Submission #958761

#	Time	Username	Problem	Language	Result	Execution time	Memory
958761		IWKR	Split the sequence (APIO14_sequence)	C++17	60 / 100	299 ms	131072 KiB

sequence

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

#define int long long

int dp[201][100001];
int pre[100001];
int ind[201][100001];

struct cht {
    vector<pair<int, pair<int, int>>> v;
    int cur = 0;
    long double is(int a, int b, int c, int d) {
        return (long double)(d - b) / (a - c);
    }
    void add(int m, int c, int num) {
        if (v.size() && v.back().first == m && v.back().second.first > c) return;
        while (v.size() - cur > 1) {
            int s = v.size();
            if ((v[s - 1].first == m && c > v[s - 1].second.first) || (is(v[s - 1].first, v[s - 1].second.first, m, c) <= is(v[s - 2].first, v[s - 2].second.first, m, c))) v.pop_back();
            else break;
        }
        v.push_back({m, {c, num}});
    }
    pair<int, int> query(int x) {
        while (v.size() - cur > 1) {
            if (v[cur].first * x + v[cur].second.first < v[cur + 1].first * x + v[cur + 1].second.first) cur++;
            else break;
        }
        return {v[cur].first * x + v[cur].second.first, v[cur].second.second};
    }
};

int32_t main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	int n, k;
	cin >> n >> k;
	for (int i = 1; i <= n; i++) {
		int a; cin >> a;
		pre[i] = pre[i - 1] + a;
	}
	for (int i = 1; i <= k; i++) {
		cht hull;
		for (int j = i; j < n; j++) {
			if (i == 1) {
				dp[i][j] = pre[j] * (pre[n] - pre[j]);
				ind[i][j] = j;
				continue;
			}
			hull.add(pre[j - 1], dp[i - 1][j - 1], j - 1);
			pair<int, int> c = hull.query(pre[j] - pre[n]);
			dp[i][j] = c.first + pre[j] * pre[n] - pre[j] * pre[j];
			ind[i][j] = c.second;
		}
	}
	pair<int, int> ans = {INT_MIN, INT_MIN};
	for (int i = k; i <= n; i++) {
		ans = max(ans, {dp[k][i], i});
	}
	cout << ans.first << '\n';
	vector<int> v;
	int cur = ans.second;
	v.push_back(cur);
	for (int i = k; i >= 2; i--) {
		cur = ind[i][cur];
		v.push_back(cur);
	}
	for (int i = k - 1; i >= 0; i--) {
		cout << v[i] << " ";
	}
}

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