#include <bits/stdc++.h>
using namespace std;
typedef long double ld;
typedef long long ll;
const ll INF = (ll)1.1e18;
struct ConvexHull {
struct Line {
ll a, b;
int id;
ll get(ll x) {
return a * x + b;
}
Line() {}
Line(ll a, ll b, int id) : a(a), b(b), id(id) {}
};
ld inter(Line l1, Line l2) {
return (ld)(l1.b - l2.b) / (l2.a - l1.a);
}
vector<Line> ch;
vector<ld> interX;
int pos;
bool bad(Line l) {
if ((int)ch.size() <= 1) return false;
return inter(l, ch[(int)ch.size() - 2]) <= interX.back();
}
void addLine(ll a, ll b, int id) {
if (!ch.empty() && a == ch.back().a && b >= ch.back().b) return;
Line l = {a, b, id};
while (bad(l)) ch.pop_back(), interX.pop_back();
if (ch.empty()) interX.push_back(-INF); else interX.push_back(inter(ch.back(), l));
ch.push_back(l);
}
pair<ll, int> get(ll x) {
assert(!interX.empty());
pos = min(pos, (int)ch.size() - 1);
while (pos + 1 < (int)ch.size() && interX[pos + 1] <= x) pos++;
return {ch[pos].get(x), ch[pos].id};
}
ConvexHull() {
ch.clear();
interX.clear();
pos = 0;
}
};
ll slow(int n, int k, vector<ll> a, vector<int> &c) {
vector<ll> pref(n + 1, 0);
for (int i = 0; i < n; i++) pref[i + 1] = pref[i] + a[i];
auto cost = [&](int l, int r)->ll {
return (pref[r] - pref[l]) * (pref[r] - pref[l]);
};
vector<vector<int>> opt(k + 1, vector<int>(n + 1, -1));
vector<ll> dp(n + 1, INF);
for (int i = 1; i <= n; i++) dp[i] = cost(0, i);
for (int t = 1; t <= k; t++) {
vector<ll> ndp(n + 1, INF);
for (int i = 0; i <= n; i++) {
for (int j = 0; j < i; j++) {
if (dp[j] + cost(j, i) < ndp[i]) ndp[i] = dp[j] + cost(j, i), opt[t][i] = j;
}
}
dp.swap(ndp);
}
ll res = (cost(0, n) - dp[n]) / 2;
int cur = n;
for (int i = k; i >= 0; i--) {
if (i != k) c.push_back(cur);
cur = opt[i][cur];
}
reverse(c.begin(), c.end());
return res;
}
ll fast(int n, int k, vector<ll> a, vector<int> &c) {
vector<ll> pref(n + 1, 0);
for (int i = 0; i < n; i++) pref[i + 1] = pref[i] + a[i];
vector<vector<int>> opt(k + 1, vector<int>(n + 1, -1));
vector<ll> dp(n + 1, INF);
for (int i = 1; i <= n; i++) dp[i] = pref[i] * pref[i];
for (int t = 1; t <= k; t++) {
vector<ll> ndp(n + 1, INF);
ConvexHull ch;
for (int i = t + 1; i <= n; i++) {
ch.addLine(-2 * pref[i - 1], pref[i - 1] * pref[i - 1] + dp[i - 1], i - 1);
auto [res, id] = ch.get(pref[i]);
ndp[i] = res + pref[i] * pref[i], opt[t][i] = id;
}
dp.swap(ndp);
}
ll res = (pref[n] * pref[n] - dp[n]) / 2;
int cur = n;
for (int i = k; i >= 0; i--) {
if (cur != n) c.push_back(cur);
cur = opt[i][cur];
}
reverse(c.begin(), c.end());
return res;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, k;
cin >> n >> k;
vector<ll> a(n);
for (ll &x : a) cin >> x;
vector<int> c;
if (0) cout << slow(n, k, a, c); else cout << fast(n, k, a, c);
cout << endl;
for (int i : c) cout << i << " ";
cout << endl;
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
0 ms |
364 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
0 ms |
364 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 |
364 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
1 ms |
492 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
2 ms |
492 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
2 ms |
492 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
2 ms |
488 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
1 ms |
364 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
492 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
1 ms |
492 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
8 ms |
1260 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
1 ms |
492 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
10 ms |
1260 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
8 ms |
1132 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
10 ms |
1260 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
8 ms |
1260 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
2 ms |
620 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
4 ms |
748 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
1564 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
3 ms |
1516 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
135 ms |
9532 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
4 ms |
1768 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
80 ms |
6140 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
78 ms |
7104 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
113 ms |
7564 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
87 ms |
6740 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
103 ms |
7340 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
126 ms |
8912 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
32 ms |
12872 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
32 ms |
12832 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
1599 ms |
91440 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
35 ms |
14284 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
1592 ms |
90804 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
615 ms |
64108 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
1281 ms |
71928 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
998 ms |
60716 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
1096 ms |
67808 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
1364 ms |
83672 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
