Submission #501243

#	Time	Username	Problem	Language	Result	Execution time	Memory
501243		Ziel	Split the sequence (APIO14_sequence)	C++17	50 / 100	2092 ms	32160 KiB

sequence

/**
 * 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 = "");

string to_string(const string s) {
	return '"' + s + '"';
}
string to_string(const char c) {
 	return char(39) + string(1, c) + char(39);
}
string to_string(const char* s) {
 	return to_string(string(s));
}
string to_string(bool f) {
	return (f ? "true" : "false");
}
template<class A, class B>
string to_string(const pair<A, B> x) {
	return "(" + to_string(x.first) + ", " + to_string(x.second) + ")";
}
template<class A, class B, class C>
string to_string(const tuple<A, B, C> x) {
	return "(" + to_string(get<0>(x)) + ", " + to_string(get<1>(x)) + ", " + to_string(get<2>(x)) + ")";
}
template<class A, class B, class C, class D>
string to_string(const tuple<A, B, C, D> x) {
	return "(" + to_string(get<0>(x)) + ", " + to_string(get<1>(x)) + ", " + to_string(get<2>(x)) + ", " + to_string(get<3>(x)) + ")";
}
template<class T>
string to_string(const T v) {
	string res = "{"; bool f = true;
	for (auto x: v)
		res += (f ? to_string(x) : ", " + to_string(x)), f = false;
	return res + "}";
}
void debug_args() { cerr << "]\n"; }
template<class H, class... T>
void debug_args(H x, T... y) {
	cerr << to_string(x);
	if (sizeof... (y))
	cerr << ", ";
	debug_args(y...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]: [", debug_args(__VA_ARGS__);
#else
#define debug(...) 47
#endif

const ll INF = 10000000000;
#define int ll

struct line {
	ll k, b, id;

	ll eval(ll x) {
		return x * k + b;
	}
};
string to_string(line x) {
	pair<ll, ll> _;
	_.first = x.k, _.second = x.b;
	return to_string(_);
}
long double crossX(line a, line b) {
	long double num = a.b - b.b;
	long double den = b.k - a.k;
	if (den == 0) {
		return -1000000000;
	}
	return (long double)(num / den);
}

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

	vector<int> a(n + 1);
	vector<ll> pref(n + 1);
	vector<vector<ll>> dp(k + 1, vector<ll>(n + 1));
	vector<vector<int>> last(k + 1, vector<int>(n + 1));

	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		pref[i] = pref[i - 1] + a[i];
		for (int j = 0; j <= k; j++)
			dp[j][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 = n - 1; i >= 1; i--) {
			int idx = -1, mx = -INF;
			for (int ii = 0; ii < sz(dq); ii++) {
				if (dq[ii].eval(pref[i]) - pref[i] * pref[i] > mx) {
					mx = dq[ii].eval(pref[i]) - pref[i] * pref[i];
					idx = ii;
				}
			}
			if (idx != -1) {
				dp[j][i] = dq[idx].eval(pref[i]) - pref[i] * pref[i];
				last[j][i] = dq[idx].id;
			}
			if (dp[j - 1][i] == -INF)
				continue;
			line cur = {pref[i], dp[j - 1][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][1], cur = 1;
	for (int i = 1; i < n; i++) {
		if (dp[k][i] > ans)
			ans = dp[k][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 (stderr)

sequence.cpp: In function 'void setIO(const string&)':
sequence.cpp:160:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  160 |         freopen((f + ".in").c_str(), "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:161:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  161 |         freopen((f + ".out").c_str(), "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29