// APIO 2014 Problem 2 - Split the Sequence
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
const long long inf = 1LL << 62;
int main() {
// step #1. read input
cin.tie(0);
ios_base::sync_with_stdio(false);
int N, K;
cin >> N >> K; ++K;
vector<int> A(N);
for(int i = 0; i < N; ++i) {
cin >> A[i];
}
// step #2. preparation for calculating the answer
vector<int> S(N + 1);
for(int i = 0; i < N; ++i) {
S[i + 1] = S[i] + A[i];
}
// step #3. calculate the answer with dynamic programming
vector<long long> dp(N + 1, inf);
vector<vector<int> > pre(K + 1, vector<int>(N + 1, -1));
dp[0] = 0;
for(int i = 1; i <= K; ++i) {
vector<long long> ndp(N + 1, inf);
vector<int> st = { 0 };
for(int j = 1; j <= N; ++j) {
int l = 0, r = st.size();
if(st.size() >= 14) {
while(r - l > 2) {
int lc = (l * 2 + r) / 3;
int rc = (l + r * 2) / 3;
long long la = dp[st[lc]] - 1LL * S[st[lc]] * S[j];
long long lb = dp[st[rc]] - 1LL * S[st[rc]] * S[j];
if(la > lb) l = lc;
else r = rc;
}
}
for(int k = l; k < r; ++k) {
long long x = dp[st[k]] - 1LL * S[st[k]] * S[j];
if(ndp[j] > x) {
ndp[j] = x;
pre[i][j] = st[k];
}
}
ndp[j] += 1LL * S[j] * S[j];
while(st.size() >= 2) {
int sz = st.size();
__int128_t lc = __int128_t(dp[j] - dp[st[sz - 1]]) * (S[j] - S[st[sz - 2]]);
__int128_t rc = __int128_t(dp[j] - dp[st[sz - 2]]) * (S[j] - S[st[sz - 1]]);
if(lc <= rc) st.pop_back();
else break;
}
st.push_back(j);
}
dp = ndp;
}
// step #4. print the answer
cout << 1LL * S[N] * S[N] - dp[N] << endl;
int pos = N;
for(int i = K; i >= 2; --i) {
cout << pre[i][pos] << (i != 2 ? ' ' : '\n');
pos = pre[i][pos];
}
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 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 |
0 ms |
384 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
1 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 |
1 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 |
0 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 |
0 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 |
0 ms |
384 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
0 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 |
0 ms |
384 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
4 ms |
512 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
3 ms |
512 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
3 ms |
512 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
5 ms |
512 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
18 ms |
1152 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
23 ms |
1152 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
20 ms |
1024 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
22 ms |
1152 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
18 ms |
1152 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
6 ms |
512 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
9 ms |
640 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
9 ms |
820 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
5 ms |
768 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
247 ms |
8648 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
7 ms |
896 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
158 ms |
5376 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
191 ms |
6144 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
212 ms |
6804 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
169 ms |
5592 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
195 ms |
6288 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
234 ms |
7980 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
60 ms |
5524 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
63 ms |
5524 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Execution timed out |
2093 ms |
83088 KB |
Time limit exceeded |
| 4 |
Halted |
0 ms |
0 KB |
- |
