Submission #674883

# Submission time Handle Problem Language Result Execution time Memory
674883 2022-12-26T12:46:03 Z penguin133 Split the sequence (APIO14_sequence) C++14
100 / 100
790 ms 82780 KB
#include <bits/stdc++.h>
using namespace std;
//#define int long long
typedef long long ll;
ll dp[2][100005];
int pre[205][100005];
ll P[100005], A[100005];
deque<pair<pair<ll, ll> , int> > dq;
ll f(pair<ll, ll> x, ll y){
	return x.first*y + x.second;
}
long double intersect(ll a, ll b, ll c, ll d){
	return (long double)(d-b)/(a-c);
}
void ins(ll m , ll c, int in){
	while(dq.size() > 1){
		int s = dq.size();
		if(intersect(dq.back().first.first, dq.back().first.second,m,c) <= intersect(dq[s-2].first.first, dq[s-2].first.second, m,c))dq.pop_back();
		else break;
	}
	dq.push_back(make_pair(make_pair(m,c), in));
} 
 
pair<ll, int> query(ll x){
	while(dq.size() > 1){
		if(f(dq[0].first, x) < f(dq[1].first, x))dq.pop_front();
		else break;
	}
	return {f(dq[0].first, x), dq[0].second};
}
main(){
	ios::sync_with_stdio(0);cin.tie(0);
	int n,k;cin >> n >> k;
	for(int i=1;i<=n;i++)cin >> A[i], P[i] = P[i-1] + A[i];
	for(int i=1;i<=n;i++)dp[1][i] = (P[n] - P[i])*P[i];
	for(int i=2;i<=k;i++){
		int tmp = i %2;
		for(int j=i;j<=n-(k-i)+1;j++){
			ins(P[j-1] + P[n], -P[n] * P[j-1] + dp[1-tmp][j-1], j-1);
			pair<ll,ll>x = query(P[j]);
			dp[tmp][j] = x.first-  P[j] * P[j];
			pre[i][j] = x.second;
		}
		dq.clear();
	}
	ll maxi = -1e9; int in;
	for(int i=1;i<=n;i++)if(dp[k%2][i] > maxi)maxi = dp[k%2][i], in = i;
	cout << maxi << '\n';
	cout << in << " ";
	int p = pre[k][in];
	while(p)cout << p << " ", k--, p = pre[k][p];
	/*
	cout << "\n\n";
	for(int i=1;i<=k;i++){
		for(int j=i;j<=n;j++)cout << dp[i][j].first << " " << dp[i][j].second << " ";
		cout << '\n';
	}
	*/
  return 0;
}

Compilation message

sequence.cpp:31:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
   31 | main(){
      | ^~~~
sequence.cpp: In function 'int main()':
sequence.cpp:50:6: warning: 'in' may be used uninitialized in this function [-Wmaybe-uninitialized]
   50 |  int p = pre[k][in];
      |      ^
# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 340 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 340 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 340 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 340 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 328 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 324 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 340 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 340 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 328 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 324 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 340 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 328 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 332 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 328 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 328 KB contestant found the optimal answer: 999919994 == 999919994
# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 340 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 468 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 324 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 340 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 324 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 468 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 340 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 340 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 340 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 340 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 1236 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 328 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 980 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 1220 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 1220 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 584 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 456 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 596 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 5 ms 1876 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 340 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 7 ms 1860 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 6 ms 1748 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 1876 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 5 ms 1876 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 724 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 980 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 2 ms 852 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 852 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 63 ms 9356 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 980 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 49 ms 5904 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 63 ms 6748 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 54 ms 7168 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 40 ms 5984 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 49 ms 6736 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 66 ms 8488 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 14 ms 5180 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 15 ms 5272 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 607 ms 82780 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 17 ms 5592 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 790 ms 82348 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 538 ms 58976 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 546 ms 63216 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 441 ms 52068 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 475 ms 59148 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 677 ms 74760 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845