Submission #724870

#	Time	Username	Problem	Language	Result	Execution time	Memory
724870		colossal_pepe	Split the sequence (APIO14_sequence)	C++17	0 / 100	19 ms	14008 KiB

sequence

#include <iostream>
#include <tuple>
#include <vector>
#include <queue>
using namespace std;

using ll = long long;
using line = tuple<ll, ll, int>;

const int N = 1e5;
const int K = 200;

int n, k;
ll a[N + 5], pfx_sum[N + 5];
pair<ll, int> dp[K + 5][N + 5];
line best[K + 1];
queue<line> q[K + 5];

ll ps(int i) {
    return pfx_sum[i];
}

ll ss(int i) {
    return pfx_sum[n] - pfx_sum[i - 1];
}

ll f(line l, ll x) {
    auto [m, b, i] = l;
    return m * x + b;
}

int id(line l) {
    return get<2>(l);
}

pair<ll, vector<int>> retrieve() {
    ll x = 0;
    vector<int> v = {-1};
    for (int i = 1; i <= n; i++) {
        if (dp[k][i].first > x) {
            x = dp[k][i].first;
            v.back() = i;
        }
    }
    for (int i = k; i >= 2; i--) {
        v.push_back(dp[i][v.back()].second);
    }
    return {x, v};
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin >> n >> k;
    a[0] = pfx_sum[0] = 0;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        pfx_sum[i] = a[i] + pfx_sum[i - 1];
    }
    for (int s = 1; s <= k; s++) {
        best[s] = make_tuple(0, -1, -1);
    }
    for (int i = 1; i <= n; i++) {
        for (int s = k; s >= 1; s--) {
            dp[s][i] = {-1, -1};
            while (not q[s - 1].empty() and f(q[s - 1].front(), ss(i + 1)) > f(best[s - 1], ss(i + 1))) {
                best[s - 1] = q[s - 1].front();
                q[s - 1].pop();
            }
            if (s == 1) {
                dp[s][i].first = ps(i) * ss(i + 1);
                dp[s][i].second = -1;
                q[s].push(make_tuple(-ps(i), dp[s][i].first, i));
            } else if (id(best[s - 1]) != -1) {
                dp[s][i].first = ps(i) * ss(i + 1) + f(best[s - 1], ss(i + 1));
                dp[s][i].second = id(best[s - 1]);
                q[s].push(make_tuple(-ps(i), dp[s][i].first, i));
            }
        }
    }
    pair<ll, vector<int>> ans = retrieve();
    cout << ans.first << '\n';
    for (int i : ans.second) {
        cout << i << ' ';
    }
    cout << '\n';
    return 0;
}

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