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Submission #554109

# Submission time Handle Problem Language Result Execution time Memory
554109 2022-04-27T16:40:56 Z tutis Split the sequence (APIO14_sequence) C++17
100 / 100
 755 ms 84748 KB 
/*input
7 3
4 1 3 4 0 2 3
*/
#pragma GCC optimize ("O3")
#pragma GCC target ("avx2")
#include <bits/stdc++.h>
using namespace std;
//using ull = __ull128_t;
using ull = unsigned long long;
using ll = long long;
using ld = long double;
ll mod = 1e9 + 7;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll power(ll a, ll b)
{
	if (abs(a) >= mod)
		a %= mod;
	if (abs(b) >= mod - 1)
		b %= (mod - 1);
	if (a < 0)
		a += mod;
	if (b < 0)
		b += mod - 1;
	ll r = 1;
	if (b % 2 == 1)
		r = a;
	b /= 2;
	while (b)
	{
		a = (a * a) % mod;
		if (b % 2 == 1)
			r = (r * a) % mod;
		b /= 2;
	}
	return r;
}
vector<pair<ll, ll>>V;
vector<int>Vi;
int itv = 0;
void reset()
{
	V.clear();
	Vi.clear();
	itv = 0;
}
ld C(pair<ll, ll>a, pair<ll, ll>b)
{
	ld k = a.first - b.first;
	ld c = a.second - b.second;
	//kx+c=0;
	return -c / k;
}
void add(ll c, ll k, int i)
{
	if (V.size() > 0 && V.back().first == k && V.back().second >= c)
		return;
	if (V.size() > 0 && V.back().first == k)
	{
		V.back().second = c;
		Vi.back() = i;
	}
	else {
		V.push_back({k, c});
		Vi.push_back(i);
	}
	while (V.size() >= 3)
	{
		pair<ll, ll>a = V[V.size() - 3];
		pair<ll, ll>b = V[V.size() - 2];
		pair<ll, ll>c = V[V.size() - 1];
		if (C(a, b) > C(b, c) + 1e-9)
		{
			V.erase(V.begin() + (V.size() - 2));
			Vi.erase(Vi.begin() + (Vi.size() - 2));
		}
		else
			break;
	}
}
pair<ll, int> get(ll x)
{
	itv = min(itv, (int)V.size() - 1);
	ll v = V[itv].first * x + V[itv].second;
	while (itv + 1 < (int)V.size())
	{
		ll v1 = V[itv + 1].first * x + V[itv + 1].second;
		if (v1 >= v)
		{
			v = v1;
			itv++;
		}
		else
			break;
	}
	while (itv > 0)
	{
		ll v1 = V[itv - 1].first * x + V[itv - 1].second;
		if (v1 >= v)
		{
			v = v1;
			itv--;
		}
		else
			break;
	}
	return {v, Vi[itv]};
}
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0), cout.tie(0);
	int n, K;
	cin >> n >> K;
	K++;
	ll a[n + 1];
	a[0] = 0;
	for (int i = 1; i <= n; i++)
	{
		cin >> a[i];
		a[i] += a[i - 1];
	}
	ll dp[n + 1][2];
	int dp1[n + 1][K + 1];
	for (int r = 1; r <= n; r++)
		dp[r][1] = 0;
	for (int k = 2; k <= K; k++)
	{
		int k1 = (k - 1) % 2;
		int k2 = k % 2;
		reset();
		for (int r = k; r <= n; r++)
		{
			add(dp[r - 1][k1] - a[r - 1] * a[r - 1], a[r - 1], r - 1);
			//for (int r1 = k - 1; r1 <= r - 1; r1++)
			{
				//ll gal = dp1[r1][k - 1].first - a[r1] * a[r1] + a[r] * a[r1];
				pair<ll, int>v = get(a[r]);
				dp[r][k2] = v.first;
				dp1[r][k] = v.second;
			}
		}
	}
	int k = K;
	cout << dp[n][k % 2] << "\n";
	vector<int>ans;
	while (k > 1)
	{
		n = dp1[n][k];
		ans.push_back(n);
		k--;
		assert(n >= 1 && k <= n);
	}
	sort(ans.begin(), ans.end());
	for (ll n : ans)
		cout << n << " ";
	cout << "\n";
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 212 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 212 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 212 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 212 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 212 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 212 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 212 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 212 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 212 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 212 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 212 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 212 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 212 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 212 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 212 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 212 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 212 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 212 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 212 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 212 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 212 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 212 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 212 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 212 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 212 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 468 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 212 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 340 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 468 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 468 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 340 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 0 ms 340 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 340 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 1108 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 340 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 7 ms 1160 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 7 ms 1040 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 7 ms 1168 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 5 ms 1108 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 540 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 596 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 980 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 980 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 58 ms 8804 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 1108 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 44 ms 5560 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 46 ms 6356 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 56 ms 6868 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 35 ms 5756 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 39 ms 6484 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 53 ms 8020 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 7180 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 19 ms 7128 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 679 ms 84748 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 17 ms 7688 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 755 ms 84452 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 535 ms 60928 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 575 ms 65156 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 436 ms 54044 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 480 ms 61124 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 602 ms 76780 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845