator()(ll x)
{
return k * x + b;
}
};
bool check(Line a, Line b, Line c)
{
if (b.k == c.k) return b.b >= c.b;
return (__int128)(a.b - c.b) * (b.k - a.k) <= (__int128)(a.b - b.b) * (c.k - a.k);
}
int main()
{
cin.tie(0)->sync_with_stdio(0);
int n, k;
cin >> n >> k;
++k;
vector<ll> a(n);
for (ll &i : a) cin >> i;
array<vector<ll>, 2> dp;
dp[0] = dp[1] = vector<ll>(n + 1, INF);
dp[0][0] = 0;
ll res = accumulate(a.begin(), a.end(), 0ll);
res = res * res;
partial_sum(a.begin(), a.end(), a.begin());
a.insert(a.begin(), 0);
vector<vector<int>> parent(n + 1, vector<int>(k, -1));
auto dac = [&dp, &a, &parent](auto self, int l, int r, int l2, int r2, int level)
{
if (l > r) return;
int m = (l + r) >> 1, ind = l2;
for (int i = l2; i <= min(r2, m - 1); ++i)
{
ll cur = dp[0][i] + (a[m] - a[i]) * (a[m] - a[i]);
if (cur < dp[1][m])
{
dp[1][m] = cur;
ind = i;
}
}
parent[m][level] = ind;
self(self, l, m - 1, l2, ind, level);
self(self, m + 1, r, ind, r, level);
};
for (int i = 0; i < k; ++i)
{
//dac(dac, i + 1, n, 0, n - 1, i);
deque<Line> dq;
dq.push_back({-2 * a[i], dp[0][i] + a[i] * a[i], i});
for (int j = i + 1; j <= n; ++j)
{
while (dq.size() >= 2 && dq[0](a[j]) > dq[1](a[j])) dq.pop_front();
dp[1][j] = dq.front()(a[j]) + a[j] * a[j];
parent[j][i] = dq.front().who;
//add
Line add{-2 * a[j], dp[0][j] + a[j] * a[j], j};
while (dq.size() >= 2 && check(dq[(int)dq.size() - 2], dq.back(), add)) dq.pop_back();
if (dq.back().k != add.k) dq.push_back(add);
}
//i -> i + 1
dp[0] = dp[1];
dp[1] = vector<ll>(n + 1, INF);
}
vector<int> path(k - 1);
for (int i = k - 1, v = n; i > 0; v = parent[v][i], --i) path[k - i - 1] = parent[v][i];
cout << (res - dp[0].back()) / 2 << '\n';
reverse(path.begin(), path.end());
for (int i : path) cout << i << ' ';
return 0;
}
/*dp[i] = min j < i
dp[j] + (p[i] - p[j])^2 = dp[j] + p[j]^2 - 2p[j]*p[i] + p[i]^2
kx + b*/
/*
4
1 3
4
0 2 3
*/
Compilation message
sequence.cpp: In function 'int main()':
sequence.cpp:59:10: warning: variable 'dac' set but not used [-Wunused-but-set-variable]
59 | auto dac = [&dp, &a, &parent](auto self, int l, int r, int l2, int r2, int level)
| ^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
1 ms |
324 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
1 ms |
324 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
1 ms |
320 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
1 ms |
320 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
0 ms |
212 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
1 ms |
316 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
1 ms |
324 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
1 ms |
320 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
1 ms |
320 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
0 ms |
212 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
0 ms |
212 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
1 ms |
312 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
1 ms |
212 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
244 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
1 ms |
340 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
2 ms |
448 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
1 ms |
340 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
1 ms |
340 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
1 ms |
468 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
1 ms |
468 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
1 ms |
340 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
1 ms |
312 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
1 ms |
320 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
1 ms |
340 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
7 ms |
1108 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
1 ms |
340 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
6 ms |
1108 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
5 ms |
980 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
7 ms |
1092 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
5 ms |
1108 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
2 ms |
468 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
3 ms |
724 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
1228 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
3 ms |
1364 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
51 ms |
9044 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
3 ms |
1364 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
41 ms |
5844 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
47 ms |
6612 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
48 ms |
7144 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
38 ms |
5972 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
44 ms |
6724 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
54 ms |
8148 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
25 ms |
10100 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
26 ms |
10240 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
577 ms |
87288 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
25 ms |
10588 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
723 ms |
87040 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
515 ms |
63304 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
527 ms |
68524 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
441 ms |
57404 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
445 ms |
63532 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
558 ms |
79288 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
