#include <bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pb push_back
using namespace std;
typedef pair<int, int> ii;
typedef pair<ii, int> pii; // Line + id
int n, k;
int a[100005], pre[100005];
int dp[205][100005];
int trace[205][100005];
struct Convex_hull_linear {
vector<pii> v;
int ptr = 0;
void init() {
v.clear();
ptr = 0;
}
// y = kx + m;
double isect(ii x, ii y) {
int k1 = x.fi, k2 = y.fi;
int m1 = x.se, m2 = y.se;
return (m2 - m1) * 1.0 / (k1 - k2) * 1.0;
}
bool bad(ii a, ii b, ii c) {
return isect(a, b) >= isect(b, c);
}
void add(ii x, int id) {
while(v.size() >= 2 and bad(v[v.size() - 2].fi, v[v.size() - 1].fi, x)) v.pop_back();
v.pb({x, id});
}
int eval(ii Line, int x) {
return Line.fi * x + Line.se;
}
ii query(int x) {
if(ptr > (int)v.size() - 1) {
ptr = (int)v.size() - 1;
} // empty ?
while(ptr < (int)v.size() - 1 and eval(v[ptr].fi, x) <= eval(v[ptr + 1].fi, x)) { // omg this used to be <
ptr++;
}
return {eval(v[ptr].fi, x), v[ptr].se};
}
} Cvh;
signed main() {
// freopen("test_input.txt", "r", stdin);
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> k;
for(int i = 1; i <= n; i++) {
cin >> a[i];
pre[i] = pre[i - 1] + a[i];
}
for(int j = 2; j <= k + 1; j++) {
Cvh.init();
Cvh.add({0, 0}, 0);
for(int i = 1; i <= n; i++) {
ii new_dp = Cvh.query(pre[i]);
Cvh.add({pre[i], dp[j - 1][i] - pre[i] * pre[i]}, i);
dp[j][i] = new_dp.fi;
trace[j][i] = new_dp.se;
}
}
cout << dp[k + 1][n] << '\n';
vector<int> res;
int trace_i = n;
for(int j = k + 1; j > 0; j--) {
res.pb(trace[j][trace_i]);
trace_i = trace[j][trace_i];
}
reverse(res.begin(), res.end());
for(auto x : res) {
if(!x) continue;
cout << x << ' ';
}
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
1 ms |
392 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
1 ms |
896 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
1 ms |
640 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
1 ms |
416 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
3 ms |
3200 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
2 ms |
2304 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
3 ms |
2944 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
3 ms |
3200 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
1 ms |
1024 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 |
1152 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
8 ms |
5760 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
1 ms |
640 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
9 ms |
5760 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Incorrect |
8 ms |
4992 KB |
contestant didn't find the optimal answer: 4699030135 < 4699030287 |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
1404 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
2 ms |
1404 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
67 ms |
34416 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
3 ms |
1404 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
45 ms |
20980 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Incorrect |
51 ms |
24312 KB |
contestant didn't find the optimal answer: 514786325281 < 514790755404 |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
21 ms |
9200 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
21 ms |
9324 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Runtime error |
276 ms |
131076 KB |
Execution killed with signal 9 (could be triggered by violating memory limits) |
| 4 |
Halted |
0 ms |
0 KB |
- |
