#include <bits/stdc++.h>
#define nl '\n'
const int mxN = 1e4 + 5, mxK = 205;
int way[mxN][mxK];
int N, K;
struct Line {
int64_t a, b;
int i;
int64_t eval(int64_t x) const {
return a * x + b;
}
int64_t intersect(const Line& rhs) const {
auto a1 = a;
auto a2 = rhs.a;
auto b1 = b;
auto b2 = rhs.b;
return (b2 - b1) / (a1 - a2);
}
};
signed main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cin >> N >> K;
std::vector<int> A(N + 1);
std::vector<int64_t> pref(N + 1);
for (int i = 1; i <= N; i++) {
std::cin >> A[i];
pref[i] = pref[i - 1] + A[i];
}
std::vector<int64_t> dp(N + 1, -1e18);
std::vector<int64_t> ndp(N + 1, -1e18);
dp[0] = 0;
for (int j = 1; j <= K + 1; j++) {
std::deque<Line> dq;
auto insert_line = [&](int64_t a, int64_t b, int i) -> void {
// slope tang dan
// add in the back
// inter(line, line[-2]) <= inter(line[-1], line[-2])
// a1x + b1 = ax + b
//
Line l = {a, b, i};
if (dq.empty()) {
dq.push_back(l);
} else if (dq.size() == 1) {
if (dq.back().a == a) {
if (dq.back().b < b) {
dq.back() = l;
}
} else {
dq.push_back(l);
}
} else {
while (dq.size() >= 2 && dq[dq.size() - 2].intersect(l) <= dq[dq.size() - 2].intersect(dq.back())) {
dq.pop_back();
}
dq.push_back(l);
}
};
auto query_point = [&](int64_t x) -> Line {
while (dq.size() >= 2 && dq.front().eval(x) <= dq[1].eval(x)) {
dq.pop_front();
}
return dq.front();
};
insert_line(pref[0], dp[0] - pref[0] * pref[0], 0);
ndp[0] = -1e18;
for (int i = 1; i <= N; i++) {
auto line = query_point(pref[i]);
ndp[i] = line.eval(pref[i]);
way[i][j] = line.i;
insert_line(pref[i], dp[i] - pref[i] * pref[i], i);
}
std::swap(dp, ndp);
}
std::cout << dp[N] << nl;
std::vector<int> ans;
int x = N;
int y = K + 1;
while (x > 0 && y > 1) {
ans.push_back(way[x][y]);
x = way[x][y];
y--;
}
for (int i : ans) std::cout << i << " ";
std::cout << nl;
}
/*
7 3
4 1 3 4 0 2 3
*/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
0 ms |
348 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
1 ms |
348 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
0 ms |
344 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
1 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 |
1 ms |
344 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
1 ms |
344 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
1 ms |
468 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
1 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 |
348 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
1 ms |
344 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 |
Incorrect |
0 ms |
348 KB |
contestant didn't find the optimal answer: 900189978 < 900189994 |
| 17 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
0 ms |
344 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
0 ms |
348 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
0 ms |
348 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Incorrect |
0 ms |
348 KB |
contestant didn't find the optimal answer: 1005304675 < 1005304678 |
| 6 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
604 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
0 ms |
604 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
1 ms |
632 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
0 ms |
600 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
1 ms |
600 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
1 ms |
604 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
2 ms |
604 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
1 ms |
604 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Incorrect |
1 ms |
604 KB |
contestant didn't find the optimal answer: 482389919782 < 482389919803 |
| 10 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
2648 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
1 ms |
2652 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
6 ms |
2648 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
1 ms |
2652 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Incorrect |
7 ms |
2648 KB |
contestant didn't find the optimal answer: 679388313 < 679388326 |
| 6 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
4 ms |
8796 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
4 ms |
8780 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
63 ms |
9048 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
3 ms |
8796 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Incorrect |
47 ms |
8896 KB |
contestant didn't find the optimal answer: 1085432196 < 1085432199 |
| 6 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
15 ms |
22364 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
