oj.uz

Submission #104511

# Submission time Handle Problem Language Result Execution time Memory
104511 2019-04-07T09:16:19 Z E869120 Split the sequence (APIO14_sequence) C++14
100 / 100
 1538 ms 86392 KB 
#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
#pragma warning (disable: 4996)

const int MAX_N = 100009;

struct Node {
	long long l, r, a, b; int num;
};

bool operator<(const Node &a1, const Node &a2) {
	if (a1.l < a2.l) return true;
	return false;
}

Node vec[MAX_N];

class ConvexHullTrick {
public:
	int sz = 0;

	void init() {
		for (int i = 0; i < MAX_N; i++) vec[i] = Node{ 0LL,0LL,0LL,0LL,0LL };
		vec[0] = Node{ -(1LL << 60), (1LL << 60), -(1LL << 30), (1LL << 60), -1LL };
		sz = 1;
	}

	long long cross_point(Node A, Node B) {
		if (A.a == B.a) {
			if (A.b < B.b) return (1LL << 59);
			return -(1LL << 59);
		}
		// A.a < B.a, 既に val の時点で B が下回っていることを表す
		long long E = A.b + (B.a - A.a) * (B.a - A.a) - B.b;
		long long F = 2LL * (B.a - A.a);
		if (E >= 0) return B.a - E / F;
		E *= -1;
		return B.a + (E + F - 1) / F;
	}
	
	void add(Node B, int id) {
		while (sz >= 1) {
			long long P = cross_point(vec[sz - 1], B);
			if (P > vec[sz - 1].l) {
				vec[sz - 1].r = P - 1;
				vec[sz] = Node{ P, (1LL << 60), B.a, B.b, (long long)id }; sz++;
				break;
			}
			else sz--;
		}
	}
	
	pair<long long, int> get_minimum(long long pos) {
		int pos1 = lower_bound(vec, vec + sz, Node{ pos + 1LL, -(1LL << 61), 0LL, 0LL, 0LL }) - vec; pos1--;
		return make_pair(vec[pos1].b + (vec[pos1].a - pos) * (vec[pos1].a - pos), vec[pos1].num);
	}
};

long long N, K, A1[100009], A2[100009], prev_[100009], dp[100009]; int pre[209][100009];

long long ranged(int l, int r) {
	long long V1 = A1[r] - A1[l - 1]; V1 *= V1;
	return V1;
}

long long solve() {
	prev_[0] = 0; for (int i = 1; i <= N; i++) prev_[i] = (1LL << 60);

	for (int i = 0; i < K; i++) {
		ConvexHullTrick G; G.init(); bool flag = false;
		for (int j = 0; j <= N; j++) {
			if (flag == true) {
				pair<long long, int> F = G.get_minimum(A1[j]);
				dp[j] = F.first;
				pre[i + 1][j] = F.second;
			}
			if (prev_[j] != (1LL << 60)) { G.add(Node{ -(1LL << 60), (1LL << 60), A1[j], prev_[j], j }, j); flag = true; }
		}
		for (int j = 0; j <= N; j++) { prev_[j] = dp[j]; dp[j] = (1LL << 60); }
	}
	return prev_[N];
}

int main() {
	scanf("%lld%lld", &N, &K); K++;
	for (int i = 1; i <= N; i++) { scanf("%lld", &A1[i]); A2[i] = A1[i] * A1[i]; }
	for (int i = 1; i <= N; i++) { A1[i] += A1[i - 1]; A2[i] += A2[i - 1]; }
	cout << (ranged(1, N) - solve()) / 2LL << endl;
	vector<int>T; int cx = K, cy = N;
	while (cx >= 1) {
		if (cx < K) T.push_back(cy);
		cy = pre[cx][cy]; cx--;
	}
	for (int i = T.size() - 1; i >= 0; i--) { printf("%d", T[i]); if (i) printf(" "); }
	printf("\n");
	return 0;
}

Compilation message

sequence.cpp:5:0: warning: ignoring #pragma warning  [-Wunknown-pragmas]
 #pragma warning (disable: 4996)
 
sequence.cpp: In member function 'void ConvexHullTrick::add(Node, int)':
sequence.cpp:48:47: warning: narrowing conversion of '(long long int)id' from 'long long int' to 'int' inside { } [-Wnarrowing]
     vec[sz] = Node{ P, (1LL << 60), B.a, B.b, (long long)id }; sz++;
                                               ^~~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:87:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%lld%lld", &N, &K); K++;
  ~~~~~^~~~~~~~~~~~~~~~~~~~
sequence.cpp:88:38: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  for (int i = 1; i <= N; i++) { scanf("%lld", &A1[i]); A2[i] = A1[i] * A1[i]; }
                                 ~~~~~^~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 4224 KB contestant found the optimal answer: 108 == 108
2 Correct 7 ms 4352 KB contestant found the optimal answer: 999 == 999
3 Correct 7 ms 4352 KB contestant found the optimal answer: 0 == 0
4 Correct 8 ms 4224 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 8 ms 4352 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 7 ms 4352 KB contestant found the optimal answer: 1 == 1
7 Correct 7 ms 4352 KB contestant found the optimal answer: 1 == 1
8 Correct 6 ms 4352 KB contestant found the optimal answer: 1 == 1
9 Correct 8 ms 4224 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 7 ms 4352 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 7 ms 4324 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 7 ms 4352 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 9 ms 4324 KB contestant found the optimal answer: 140072 == 140072
14 Correct 7 ms 4224 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 6 ms 4224 KB contestant found the optimal answer: 805 == 805
16 Correct 7 ms 4224 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 7 ms 4224 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 4224 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 7 ms 4224 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 21 ms 4480 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 6 ms 4224 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 10 ms 4352 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 8 ms 4224 KB contestant found the optimal answer: 933702 == 933702
7 Correct 15 ms 4320 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 11 ms 4352 KB contestant found the optimal answer: 687136 == 687136
9 Correct 8 ms 4352 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 9 ms 4352 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 4352 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 8 ms 4224 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 63 ms 5172 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 7 ms 4224 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 58 ms 4984 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 59 ms 5240 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 65 ms 5240 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 19 ms 4476 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 16 ms 4480 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 25 ms 4572 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 4352 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 6 ms 4352 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 61 ms 5880 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 8 ms 4352 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 69 ms 6008 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 59 ms 5624 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 64 ms 5880 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 80 ms 6008 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 20 ms 4608 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 30 ms 4984 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 4736 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 4736 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 161 ms 13176 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 10 ms 4736 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 136 ms 9920 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 175 ms 10732 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 169 ms 11116 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 128 ms 10052 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 150 ms 10744 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 177 ms 12380 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 43 ms 8956 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 39 ms 8952 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1321 ms 86264 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 55 ms 9464 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1538 ms 86392 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1202 ms 62792 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1087 ms 67180 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 939 ms 56068 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 960 ms 63044 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1350 ms 78540 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845