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답안 #206963

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
206963 2020-03-06T02:05:28 Z ttnhuy313 수열 (APIO14_sequence) C++14
100 / 100
 808 ms 82936 KB 
#include <bits/stdc++.h>
 
using namespace std;
typedef long long ll;
typedef pair <ll, ll> ii;
 
const ll N = 1e5 + 5, oo = 1e18, K = 200;
ll a[N], pref[N], n, dp[2][N];
int trace[N][K];
 
struct Line {
	ll a, b, id;
	Line() {}
	Line(ll _a, ll _b, ll _id) : a(_a), b(_b), id(_id) {}
	ll val(ll x) {
		return a * x + b;
	}
};
 
struct CHT {
	deque <Line> st;
	CHT() {st.clear();}
	bool bad(Line a, Line b, Line c) {
		return (1.0 * (c.b - a.b) / (a.a - c.a) < 1.0 * (c.b - b.b) / (b.a - c.a));
	}
	void addLine(Line d) {
		if (!st.empty() && d.a == st.back().a && d.b == st.back().b) return;
		while (st.size() >= 2 && bad(d, st.back(), st[st.size() - 2])) {
			// cerr << "delete Line y = " << st.back().a << "x + " << st.back().b << endl;
			st.pop_back();
		}
		// cerr << "addLine y = " << d.a << "x + " << d.b << endl;
		st.push_back(d);
	}
	ii query(ll x) {
		ll ans = -oo, id = -1;
		while (st.size() >= 2 && st[0].val(x) < st[1].val(x))
			st.pop_front();
		return {st[0].val(x), st[0].id};
	}
};
 
signed main() {
	ios_base::sync_with_stdio(0); cin.tie(0);
 
 	ll k;
	cin >> n >> k;
	for (ll i = 1; i <= n; ++i) {
		cin >> a[i];
	}
	for (ll i = 1; i <= n; ++i) {
		pref[i] = pref[i - 1] + a[i];
	}
	memset(dp, -1, sizeof dp);
	for (ll i = 1; i <= n; ++i) {
		dp[1][i] = pref[i] * (pref[n] - pref[i]);
	}
	ll res = -1, id = -1;
	for (ll t = 2; t <= k; ++t) {
		CHT Solver;
		ll ff = t & 1;
		for (ll i = 1; i <= n; ++i) {
			if (i >= t) {
				ii d = Solver.query(pref[i]);
				trace[i][t] = d.second;
				dp[ff][i] = d.first + pref[i] * (pref[n] - pref[i]);
			}
			if (t == k && res < dp[ff][i]) res = max(res, dp[ff][i]), id = i;
			// cerr << i << ' ' << t << ' '  << (~dp[ff][i]?dp[ff][i] - pref[i] * pref[n] : -1) << endl;
			if (~dp[ff ^ 1][i]) Solver.addLine({pref[i], dp[ff ^ 1][i] - pref[i] * pref[n], i});
		}
		memset(dp[ff ^ 1], -1, sizeof dp[ff ^ 1]);
	}
	if (k == 1) {
		ll t = -1, dd = 0;
		for (ll i = 1; i <= n; ++i) if (t < dp[1][i])
			t = dp[1][i], dd = i;
		cout << t << endl << dd << endl;
		return 0;
	}
	cout << res << endl;
	vector <ll> nn; nn.clear();
	for (ll i = k; i >= 1; --i) {
		nn.push_back(id);
		id = trace[id][i];
	}
	reverse(nn.begin(), nn.end());
	for (ll v : nn) cout << v << ' ';
 
	return 0;
}

Compilation message

sequence.cpp: In member function 'ii CHT::query(ll)':
sequence.cpp:36:6: warning: unused variable 'ans' [-Wunused-variable]
   ll ans = -oo, id = -1;
      ^~~
sequence.cpp:36:17: warning: unused variable 'id' [-Wunused-variable]
   ll ans = -oo, id = -1;
                 ^~

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 1912 KB contestant found the optimal answer: 108 == 108
2 Correct 5 ms 1912 KB contestant found the optimal answer: 999 == 999
3 Correct 5 ms 1912 KB contestant found the optimal answer: 0 == 0
4 Correct 5 ms 1912 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 6 ms 1912 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 5 ms 1912 KB contestant found the optimal answer: 1 == 1
7 Correct 5 ms 1912 KB contestant found the optimal answer: 1 == 1
8 Correct 5 ms 1912 KB contestant found the optimal answer: 1 == 1
9 Correct 6 ms 1912 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 6 ms 1912 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 6 ms 1912 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 6 ms 1912 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 6 ms 1912 KB contestant found the optimal answer: 140072 == 140072
14 Correct 6 ms 1912 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 6 ms 1912 KB contestant found the optimal answer: 805 == 805
16 Correct 6 ms 1912 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 6 ms 1912 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 5 ms 1912 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 5 ms 1912 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 7 ms 1912 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 5 ms 1912 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 6 ms 1912 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 6 ms 1912 KB contestant found the optimal answer: 933702 == 933702
7 Correct 6 ms 1912 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 6 ms 1912 KB contestant found the optimal answer: 687136 == 687136
9 Correct 6 ms 1912 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 6 ms 1912 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 2040 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 5 ms 2040 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 12 ms 2040 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 6 ms 2040 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 9 ms 2040 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 10 ms 2040 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 16 ms 2040 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 9 ms 2040 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 7 ms 2040 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 7 ms 2040 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 2680 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 6 ms 2680 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 17 ms 2680 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 6 ms 2812 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 17 ms 2680 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 15 ms 2680 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 20 ms 2680 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 16 ms 2680 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 8 ms 2808 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 11 ms 2680 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 10 ms 9976 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 10104 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 82 ms 9976 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 12 ms 9976 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 55 ms 10104 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 62 ms 9976 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 75 ms 9976 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 58 ms 9976 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 66 ms 10104 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 81 ms 9976 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 54 ms 82680 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 51 ms 82808 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 781 ms 82936 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 55 ms 82936 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 808 ms 82936 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 590 ms 82680 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 683 ms 82936 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 590 ms 82936 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 527 ms 82936 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 690 ms 82808 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845