Submission #112349

# Submission time Handle Problem Language Result Execution time Memory
112349 2019-05-19T02:25:25 Z ainta Split the sequence (APIO14_sequence) C++17
100 / 100
560 ms 6620 KB
#include<cstdio>
#include<algorithm>
#include<vector>
#define N_ 101000
using namespace std;
int n, K, w[N_], MnC[N_], MxC[N_], MxP[N_], MnP[N_];
long long S[N_], D[N_];
struct Seg {
	long long A, B;
	int num;
}Deq[N_];
bool Over(Seg a, Seg b, Seg c) {
	if (a.A == b.A) return true;
	long long A = b.B - a.B, B = a.A - b.A, C = c.B - a.B, D = a.A - c.A;
	if (A/B != C/D)return A/B >= C/D;
	A %= B, C %= D;
	return A * D >= B * C;
}
long long Get(Seg a, long long x) {
	return a.A*x + a.B;
}
void Calc(long long M) {
	int i;
	int head = 1, tail = 0;
	Deq[++tail] = { 0,0,0 };
	for (i = 1; i <= n; i++) {
		while (head < tail && Get(Deq[head], S[i]) >= Get(Deq[head + 1], S[i]))head++;
		MxC[i] = MxC[Deq[head].num] + 1;
		MxP[i] = Deq[head].num;
		D[i] = Get(Deq[head], S[i]) + S[i] * S[i] + M;
		Seg tp = { -2 * S[i],D[i] + S[i] * S[i],i };
		while (head < tail && Over(Deq[tail - 1], Deq[tail], tp))tail--;
		Deq[++tail] = tp;
	}
	head = 1, tail = 0;
	Deq[++tail] = { 0,0,0 };
	for (i = 1; i <= n; i++) {
		while (head < tail && Get(Deq[head], S[i]) > Get(Deq[head + 1], S[i]))head++;
		MnC[i] = MnC[Deq[head].num] + 1;
		MnP[i] = Deq[head].num;
		D[i] = Get(Deq[head], S[i]) + S[i] * S[i] + M;
		Seg tp = { -2 * S[i],D[i] + S[i] * S[i],i };
		while (head < tail && Over(Deq[tail - 1], Deq[tail], tp))tail--;
		Deq[++tail] = tp;
	}
}
int main() {
	int i;
	scanf("%d%d", &n, &K);
	for (i = 1; i <= n; i++) {
		scanf("%d", &w[i]);
		S[i] = S[i - 1] + w[i];
	}
	K++;
	long long b = 0, e = 4e18, mid, r = 0;
	while (b <= e) {
		mid = (b + e) >> 1;
		Calc(mid);
		if (MxC[n] >= K) {
			r = mid;
			b = mid + 1;
		}
		else e = mid - 1;
	}
	Calc(r);
	int ed = n, c = 0;
	long long s = 0;
	vector<int>Res;
	for (i = n - 1; i >= 0; i--) {
		if (MnC[i] + c + 1 <= K && MxC[i] + c + 1 >= K && s + (S[ed] - S[i])*(S[ed] - S[i]) + r + D[i] == D[n]) {
			if (i)Res.push_back(i);
			c++, s += (S[ed] - S[i])*(S[ed] - S[i]) + r;
			ed = i;
		}
	}
	reverse(Res.begin(), Res.end());
	long long Ans = (S[n] * S[n] - D[n] + r * K) / 2;
	printf("%lld\n", Ans);
	for (auto &t : Res)printf("%d ", t);
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:49:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d%d", &n, &K);
  ~~~~~^~~~~~~~~~~~~~~~
sequence.cpp:51:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d", &w[i]);
   ~~~~~^~~~~~~~~~~~~
# 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 412 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 384 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 384 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 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 2 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 2 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 2 ms 384 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 384 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 384 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 384 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 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 384 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 384 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 384 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 384 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 384 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 2 ms 384 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 3 ms 384 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 3 ms 384 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 384 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 3 ms 384 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 3 ms 384 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 384 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 384 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 384 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 384 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 384 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 6 ms 384 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 6 ms 384 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 384 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 6 ms 440 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 7 ms 384 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 7 ms 384 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 384 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 384 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 7 ms 384 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 384 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 45 ms 768 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 54 ms 888 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 42 ms 1016 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 45 ms 888 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 51 ms 888 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 53 ms 888 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 49 ms 1144 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 47 ms 876 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 50 ms 1016 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 52 ms 1016 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 527 ms 4924 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 546 ms 5240 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 407 ms 6252 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 444 ms 5756 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 520 ms 5920 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 560 ms 6008 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 506 ms 6620 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 457 ms 6392 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 491 ms 6392 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 490 ms 6392 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845