Submission #95533

#	Time	Username	Problem	Language	Result	Execution time	Memory
95533		fedoseevtimofey	Split the sequence (APIO14_sequence)	C++14	0 / 100	101 ms	17664 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;

struct line {
    ll k, b;
    line (ll k, ll b) : k(k), b(b) {}
};

ll f(const line &l, ll x) {
    return l.k * x + l.b;
}

ld inter(const line &a, const line &b) {
    return (ld)(a.b - b.b) / (b.k - a.k);
}

vector <line> s;
vector <int> idx;

void push(const line &l, int id) {
    while ((int)s.size() && s[(int)s.size() - 1].k == l.k && s[(int)s.size() - 1].b < l.b) {
        s.pop_back();
        idx.pop_back();
    }
    if (!s.empty() && s.back().k == l.k && s.back().b > l.b) return;
    while ((int)s.size() >= 2) {
        line a = s[(int)s.size() - 1];
        line b = s[(int)s.size() - 2];
        if (inter(l, a) < inter(l, b)) {
            s.pop_back();
            idx.pop_back();
        }
        else {
            break;
        }
    }
    s.push_back(l);
    idx.push_back(id);
}

pair <ll, int> get(ll x) {
    int l = -1, r = (int)s.size() - 1;
    while (r - l > 1) {
        int m = (l + r) >> 1;
        if (f(s[m], x) < f(s[m + 1], x)) {
            l = m;
        }
        else r = m;
    }
    return {f(s[r], x), idx[r]};
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0); cout.setf(ios::fixed); cout.precision(20);
    #ifdef LOCAL
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif
    int n, k;
    cin >> n >> k;
    vector <int> a(n);
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }
    vector <vector <ll>> dp(n + 1, vector <ll> (k + 1));
    vector <ll> pref(n + 1);
    for (int i = 0; i < n; ++i) {
        pref[i + 1] = pref[i] + a[i];
    }
    vector <vector <int>> who(n + 1, vector <int> (k + 1, -1));
    //(pref[i] - pref[t]) * (pref[n] - pref[i]) + dp[t][j]
    // pref[i] * (pref[n] - pref[i]) - pref[t] * pref[n] + pref[t] * pref[i] + dp[t][j]
    for (int j = 1; j <= k; ++j) {
        s.clear();
        for (int i = 1; i <= n; ++i) {
            push(line(pref[i - 1], -pref[i - 1] * pref[n] + dp[i - 1][j - 1]), i - 1);
            auto p = get(pref[i]);
            dp[i][j] = p.first + pref[i] * (pref[n] - pref[i]);
            who[i][j] = p.second;
        }
    }
    ll ans = -1;
    int id = -1;
    for (int i = 1; i <= n; ++i) {
        if (dp[i][k] > ans) {
            ans = dp[i][k];
            id = i;
        }
    }
    vector <int> where;
    for (int cr = k; cr >= 1; --cr) {
        where.push_back(id);
        id = who[id][cr];
    }
    reverse(where.begin(), where.end());
    cout << ans << '\n';
    for (auto x : where) {
        cout << x << ' ';
    }
}

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