Submission #541690

#	Time	Username	Problem	Language	Result	Execution time	Memory
541690		Aldas25	Split the sequence (APIO14_sequence)	C++14	49 / 100	1640 ms	131072 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;
}

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

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

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

int getMaxId (int g, ll x) {
    int sz = dq[g].size();

    if (sz == 1) return dq[g][0].id;

    if (x >= intersection(dq[g][sz-2], dq[g][sz-1]))
        return dq[g][sz-1].id;

    int le = 0, ri = sz-2;
    while (le < ri) {
        int m = (le+ri)/2;
        ld inter = intersection(dq[g][m], dq[g][m+1]);
        if (x > inter) le = m+1;
        else ri = m;
    }

    return dq[g][le].id;
}

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];

    dp[0][0] = 0;
    //FOR(i, 1, n) dp[0][i] = -INF;
    ins(0, 0);

    FOR(g, 1, k+1) FOR(i, g, n) {
        dp[g][i] = -INF;
        //if (i < g) continue;
       /* FOR(j, g-1, i-1) {
            ll k = pref[j];
            ll b = dp[g-1][j] - pref[j] * pref[j];
            ll x = pref[i];
            ll cr = k*x + b;
            if (cr > dp[g][i]) {
                dp[g][i] = k * x + b;
                pr[g][i] = j;
            }
        } */

        ll x = pref[i];
        int j = getMaxId(g-1, x);
        ll k = pref[j];
        ll b = dp[g-1][j] - pref[j] * pref[j];
        pr[g][i] = j;
        dp[g][i] = k * x + b;

        ins(g, i);
    }

    cout << dp[k+1][n] << "\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: 0 / 11
• Subtask 2: 11 / 11
• Subtask 3: 0 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29