Submission #725140

#	Time	Username	Problem	Language	Result	Execution time	Memory
725140		colossal_pepe	Split the sequence (APIO14_sequence)	C++17	60 / 100	330 ms	131072 KiB

sequence

#include <iostream>
#include <tuple>
#include <vector>
#include <deque>
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 + 5];
deque<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, c, i] = l;
    return m * x + c;
}

bool lastIsBad(line lz, line ly, line lx) {
    auto [mz, cz, iz] = lz;
    auto [my, cy, iy] = ly;
    auto [mx, cx, ix] = lx;
    return (cy - cx) * (mx - mz) <= (cz - cx) * (mx - my); // ((cy - cx) / (mx - my)) <= ((cz - cx) / (mx - mz))
}

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 i = 1; i <= n; i++) {
        for (int s = k; s >= 1; s--) {
            dp[s][i] = {-1, -1};
            while (q[s - 1].size() > 1 and f(q[s - 1][0], ss(i + 1)) <= f(q[s - 1][1], ss(i + 1))) q[s - 1].pop_front();
            if (s == 1) dp[s][i].first = ps(i) * ss(i + 1);
            else if (not q[s - 1].empty()) {
                dp[s][i].first = ps(i) * ss(i + 1) + f(q[s - 1][0], ss(i + 1));
                dp[s][i].second = get<2>(q[s - 1][0]);
            }
            // cout << i << ' ' << s << ' ' << dp[s][i].first << ' ' << dp[s][i].second << endl;
            if (s != 1 and dp[s][i].first == -1) continue;
            line cur = make_tuple(-ps(i), dp[s][i].first, i);
            while (q[s].size() > 1 and lastIsBad(q[s][q[s].size() - 1], q[s][q[s].size() - 2], cur)) q[s].pop_back();
            q[s].push_back(cur);
        }
    }
    pair<ll, vector<int>> ans = retrieve();
    cout << ans.first << endl;
    for (int i : ans.second) {
        cout << i << ' ';
    }
    cout << endl;
    return 0;
}

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