Submission #501264

#	Time	Username	Problem	Language	Result	Execution time	Memory
501264		Ziel	Split the sequence (APIO14_sequence)	C++17	71 / 100	78 ms	131076 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 = "");

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

ll a[N], pref[N], dp[K][N], last[K][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);
}

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];
		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--) {
			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][i] = dq.back().eval(pref[i]) - pref[i] * pref[i];
				last[j][i] = dq.back().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:103:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  103 |         freopen((f + ".in").c_str(), "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:104:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  104 |         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: 21 / 21
• Subtask 6: 0 / 29