#include <bits/stdc++.h>
using namespace std;
const int NMAX = 100000 + 5;
const int KMAX = 200 + 5;
typedef long long int lint;
const lint INF = 2E18;
int N, K;
int sPart[NMAX];
lint dpBrute[2][NMAX];
int father[KMAX][NMAX];
void brute() {
dpBrute[1][0] = INF;
for (int j = 1; j <= N; ++ j)
dpBrute[1][j] = 1LL * sPart[j] * sPart[j];
for (int i = 2; i <= K; ++ i) {
for (int j = 0; j < i; ++ j)
dpBrute[i & 1][j] = INF;
for (int j = i; j <= N; ++ j) {
pair <lint, int> sol = {1LL * (sPart[j] - sPart[j - 1]) * (sPart[j] - sPart[j - 1]) + dpBrute[(i - 1) & 1][j - 1], j - 1};
for (int k = i - 1; k <= j; ++ k)
sol = min(sol, {1LL * (sPart[j] - sPart[k - 1]) * (sPart[j] - sPart[k - 1]) + dpBrute[(i - 1) & 1][k - 1], k - 1});
dpBrute[i & 1][j] = sol.first;
father[i][j] = sol.second;
}
}
}
lint dp[2][NMAX];
bool fail;
inline long double intersect(int i, int k1, int k2) {
if (sPart[k2 - 1] == sPart[k1 - 1]) {
fail = true;
return -1;
}
else {
fail = false;
return 1.0L * (1LL * sPart[k2 - 1] * sPart[k2 - 1] + dp[(i - 1) & 1][k2 - 1] - 1LL * sPart[k1 - 1] * sPart[k1 - 1] - dp[(i - 1) & 1][k1 - 1]) / (2LL * (sPart[k2 - 1] - sPart[k1 - 1]));
}
}
void solve() {
dp[1][0] = INF;
for (int j = 1; j <= N; ++ j)
dp[1][j] = 1LL * sPart[j] * sPart[j];
deque <int> dq;
for (int i = 2; i <= K; ++ i) {
for (int j = 0; j < i; ++ j)
dp[i & 1][j] = INF;
dq.clear();
for (int j = i; j <= N; ++ j) {
//Add j
while (dq.size() > 1) {
int k1 = dq.at(dq.size() - 2);
int k2 = dq.at(dq.size() - 1);
int k3 = j;
bool decision = (intersect(i, k1, k2) + 1E-10 >= intersect(i, k1, k3));
assert(!fail);
if (decision)
dq.pop_back();
else
break;
}
if (dq.empty())
dq.push_back(j);
else {
intersect(i, dq.back(), j);
if (!fail)
dq.push_back(j);
}
//While first gets beaten by second
while (dq.size() > 1) {
int k1 = dq.at(0);
int k2 = dq.at(1);
lint val1 = 1LL * (sPart[j] - sPart[k1 - 1]) * (sPart[j] - sPart[k1 - 1]) + dp[(i - 1) & 1][k1 - 1];
lint val2 = 1LL * (sPart[j] - sPart[k2 - 1]) * (sPart[j] - sPart[k2 - 1]) + dp[(i - 1) & 1][k2 - 1];
if (val2 <= val1)
dq.pop_front();
else
break;
}
int k = dq.front();
dp[i & 1][j] = 1LL * (sPart[j] - sPart[k - 1]) * (sPart[j] - sPart[k - 1]) + dp[(i - 1) & 1][k - 1];
father[i][j] = k - 1;
}
}
}
int main()
{
//freopen("data.in", "r", stdin);
cin >> N >> K;
++ K;
for (int i = 1; i <= N; ++ i) {
int val;
cin >> val;
sPart[i] = val + sPart[i - 1];
}
//brute();
solve();
cout << (1LL * sPart[N] * sPart[N] - dp[K & 1][N]) / 2 << '\n';
vector <int> sol;
int where = N;
int k = K;
while (father[k][where]) {
sol.push_back(father[k][where]);
where = father[k --][where];
}
reverse(sol.begin(), sol.end());
for (int i = 0; i < sol.size(); ++ i)
cout << sol[i] << " \n"[i + 1 == sol.size()];
return 0;
}
Compilation message
sequence.cpp: In function 'int main()':
sequence.cpp:126:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0; i < sol.size(); ++ i)
^
sequence.cpp:127:39: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
cout << sol[i] << " \n"[i + 1 == sol.size()];
^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
6 ms |
85620 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
9 ms |
85620 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
6 ms |
85620 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
9 ms |
85620 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
6 ms |
85620 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
0 ms |
85620 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
3 ms |
85620 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
85620 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
3 ms |
85620 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
86 ms |
85620 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
3 ms |
85620 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
73 ms |
85620 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
69 ms |
85620 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
83 ms |
85620 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
56 ms |
85620 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
73 ms |
85620 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
93 ms |
85620 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
33 ms |
85752 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
43 ms |
85880 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
879 ms |
85884 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
49 ms |
85884 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
1169 ms |
85884 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
786 ms |
85752 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
699 ms |
85884 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
649 ms |
85884 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
709 ms |
85884 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
939 ms |
85884 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
