Submission #98427

# Submission time Handle Problem Language Result Execution time Memory
98427 2019-02-23T14:10:44 Z Anai Split the sequence (APIO14_sequence) C++14
100 / 100
1530 ms 82968 KB
#include <bits/stdc++.h>
#define rev(v) (v.rbegin())
using namespace std;

using i64 = long long;
using f64 = double;

const int K = 201, N = 100005;


struct Line {
	i64 a, b;
	int idx;

	Line(i64 _a, i64 _b, int _idx) {
		a = _a, b = _b, idx = _idx; }

	Line() {
		a = 0, b = 1e18; }

	inline i64 operator () (const i64 &x) {
		return a * x + b; } };


int far[K][N];
vector<i64> dp[2];

deque<Line> dq;
vector<i64> v, s;
vector<int> ans;
int n, k;


static f64 intersect(const Line &l1, const Line &l2) {
	return (l1.b - l2.b) / (l2.a - l1.a); }


int main() {
#ifdef HOME
	freopen("sequences.in", "r", stdin);
	freopen("sequences.out", "w", stdout);
#endif
	ios::sync_with_stdio(false);
	cin.tie(0), cout.tie(0);

	Line my_line;

	cin >> n >> k;
	dp[0].resize(n);
	v.resize(n);
	for (auto &i: v)
		cin >> i;

	s.resize(n);
	s[0] = v[0];
	for (int i = 1; i < n; ++i)
		s[i] = s[i - 1] + v[i];

	for (int i = 0; i < n; ++i)
		dp[0][i] = s[i] * (s.back() - s[i]);

	dp[1].resize(n);
	for (int it = 1; it < k; ++it) {
		dq.emplace_back(s[it - 1] + s.back(), dp[0][it - 1] - s.back() * s[it - 1], it - 1);

		for (int i = it; i < n; ++i) {
			while (dq.size() > 1 && dq[0](s[i]) <= dq[1](s[i]))
				dq.pop_front();

			dp[1][i] = dq[0](s[i]) - s[i] * s[i];
			far[it][i] = dq[0].idx;

			my_line = {s.back() + s[i], dp[0][i]- s.back() * s[i], i};
			while (dq.size() > 1 && (dq.back().a == my_line.a || intersect(rev(dq)[0], rev(dq)[1]) > intersect(rev(dq)[0], my_line)))
				dq.pop_back();
			dq.push_back(my_line); }

		dq.clear();
		swap(dp[0], dp[1]); }

	auto it = max_element(begin(dp[0]), end(dp[0]));

	cout << *it << '\n';
	ans.reserve(k);

	ans.push_back(it - begin(dp[0]));
	for (int i = k - 1; i > 0; --i)
		ans.push_back(far[i][ans.back()]);

	reverse(begin(ans), end(ans));
	for (auto i: ans)
		cout << i + 1 << ' ';
	cout << endl;

	return 0; }
# Verdict Execution time Memory Grader output
1 Correct 2 ms 384 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 384 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 384 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 384 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 3 ms 384 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 3 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 384 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 384 KB contestant found the optimal answer: 1 == 1
9 Correct 3 ms 384 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 384 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 3 ms 384 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 384 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 3 ms 384 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 384 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 284 KB contestant found the optimal answer: 805 == 805
16 Correct 1 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 2 ms 384 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 384 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 2 ms 640 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 384 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 3 ms 384 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 3 ms 384 KB contestant found the optimal answer: 933702 == 933702
7 Correct 3 ms 512 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 384 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 384 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 3 ms 384 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 2 ms 384 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 3 ms 512 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 4 ms 1408 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 384 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 5 ms 1024 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 4 ms 1280 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 7 ms 1408 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 512 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 512 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 640 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 2 ms 384 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 384 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 13 ms 2048 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 384 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 14 ms 2048 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 17 ms 1792 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 16 ms 2048 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 10 ms 2048 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 6 ms 768 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 8 ms 1024 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 5 ms 896 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 5 ms 1024 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 140 ms 9464 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 5 ms 896 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 104 ms 6008 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 97 ms 6748 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 128 ms 7288 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 97 ms 6136 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 101 ms 6972 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 117 ms 8568 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 34 ms 5344 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 30 ms 5436 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1288 ms 82968 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 27 ms 5752 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1530 ms 82488 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1151 ms 59228 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1168 ms 63304 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 839 ms 52340 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 1030 ms 59468 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1157 ms 74984 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845