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답안 #977555

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
977555 2024-05-08T06:46:06 Z josanneo22 수열 (APIO14_sequence) C++17
100 / 100
 337 ms 83084 KB 
#pragma GCC optimize("O3")

#include <bits/stdc++.h>
using namespace std;
using i64 = long long;

#define L(i, j, k) for (int i = (j); i <= (k); ++i)
#define R(i, j, k) for (int i = (j); i >= (k); --i)
#define all(x) x.begin(), x.end()

const int nax = 100050;
const int kax = 204;

int N, K;
int a[nax];
int from[kax][nax];
i64 dp[2][nax];
i64 pre[nax];
int q[nax];
int L = 1, R = 1;

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr); cout.tie(nullptr);

	cin >> N >> K;
	L(i, 1, N) {
		cin >> a[i];
		pre[i] = pre[i - 1] + a[i];
	}
	L(i, 0, N) dp[0][i] = 0;
	L(k, 1, K) {
		q[R++] = 0;
		int nw = k & 1;
		int pv = nw ^ 1;
		auto Y = [&](int x) { return dp[pv][x]; };
		auto X = [&](int x) { return pre[x]; };
		auto dY = [&](int x, int y) { return Y(x) - Y(y); };
		auto dX = [&](int x, int y) { return X(x) - X(y); };
		auto DP = [&](int x, int y) { return dp[pv][y] + (pre[x] - pre[y]) * (pre[N] - pre[x]); };
		L(i, 1, N) {
			while (R - L > 1 && dY(q[L + 1], q[L]) >= (pre[N] - pre[i]) * dX(q[L + 1], q[L])) L++;
			int j = q[L];
			dp[nw][i] = DP(i, j);
			from[k][i] = j;
			while (R - L > 1 && dY(i, q[R - 1]) * dX(q[R - 1], q[R - 2]) >= dY(q[R - 1], q[R - 2]) * dX(i, q[R - 1])) R--;
			q[R++] = i;
		}
		L(i, 1, N) dp[pv][i] = dp[nw][i];
		L = R = 1;
	}
	i64 mx = -1;
	int start = -1;
	L(i, 1, N) {
		if (mx < dp[K & 1][i]) {
			mx = dp[K & 1][i];
			start = i;
		}
	}
	cout << mx << '\n';
	L(i, 0, K - 1) {
		cout << start << ' ';
		start = from[K - i][start];
	}
}
/* 
contribution = sum in segment * sum after the segment

dp[i][j] = considered until i and have j splits
for all p < i
dp[i][j] = max(dp[p][j - 1] + (pre[i] - pre[p]) * (pre[N] - pre[i]))
dp[i][j] = max(dp[p][j - 1] + - pre[p] * (pre[N] - pre[i])) + (pre[i]) * (pre[N] - pre[i])

m = -pre[p]
x = pre[N] - pre[i]
c = dp[p][j - 1]

CHT:
	if x is better than y:
		dp[x][j - 1] - pre[x] * (pre[N] - pre[i]) >= dp[y][j - 1] - pre[y] * (pre[N] - pre[i])
		dp[x][j - 1] - dp[y][j - 1] >= (pre[x] - pre[y]) * (pre[N] - pre[i])
		
		Y(x) = dp[x]
		X(x) = pre[x]
		Y(x) - (y) >= (X(x) - X(y)) * (pre[N] - pre[i])
		slope(i, q[r]) <= slope(q[r], q[r - 1]) pop
*/

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2392 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 2396 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 2396 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 4444 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 4444 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 2392 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 2396 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 2396 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 2396 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 4444 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 4444 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 2396 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 4444 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 2392 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 4440 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2392 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 2396 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 6 ms 20828 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 2396 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 6492 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 4444 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 12636 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 6488 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 4444 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 6492 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 2480 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 29 ms 80484 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 2392 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 6 ms 55644 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 8 ms 72284 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 9 ms 80416 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 18780 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 12636 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 22876 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2396 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 11 ms 80428 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 2396 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 12 ms 80728 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 11 ms 68188 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 80476 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 11 ms 80476 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 16916 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 5 ms 33116 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2652 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 1 ms 2652 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 29 ms 80788 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 2652 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 25 ms 50032 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 26 ms 56120 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 30 ms 60252 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 19 ms 49980 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 23 ms 56152 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 30 ms 72592 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 9 ms 7000 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 9 ms 7000 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 184 ms 83084 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 13 ms 7056 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 337 ms 82904 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 205 ms 60240 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 241 ms 64636 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 169 ms 52312 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 164 ms 60240 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 214 ms 75096 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845