Submission #541711

#	Time	Username	Problem	Language	Result	Execution time	Memory
541711		Aldas25	Split the sequence (APIO14_sequence)	C++14	100 / 100	1282 ms	96044 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

#define FAST_IO ios_base::sync_with_stdio(0); cin.tie(nullptr)
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define REP(n) FOR(O, 1, (n))
#define f first
#define s second
#define pb push_back
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pii;
typedef long double ld;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int MAXN = 100100;
const ll INF = 1e16;

/*struct line {
    ll k, b;
    int id;

    line (ll _k, ll _b, int _id) : k (_k), b (_b), id (_id) {}

    ll operator() (ll x) {
        return k * x + b;
    }
};*/

/*ld intersection (line p, line q) {
    ld dy = ((ld)(q.b - p.b));
    ld dx = ((ld)(p.k - q.k));
    return dy / dx;
}*/

ld intersection (pair<pair<ll, ll>, int> p, pair<pair<ll, ll>, int> q) {
    ld dy = ((ld)(q.f.s - p.f.s));
    ld dx = ((ld)(p.f.f - q.f.f));
    return dy / dx;
}

//ll dp[210][MAXN];
int pr[210][MAXN];
int n, k;
ll a[MAXN], pref[MAXN];
deque<pair<pair<ll, ll>, int>> dq[210];
//int lstId[210];

void ins (int g, int id, ll dp) {
    ll k = pref[id];
    ll b = dp - pref[id] * pref[id];
   // line newL (k, b, id);
    pair<pair<ll, ll>, int> newL = {{k, b}, id};

    while (dq[g].size() > 0 && dq[g][dq[g].size()-1].f.f == newL.f.f) {
        dq[g].pop_back();
    }

    while (dq[g].size() > 1 &&
           intersection(dq[g][dq[g].size()-2], newL) < intersection(dq[g][dq[g].size()-2], dq[g][dq[g].size()-1])) {
        dq[g].pop_back();
    }

    dq[g].push_back(newL);
}

pair<int, ll> getMaxId (int g, ll x) {
    while (dq[g].size() > 1 && x >= intersection(dq[g][0], dq[g][1])) {
        dq[g].pop_front();
    }

    return {dq[g][0].s, dq[g][0].f.f * x + dq[g][0].f.s};
}

int main()
{
    FAST_IO;

    cin >> n >> k;
    FOR(i, 1, n) cin >> a[i];
    FOR(i, 1, n) pref[i] = pref[i-1] + a[i];

    ins(0, 0, 0);

    FOR(i, 1, n) for (int g = k+1; g > 0; g--) {
        if (i < g) continue;

        ll x = pref[i];
        auto p = getMaxId(g-1, x);
        int j = p.f;
        ll dp = p.s;
        pr[g][i] = j;

        //lstDp = dp;

        if (i == n && g == k+1)
            cout << dp << "\n";

        //cout << " i = " << i << " g = " << g << " dp = " << dp << endl;

        ins(g, i, dp);
    }

    //cout << lstDp << "\n";
    int g = k+1, i = n;
    while (g > 0) {
        i = pr[g][i];
        g--;
        if (g > 0) cout << i << " ";
    }
    cout << "\n";

    return 0;
}

/*

7 3
4 1 3 4 0 2 3

*/

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