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답안 #948849

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
948849 2024-03-18T15:30:16 Z happypotato 수열 (APIO14_sequence) C++17
71 / 100
 2000 ms 102300 KB 
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("Ofast")
#define int long long
#define ll long long

struct Line {
	mutable ll k, m, p;
	bool operator<(const Line& o) const { return k < o.k; }
	bool operator<(ll x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) return x->p = inf, 0;
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	void add(ll k, ll m) {
		auto z = insert({k, m, 0}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p)
			isect(x, erase(y));
	}
	ll query(ll x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};

/*
dp[x][k] = min(dp[p][k-1] + (ps[x] - ps[p])^2)
dp[x][k] = ps[x]^2 + min(-2(ps[x])(ps[p]) + (ps[p]^2 + dp[p][k-1]))
dp[x][k] = ps[x]^2 + max(2(ps[x])(ps[p]) - (ps[p]^2 + dp[p][k-1]))
*/
const int MAX = 2e18;
const int mxN = 1e5 + 1, mxK = 202;
int dp[mxK][mxN];
int a[mxN], ps[mxN];
LineContainer LC;
void solve() {
	int n, k;
	cin >> n >> k;
	ps[0] = 0;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		ps[i] = ps[i - 1] + a[i];
	}
	for (int i = 1; i <= n; i++) {
		dp[1][i] = ps[i] * ps[i];
	}
	for (int i = 2; i <= k + 1; i++) {
		LC.clear();
		LC.add(2LL * ps[i - 1], -(ps[i - 1] * ps[i - 1] + dp[i - 1][i - 1]));
		for (int p = i; p <= n; p++) {
			dp[i][p] = (ps[p] * ps[p]) - LC.query(ps[p]);
			LC.add(2LL * ps[p], -(ps[p] * ps[p] + dp[i - 1][p]));
		}
	}

	int ans = ((ps[n] * ps[n]) - dp[k + 1][n]) / 2;
	vector<int> res;
	int cnt = k + 1, prev = n;
	for (int i = n - 1; cnt > 1 && i >= 1; i--) {
		if (dp[cnt - 1][i] + (ps[prev] - ps[i]) * (ps[prev] - ps[i]) == dp[cnt][prev]) {
			res.push_back(i); cnt--; prev = i;
		}
	}
	sort(res.begin(), res.end());
	cout << ans << '\n';
	for (int x : res) cout << x << ' ';
	cout << '\n';
}
int32_t main() {
	ios::sync_with_stdio(0); cin.tie(0);
	solve();
}

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 6488 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 4440 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 4444 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 6492 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 10588 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 4444 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 4444 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 4444 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 6492 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 6492 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 6612 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 6492 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 6492 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 6492 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 6492 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 6492 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 6492 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 6492 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 6492 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 4 ms 41308 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 6624 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 10588 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 8540 KB contestant found the optimal answer: 933702 == 933702
7 Correct 3 ms 22876 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 12636 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 8540 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 14824 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 6492 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 6492 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 13 ms 101212 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 6492 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 12 ms 98908 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 11 ms 88924 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 12 ms 89180 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 5 ms 37364 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 24924 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 7 ms 47452 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 6492 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 6492 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 32 ms 99928 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 6492 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 33 ms 95636 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 30 ms 97368 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 33 ms 97728 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 31 ms 91688 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 11 ms 35164 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 17 ms 66140 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 7 ms 7004 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 8 ms 7004 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 408 ms 102300 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 8 ms 7260 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 213 ms 86284 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 228 ms 87896 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 267 ms 98128 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 220 ms 90452 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 245 ms 89960 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 302 ms 93380 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 71 ms 11548 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 69 ms 11784 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2065 ms 66544 KB Time limit exceeded
4 Halted 0 ms 0 KB -