Submission #231411

#	Time	Username	Problem	Language	Result	Execution time	Memory
231411		peijar	Split the sequence (APIO14_sequence)	C++17	60 / 100	2098 ms	46200 KiB

sequence

#include <bits/stdc++.h>
using namespace std;

#define SZ(v) ((int)(v).size())
using ll = long long;

const ll is_query = -(1LL<<62);
struct Line {
    ll m, b, id;
    mutable function<const Line*()> succ;
    bool operator<(const Line& rhs) const {
        if (rhs.b != is_query) return m < rhs.m;
        const Line* s = succ();
        if (!s) return 0;
        ll x = rhs.m;
        if (b - s-> b == (s-> m - m) * x)
        	return id  > rhs.id;
        return b - s->b < (s->m - m) * x;
    }
};
struct HullDynamic : public multiset<Line> { // will maintain upper hull for maximum
    bool bad(iterator y) {
        auto z = next(y);
        if (y == begin()) {
            if (z == end()) return 0;
            return y->m == z->m && y->b <= z->b;
        }
        auto x = prev(y);
        if (z == end()) return y->m == x->m && y->b <= x->b;
        return (x->b - y->b)*(z->m - y->m) >= (y->b - z->b)*(y->m - x->m);
    }
    void insert_line(ll m, ll b, int id) {
        auto y = insert({ m, b, id});
        y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
        if (bad(y)) { erase(y); return; }
        while (next(y) != end() && bad(next(y))) erase(next(y));
        while (y != begin() && bad(prev(y))) erase(prev(y));
    }
    pair<ll, ll>  eval(ll x) {
        auto l = *lower_bound((Line) { x, is_query });
        return make_pair(l.id, l.m * x + l.b);
    }
};

const int MAXN = 1e5+1;
const int MAXK = 201;

ll dp[MAXK][MAXN];

ll arr[MAXN];
ll transition[MAXK][MAXN];

int nb_elem;


int main(void)
{
	int nb_split;
	cin >> nb_elem >> nb_split;
	for (int i(0); i < nb_elem; ++i)
		cin >> arr[i];

	vector<ll> suffix_sum(nb_elem+1);
	suffix_sum[nb_elem] = 0;
	for (int i(nb_elem-1); i >= 0; --i)
		suffix_sum[i] = suffix_sum[i+1] + arr[i];
	for (int splits(1); splits <= nb_split; ++splits)
		dp[splits][nb_elem-1] = -2e18;

	for (int splits(1); splits <= nb_split; ++splits)
	{
		HullDynamic lichao;
		for (int id(nb_elem -1); id >= 0; --id)
		{
			lichao.insert_line(suffix_sum[id+1], dp[splits-1][id+1] - suffix_sum[id+1] * suffix_sum[id+1], id);
			auto [nxt, val] = lichao.eval(suffix_sum[id]);
			dp[splits][id] = val;
			transition[splits][id] = nxt;
		}
	}

	cout << dp[nb_split][0] << endl;

	int cur(0);
	for (int i(0); i < nb_split; ++i)
	{
		cur = transition[nb_split-i][cur] + 1;
		cout << cur << ' ';
	}
	cout << endl;

}

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