oj.uz

Submission #34828

# Submission time Handle Problem Language Result Execution time Memory
34828 2017-11-16T04:07:32 Z cheater2k Split the sequence (APIO14_sequence) C++14
71 / 100
 2000 ms 89248 KB 
#include <bits/stdc++.h>
using namespace std;

struct line {
	long long a; long long b; int id;
	line(long long a=0, long long b=0, int id=0): a(a), b(b), id(id) {}
};

bool bad(line l1, line l2, line l3) {
	double X13 = (double)(l1.b - l3.b) / (l3.a - l1.a);
	double X12 = (double)(l1.b - l2.b) / (l2.a - l1.a);
	return X13 < X12;
}

vector<line> L;
void add(long long a, long long b, int id) {
	line d = line(a, b, id);
	if (!L.empty() && L.back().a == d.a) {
		if (L.back().b <= d.b) return; else L.pop_back();
	}
	while(L.size() >= 2 && bad(L[L.size()-2], L[L.size()-1], d)) L.pop_back();
	L.push_back(d);
}

int cur = 0;

pair<long long, int> get(long long x) {
	if (cur >= L.size()) cur = L.size() - 1;
	while(cur < (int)L.size()-1 && L[cur].a * x + L[cur].b > L[cur+1].a * x + L[cur+1].b) ++cur;
	return make_pair(L[cur].a * x + L[cur].b, L[cur].id);
}

const int N = 1e5 + 5, K = 205;
const long long inf = 1e18;

int n, k;
long long a[N];
long long f[N][2];
int trace[N][K];

int main() {
	ios_base::sync_with_stdio(false); cin.tie(0);
	cin >> n >> k; ++k;
	for (int i = 1; i <= n; ++i) cin >> a[i], a[i] += a[i-1];

	for (int i = 0; i <= n; ++i) f[i][0] = inf;
	f[0][0] = 0;

	for (int j = 1; j <= k; ++j) {
		L.clear();
		cur = 0;
		add(0, f[0][0], 0);
		for (int i = 1; i <= n; ++i) {
			f[i][1] = inf;
			pair<long long, int> res = get(a[i]);
			if (f[i][1] > res.first + a[i] * a[i]){
				trace[i][j] = res.second;
				f[i][1] = res.first + a[i] * a[i];
			}
			add(-2 * a[i], f[i][0] + a[i] * a[i], i);
			f[i][0] = f[i][1];
		}
		f[0][0] = inf;
	}

	long long ans = f[n][0];
	ans = (a[n] * a[n] - ans) / 2;

	printf("%lld\n", ans);
	vector<int> vec;
	while(n) {
		n = trace[n][k]; --k;
		vec.push_back(n);
	}
	vec.pop_back();
	for (int i = vec.size()-1; i >= 0; --i) printf("%d ", vec[i]); printf("\n");
}

Compilation message

sequence.cpp: In function 'std::pair<long long int, int> get(long long int)':
sequence.cpp:28:10: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if (cur >= L.size()) cur = L.size() - 1;
          ^

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 84600 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 84600 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 84600 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 84600 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 84600 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 84600 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 84600 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 84600 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 84600 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 84600 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 84600 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 84600 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 84600 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 84600 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 84600 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 84600 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 84600 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 84600 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 84600 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 84600 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 84600 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 84600 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 84600 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 84600 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 84600 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 84600 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 84600 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 84600 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 84600 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 0 ms 84600 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 84600 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 0 ms 84600 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 0 ms 84600 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 0 ms 84600 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 0 ms 84600 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 0 ms 84600 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 0 ms 84600 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 84600 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 0 ms 84600 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 84600 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 0 ms 84600 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 6 ms 84600 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 3 ms 84600 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 84600 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 84600 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 0 ms 84600 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 84600 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 85020 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 6 ms 85020 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 106 ms 85216 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 0 ms 85216 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 53 ms 85020 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 69 ms 85020 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 89 ms 85216 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 66 ms 85216 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 73 ms 85216 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 89 ms 85216 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 73 ms 89248 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 63 ms 89248 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2000 ms 89248 KB Execution timed out
4 Halted 0 ms 0 KB -