Submission #655272

#TimeUsernameProblemLanguageResultExecution timeMemory
655272benjaminkleynSplit the sequence (APIO14_sequence)C++17
60 / 100
388 ms131072 KiB
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

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

struct LineContainer : multiset<Line, less<>> {
	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) {
		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, int idx) {
		auto z = insert({k, m, 0, idx}), 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));
	}
	pair<ll,int> query(ll x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return {l.k * x + l.m, l.idx};
	}
};

int N, K, a[100001];
ll pref[100001] = {0};
ll dp[100001][201];
int last_split[100001][201];

int main()
{
    cin >> N >> K;
    for (int i = 1; i <= N; i++)
    {
         cin >> a[i];
         pref[i] = pref[i-1] + a[i];
    }

    LineContainer cht;
    for (int k = 1; k <= K; k++)
    {
        cht.clear();
        for (int i = 1; i <= N; i++)
        {
            dp[i][k] = 0;
            cht.add(pref[i-1], dp[i-1][k-1] - pref[i-1] * pref[i-1], i-1);
            auto [val, idx] = cht.query(pref[i]);
            dp[i][k] = val;
            last_split[i][k] = idx;
        }
    }

    cout << dp[N][K] << '\n';

    int i = N;
    do
    {
        i = last_split[i][K--];
        cout << i << ' ';
    } while (last_split[i][K] > 0);
    cout << '\n';

    return 0;
}
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