Submission #697909

#	Time	Username	Problem	Language	Result	Execution time	Memory
697909		bebra	Split the sequence (APIO14_sequence)	C++17	78 / 100	1726 ms	87628 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
 
#define dbg(x) cerr << #x << ": " << x << endl;
 
 
struct Line {
    ll k;
    ll b;
 
    Line(ll _k = 0, ll _b = 0) : k(_k), b(_b) {}
 
    ll get(ll x) const {
        return k * x + b;
    }
 
    friend double intersect(const Line& lhs, const Line& rhs) {
        return (double)(lhs.b - rhs.b) / (rhs.k - lhs.k);
    }
};
 
struct CHT : vector<Line> {
    int n;
    vector<int> indices;
 
    CHT() {
        n = 0;
    }
 
    void add_line(ll k, ll b, int idx) {
        Line new_line(k, b);
 
        while (n > 0 && back().k == k) {
            if (back().b > new_line.b) {
                new_line.b = back().b;
                idx = indices.back();
            }
            --n;
            pop_back();
            indices.pop_back();
        }
 
        while (n >= 2 && intersect(at(n - 1), at(n - 2)) > intersect(at(n - 2), new_line)) {
            --n;
            pop_back();
            indices.pop_back();
        }
 
        ++n;
        push_back(new_line);
        indices.push_back(idx);
    }
 
    pair<ll, int> get_max(ll x) {
        int l = -1;
        int r = n - 1;
        while (l != r - 1) {
            int m = (l + r) / 2;
            if (intersect(at(m), at(m + 1)) < (double)x) {
                l = m;
            } else {
                r = m;
            }
        }
        return {at(r).get(x), indices[r]};
    }
};
 
 
 
const int MAX_N = 1e5 + 5;
const int MAX_K = 200 + 5;
int p[MAX_N][MAX_K];
ll a[MAX_N];
ll pref[MAX_N];
 
 
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
 
    int n, k;
    cin >> n >> k;
    ll total_sum = 0;
    for (int i = 1; i <= n; ++i) {
        cin >> a[i];
        pref[i] = pref[i - 1] + a[i];
        total_sum += a[i];
    }
 
    CHT lines;
    vector<ll> dp(n + 1);
    for (int j = 1; j <= k; ++j) {
        vector<ll> new_dp(n + 1);
        for (int i = 0; i <= n; ++i) {
            if (i > 0) {
                tie(new_dp[i], p[i][j]) = lines.get_max(pref[i]);
                new_dp[i] += pref[i] * (total_sum - pref[i]);
            }
            lines.add_line(pref[i], dp[i] - pref[i] * total_sum, i);
        }
        CHT new_lines;
        swap(lines, new_lines);
        swap(dp, new_dp);
    }
 
    ll ans = 0;
    int opt = -1;
    for (int i = 1; i <= n; ++i) {
        if (dp[i] >= ans) {
            ans = dp[i];
            opt = i;
        }
    }
    vector<int> splits;
    int curr_i = opt;
    int curr_k = k;
    while (curr_k > 0) {
        splits.push_back(curr_i);
        curr_i = p[curr_i][curr_k];
        --curr_k;
    }
    reverse(splits.begin(), splits.end());
    cout << ans << '\n';
    for (auto x : splits) {
        cout << x << ' ';
    }
    cout << '\n';
    
    return 0;
}
 
/*
7 3
4 1 3 4 0 2 3
*/

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