## Submission #478231

# Submission time Handle Problem Language Result Execution time Memory
478231 2021-10-06T15:33:08 Z dennisstar Split the sequence (APIO14_sequence) C++17
100 / 100
342 ms 9400 KB
```#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using i128 = __int128;

struct line {
ll a, b; int ind;
ll get(ll x) { return a*x+b; }
line() {}
line(ll a, ll b, ll i) : a(a), b(b), ind(i) {}
};

struct cht {
vector<line> l;
int t;
cht() : t(0) {}
void upd(line v) {
while (t+1<l.size() && (l.back().b<=v.b || (i128)(l[l.size()-2].b-v.b)*(l.back().a-l[l.size()-2].a)<=(i128)(l[l.size()-2].b-l.back().b)*(v.a-l[l.size()-2].a))) l.pop_back();
l.emplace_back(v);
}
pair<ll, ll> get(ll x) {
while (t+1<l.size() && l[t].get(x)<l[t+1].get(x)) t++;
return {l[t].get(x), l[t].ind};
}
};

vector<int> rt, ans;

pair<ll, ll> sol(vector<ll> &a, ll s, bool q=false) {
int n=a.size();
vector<ll> d(n), l(n), c(n);
cht st;
st.upd(line(2*a[n-1], 0, -1));
for (int i=0; i<n; i++) {
auto [v, j]=st.get(a[i]);
d[i]=v-2*a[i]*a[i]+s;
l[i]=j;
c[i]=(j<0?0:c[j])+1;
st.upd(line(2*(a[i]+a[n-1]), d[i]-2*a[i]*a[n-1], i));
}

if (q) {
rt.clear();
for (int i=n-1; i!=-1; i=l[i]) rt.emplace_back(i);
reverse(rt.begin(), rt.end());
}

return {d[n-1], c[n-1]};
}

void track(vector<ll> &a, ll s, int p) {
sol(a, -(2*s+1), true);
auto l=rt;
sol(a, -(2*s-1), true);
auto r=rt;
if (l.size()==p) { ans=l; return ; }
if (r.size()==p) { ans=r; return ; }
for (int i=0, j=0; i+1<r.size(); i++) {
while (l[j]<=r[i]) j++;
if (r[i+1]<=l[j]&&i+1+l.size()-j==p) {
for (int k=0; k<=i; k++) ans.emplace_back(r[k]);
for (int k=j; k<l.size(); k++) ans.emplace_back(l[k]);
return ;
}
}
puts("fuck");
assert(0);
}

int main() {
cin.tie(0)->sync_with_stdio(0);

int n, k;
cin>>n>>k;
k++;
vector<ll> a(n);
for (auto &i:a) cin>>i;
for (int i=1; i<n; i++) a[i]+=a[i-1];

ll s=0, e=1e18;
while (s<e) {
ll m=(s+e)/2;
auto c=sol(a, -(2*m+1)).second;
if (c>k) s=m+1;
else e=m;
}

track(a, s, k);
ll v=0;
for (int i=0; i<k-1; i++) v+=(a[n-1]-a[ans[i]])*(a[ans[i]]-(i?a[ans[i-1]]:0));
cout<<v<<'\n';
for (int i=0; i<k-1; i++) cout<<ans[i]+1<<' ';

return 0;
}```

### Compilation message

```sequence.cpp: In member function 'void cht::upd(line)':
sequence.cpp:19:13: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
19 |   while (t+1<l.size() && (l.back().b<=v.b || (i128)(l[l.size()-2].b-v.b)*(l.back().a-l[l.size()-2].a)<=(i128)(l[l.size()-2].b-l.back().b)*(v.a-l[l.size()-2].a))) l.pop_back();
|          ~~~^~~~~~~~~
sequence.cpp: In member function 'std::pair<long long int, long long int> cht::get(ll)':
sequence.cpp:23:13: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
23 |   while (t+1<l.size() && l[t].get(x)<l[t+1].get(x)) t++;
|          ~~~^~~~~~~~~
sequence.cpp: In function 'void track(std::vector<long long int>&, ll, int)':
sequence.cpp:57:14: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
57 |  if (l.size()==p) { ans=l; return ; }
|      ~~~~~~~~^~~
sequence.cpp:58:14: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
58 |  if (r.size()==p) { ans=r; return ; }
|      ~~~~~~~~^~~
sequence.cpp:59:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
59 |  for (int i=0, j=0; i+1<r.size(); i++) {
|                     ~~~^~~~~~~~~
sequence.cpp:61:35: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
61 |   if (r[i+1]<=l[j]&&i+1+l.size()-j==p) {
|                     ~~~~~~~~~~~~~~^~~
sequence.cpp:63:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
63 |    for (int k=j; k<l.size(); k++) ans.emplace_back(l[k]);
|                  ~^~~~~~~~~```

#### Subtask #1 11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 204 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 204 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 204 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 204 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 204 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 204 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 204 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 204 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 204 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 204 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 204 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 204 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 204 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 204 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 204 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 204 KB contestant found the optimal answer: 999919994 == 999919994

#### Subtask #2 11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 204 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 204 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 204 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 204 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 204 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 204 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 204 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 204 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 204 KB contestant found the optimal answer: 29000419931 == 29000419931

#### Subtask #3 11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 204 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 332 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 204 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 332 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 332 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 204 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 204 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 204 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 204 KB contestant found the optimal answer: 490686959791 == 490686959791

#### Subtask #4 17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 332 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 332 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 2 ms 332 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 332 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 2 ms 332 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 2 ms 332 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 3 ms 332 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 2 ms 332 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 332 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 332 KB contestant found the optimal answer: 12345131038664 == 12345131038664

#### Subtask #5 21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 812 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 18 ms 956 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 31 ms 1260 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 20 ms 976 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 26 ms 972 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 20 ms 1008 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 26 ms 1264 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 24 ms 1260 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 23 ms 1232 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 27 ms 1232 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

#### Subtask #6 29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 224 ms 6204 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 228 ms 6360 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 295 ms 8884 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 225 ms 7264 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 262 ms 8560 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 252 ms 8440 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 342 ms 9400 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 254 ms 9120 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 310 ms 9132 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 300 ms 8964 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845