#include <bits/stdc++.h>
using namespace std;
using ll = long long;
typedef long double ld;
const int maxn = 1e5+5, maxk = 205;
int N, K, a[maxn];
ll pre[maxn];
ll dp[2][maxn];
int previous[maxk][maxn];
struct FN
{
int id;
ll m, b; //in this case, function is a line
FN(ll _m, ll _b, int _id) : m(_m), b(_b), id(_id) {}
ll eval(ll x) const {
return m*x + b;
}
ld intersect(const FN& r) const { //returns x coordinate of intersection
//assert(m != r.m);
return (ld)(r.b-b)/(ld)(m-r.m);
}
friend bool comp(const FN& l1, const FN& l2, const FN& l) {
//order in deque: l1, l2, l
//true --> l2 is unnecessary
/*
if (l1.m == l2.m || l1.m == l.m || l2.m == l.m) {
printf("(%d, %d), (%d, %d), (%d, %d)\n",l1.m,l1.b,l2.m,l2.b,l.m,l.b);
fflush(stdout);
//cout << l1.m << ' ' << l2.m << ' ' << l.m << endl;
}
*/
ld x1 = l1.intersect(l);
ld x2 = l1.intersect(l2);
return x1 <= x2;
}
};
struct Hull: public deque<FN> //convex hull for maximum
{
void add(const FN& l) {
//slopes coming in -1,-2,-3,...so add to front of deque rather than back (querying for maximum)
//if adding to back, need to change the indices
while (!empty() && back().m == l.m) {
//assert(back().b <= l.b);
pop_back();
}
while (size() >= 2 &&
comp(*next(rbegin()),*rbegin(),l)) {
pop_back();
}
/*
while (!empty() && back().m == l.m) {
//assert(back().b <= l.b);
pop_back();
}
*/
push_back(l);
/*
cout << "----\n";
for (auto it = begin(); it != end(); ++it) {
cout << it->m << ' ' << it->b << '\n';
}
*/
/*
if (size() >= 2) {
assert(next(rbegin())->m != (*rbegin()).m);
}
*/
}
pair<ll,int> query(ll x) {
while (size() >= 2 && begin()->eval(x) <= next(begin())->eval(x)) {
pop_front();
}
return {begin()->eval(x),begin()->id};
/*
pair<ll,int> best = {0,0};
//cout << "----\n";
for (auto it = begin(); it != end(); ++it) {
best = max(best,{it->eval(x),it->id});
//cout << it->m << ' ' << it->b << '\n';
if (next(it) != end()) {
assert(it->m != next(it)->m);
}
}
return best;
*/
}
};
int main()
{
//ios_base::sync_with_stdio(false); cin.tie(NULL);
cin >> N >> K;
for (int i = 1; i <= N; i++) {
cin >> a[i];
pre[i] = a[i] + pre[i-1];
}
for (int k = 1; k <= K; k++) {
Hull hull;
for (int i = 1; i <= N; i++) {
//if (i-1 == 0 || pre[i-1] > pre[i-2] ||
// (pre[i-1] == pre[i-2] &&
// dp[i-1][k-1] > dp[i-2][k-1])) {
hull.add(FN(pre[i-1],dp[1-(k&1)][i-1]-pre[i-1]*pre[i-1],i-1));
//}
//else cout << "discounted " << (i-1) << ' ' << (k-1) << '\n';
auto p = hull.query(pre[i]);
dp[k&1][i] = p.first;
previous[k][i] = p.second;
//printf("[%d][%d]: %d\n",i,k,dp[i][k]);
}
}
/*
for (int k = 1; k <= K; k++) {
for (auto p: hulls[k-1]) {
cout << p.m << ' ' << p.b << '\n';
}
}
*/
//output
cout << dp[K&1][N] << '\n';
int curr = N;
int k = K;
vector<int> ans;
while (k > 0) {
curr = previous[k][curr];
k--;
ans.push_back(curr);
}
reverse(ans.begin(),ans.end());
for (int i: ans) {
cout << i << ' ';
}
cout << '\n';
}
Compilation message
sequence.cpp: In constructor 'FN::FN(ll, ll, int)':
sequence.cpp:15:11: warning: 'FN::b' will be initialized after [-Wreorder]
ll m, b; //in this case, function is a line
^
sequence.cpp:14:9: warning: 'int FN::id' [-Wreorder]
int id;
^~
sequence.cpp:16:5: warning: when initialized here [-Wreorder]
FN(ll _m, ll _b, int _id) : m(_m), b(_b), id(_id) {}
^~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
2 ms |
380 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
2 ms |
424 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
3 ms |
632 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
3 ms |
376 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
2 ms |
504 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
2 ms |
380 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
7 ms |
376 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
4 ms |
1400 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
4 ms |
1144 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
4 ms |
1400 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
4 ms |
1528 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
3 ms |
504 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
2 ms |
504 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
3 ms |
632 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
356 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
9 ms |
2040 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
2 ms |
376 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
10 ms |
2168 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
9 ms |
1912 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
11 ms |
2040 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
9 ms |
2168 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
4 ms |
760 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
5 ms |
1144 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
888 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
6 ms |
928 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
69 ms |
9436 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
8 ms |
888 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
52 ms |
6068 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
58 ms |
6800 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
65 ms |
7288 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
49 ms |
6112 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
55 ms |
6904 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
68 ms |
8568 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
41 ms |
4648 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
41 ms |
4796 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
643 ms |
82048 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
59 ms |
5376 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
821 ms |
81844 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
563 ms |
58188 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
627 ms |
62376 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
505 ms |
51412 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
505 ms |
58352 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
640 ms |
74132 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
