#include <iostream>
#include <vector>
#include <unordered_map>
#include <map>
#include <utility>
#include <algorithm>
#include <list>
#include <limits>
#include <cassert>
typedef long long ll;
static std::vector<int> A;
static std::vector<long long> psum;
static int n, k;
static std::vector<std::vector<int>> offset; // (k+1) x (n+1) -> offset
static std::list<int> answer;
// assume a1 <= a2. Want smallest x(>=0) s.t. a2.x + b2 >= a1.x + b1
ll intersect(ll a1, ll b1, ll a2, ll b2) {
if (a1 != a2) {
ll x = (b1 - b2) / (a2 - a1);
if ((a2 * x + b2) >= (a1 * x + b1))
return x;
else
return x + 1;
}
if (b1 > b2)
return std::numeric_limits<ll>::max();
return 0LL;
}
static long long dp(void) {
int k1;
for (k1=0; k1<=k; k1++)
offset.push_back(std::vector<int> (n+1, 0));
std::vector<long long> prevrow(n+1, 0);
std::vector<long long> row(n+1, 0);
// k = 0 => all offsets are zero
for (k1=1; k1<=k; k1++) {
std::swap(row, prevrow);
for (int i=2; i<=k1; i++)
row[i] = 0LL;
row[k1+1] = prevrow[k1] + psum[k1] * A[k1];
offset[k1][k1+1] = k1;
std::vector<ll> slopes;
std::vector<ll> intercepts;
std::vector<int> indices;
std::vector<ll> xmins;
slopes.push_back(psum[k1]);
intercepts.push_back(- psum[k1] * psum[k1] + prevrow[k1]);
indices.push_back(k1);
xmins.push_back(0);
int lastidx = 0; // remember the convex hull location for previous i
for (int i=(k1+2); i<=n; i++) {
// find j to maximize: prevrow[j] + psum[j] * (psum[i] - psum[j]);
// j goes from k1 to i-1
ll slope = psum[i-1];
ll intercept = -psum[i-1] * psum[i-1] + prevrow[i-1];
while (true) {
ll x = intersect(slopes.back(), intercepts.back(), slope, intercept);
if (x <= xmins.back()) {
slopes.pop_back();
intercepts.pop_back();
indices.pop_back();
xmins.pop_back();
if (!slopes.empty())
continue;
}
slopes.push_back(slope);
intercepts.push_back(intercept);
indices.push_back(i-1);
xmins.push_back(x);
break;
}
if (lastidx > (xmins.size() - 1))
lastidx = xmins.size() - 1;
int idx = lastidx;
for (idx=lastidx; (idx+1) < xmins.size(); idx++) {
if (psum[i] >= xmins[idx] and psum[i] < xmins[idx + 1])
break;
}
int j = indices[idx];
row[i] = prevrow[j] + psum[j] * (psum[i] - psum[j]);
offset[k1][i] = j;
lastidx = idx;
}
/*
std::cout << "k " << k1 << " val ";
for (long long x: row)
std::cout << x << " ";
std::cout << std::endl;
std::cout << "k " << k1 << " off ";
for (long x: offset[k1])
std::cout << x << " ";
std::cout << std::endl;
*/
}
int lastoffset = n;
k1 = k;
while (k1 > 0) {
lastoffset = offset[k1][lastoffset];
answer.push_front(lastoffset);
k1 --;
}
return row[n];
}
int main(int argc, char const *argv[]) {
std::cin >> n >> k;
for (int i=0; i<n; i++) {
int a;
std::cin >> a;
A.push_back(a);
}
psum.push_back(0);
for (int i=0; i<n; i++)
psum.push_back(A[i] + psum[i]);
std::cout << dp() << std::endl;
for (int a: answer)
std::cout << a << " ";
std::cout << std::endl;
return 0;
}
Compilation message
sequence.cpp: In function 'long long int dp()':
sequence.cpp:90:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
if (lastidx > (xmins.size() - 1))
~~~~~~~~^~~~~~~~~~~~~~~~~~~~
sequence.cpp:95:33: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (idx=lastidx; (idx+1) < xmins.size(); idx++) {
~~~~~~~~^~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
504 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
2 ms |
504 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
3 ms |
572 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
3 ms |
584 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
2 ms |
584 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
3 ms |
644 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
3 ms |
644 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
2 ms |
644 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
3 ms |
764 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
2 ms |
764 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
3 ms |
764 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
3 ms |
764 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
4 ms |
892 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
3 ms |
892 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
2 ms |
892 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
3 ms |
892 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
892 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
3 ms |
892 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
9 ms |
1404 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
3 ms |
1404 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
11 ms |
1404 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
10 ms |
1404 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
17 ms |
1404 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
9 ms |
1408 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
6 ms |
1408 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
5 ms |
1408 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
7 ms |
1408 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
5 ms |
1408 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
161 ms |
9404 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
8 ms |
9404 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
67 ms |
9404 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
72 ms |
9404 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
97 ms |
9404 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
95 ms |
9404 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
102 ms |
9404 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
165 ms |
9404 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
43 ms |
9404 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
49 ms |
9404 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
1149 ms |
86304 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
54 ms |
86304 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
1276 ms |
86304 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
810 ms |
86304 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
1043 ms |
86304 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
814 ms |
86304 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
930 ms |
86304 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
1109 ms |
86304 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
