Submission #213295

#	Time	Username	Problem	Language	Result	Execution time	Memory
213295		someone_aa	Split the sequence (APIO14_sequence)	C++17	71 / 100	2102 ms	43512 KiB

sequence

#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define mp make_pair
#define ld long double
#define pll pair<ll,ll>
using namespace std;
const ld inf = 1e18;
const ll infll = 1e18;
const int maxn = 100100;
ll arr[maxn], pref[maxn];
ll dp[210][maxn], n, k;
ll parent[210][maxn];

const ll is_query = -(1LL<<62);
struct Line {
    ll m, b, ind;
    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;
        return b - s->b < (s->m - m) * x;
    }
};
struct HullDynamic : public multiset<Line> { 
    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 1.0 * (x->b - y->b)*(z->m - y->m) >= 1.0 * (y->b - z->b)*(y->m - x->m);
    }
    void insert_line(ll m, ll b, ll ind) {
        auto y = insert({ m, b, ind});
        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));
    }
    pll eval(ll x) {
        auto l = *lower_bound((Line) { x, is_query });
        return mp(l.m * x + l.b, l.ind);
    }
};

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);

	cin>>n>>k;
	for(int i=1;i<=n;i++) {
		cin>>arr[i];
		pref[i] = pref[i-1] + arr[i];
	}

	for(int d=1;d<=k;d++) {
		if(d == 1) {
			for(int i=1;i<n;i++) {
				dp[d][i] = pref[i] * (pref[n] - pref[i]);
			}
			continue;
		}

		HullDynamic ds;
		for(int i=d;i<n;i++) {
			// add info for state(d-1, i-1)
			ds.insert_line(pref[i-1], dp[d-1][i-1] - pref[i-1]*pref[n], i-1);
			pll curr = ds.eval(pref[i]);
			dp[d][i] = curr.first + pref[i]*pref[n] - pref[i] * pref[i]; 
			parent[d][i] = curr.second;
		}
	}

	ll result = -inf;
	ll resultind = -1;
	for(int i=k;i<n;i++) {
		if(dp[k][i] > result) {
			result = dp[k][i];
			resultind = i;
		}
	}
	cout<<result<<"\n";
	vector<int>v;
	for(int i=k;i>=1;i--) {
		v.pb(resultind);
		resultind = parent[i][resultind];
	}
	reverse(v.begin(), v.end());
	for(int i:v) {
		cout<<i<<" ";
	} cout<<"\n";
}

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