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Submission #501270

# Submission time Handle Problem Language Result Execution time Memory
501270 2022-01-02T17:25:44 Z Ziel Split the sequence (APIO14_sequence) C++17
100 / 100
 942 ms 82812 KB 
/**
 * LES GREATEABLES BRO TEAM
**/

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
#define sz(x) (int)x.size()
const bool FLAG = false;
void setIO(const string &f = "");

const ll INF = 10000000000000;
const int N = 100012, K = 212;
int last[K][N];
#define int ll

ll a[N], pref[N], dp[3][N];

struct line {
	ll k, b, id;

	ll eval(ll x) {
		return x * k + b;
	}
};
double crossX(line a, line b) {
	double num = a.b - b.b;
	double den = b.k - a.k;
	if (den == 0) {
		return -INF;
	}
	return (double)(num / den);
}

inline void solve() {
    int n, k;
    cin >> n >> k;

	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		pref[i] = pref[i - 1] + a[i];
		dp[0][i] = dp[1][i] = -INF;
	}

	deque<line> dq;
	for (int i = 1; i < n; i++) {
		dp[1][i] = pref[i] * pref[n] - pref[i] * pref[i];
		last[1][i] = n + 1;
	}
	for (int j = 2; j <= k; j++) {
		dq.clear();
		for (int i = 1; i <= n; i++) {
			dp[j % 2][i] = -INF;
		}
		for (int i = n - 1; i >= 1; i--) {
			while (sz(dq) >= 2 && dq[sz(dq) - 2].eval(pref[i]) > dq[sz(dq) - 1].eval(pref[i]))
				dq.pop_back();

			if (sz(dq)) {
				dp[j % 2][i] = dq.back().eval(pref[i]) - pref[i] * pref[i];
				last[j][i] = dq.back().id;
			}
			if (dp[1 - (j % 2)][i] == -INF)
				continue;
			line cur = {pref[i], dp[1 - (j % 2)][i], i};
			while (sz(dq) >= 2 && crossX(cur, dq[0]) >= crossX(dq[0], dq[1]))
				dq.pop_front();
		   	dq.push_front(cur);
		}
	}

	ll ans = dp[k % 2][1], cur = 1;
	for (int i = 1; i < n; i++) {
		if (dp[k % 2][i] > ans)
			ans = dp[k % 2][i], cur = i;
	}
	cout << ans << '\n';
	for (int i = k; i >= 1; i--) {
		if (cur > n || cur < 1)
			break;
		cout << cur << ' ';
		cur = last[i][cur];
	}
}

signed main() {
    setIO();
    
    int tt = 1;
    if (FLAG) {
    	cin >> tt;
    }
    while (tt--) {
    	solve();
    }
    
    return 0;
}

void setIO(const string &f) {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    if (fopen((f + ".in").c_str(), "r")) {
        freopen((f + ".in").c_str(), "r", stdin);
        freopen((f + ".out").c_str(), "w", stdout);
    }
}

Compilation message

sequence.cpp: In function 'void setIO(const string&)':
sequence.cpp:106:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  106 |         freopen((f + ".in").c_str(), "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:107:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  107 |         freopen((f + ".out").c_str(), "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 332 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 332 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 332 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 332 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 332 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 332 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 332 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 332 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 332 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 332 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 332 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 332 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 332 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 332 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 332 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 332 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 332 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 460 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 332 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 332 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 332 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 460 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 332 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 332 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 332 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 332 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 1236 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 332 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 972 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 1100 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 1228 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 460 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 460 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 588 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 332 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 10 ms 2124 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 332 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 8 ms 2036 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 6 ms 1868 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 7 ms 2060 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 5 ms 2124 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 716 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 972 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 972 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 844 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 77 ms 9348 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 844 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 63 ms 5960 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 53 ms 6696 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 64 ms 7268 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 41 ms 6016 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 48 ms 6708 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 76 ms 8516 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 5704 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 14 ms 5552 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 609 ms 82596 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 15 ms 6272 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 942 ms 82812 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 526 ms 59288 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 643 ms 63568 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 420 ms 52492 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 546 ms 59608 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 634 ms 75192 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845