Submission #154923

#	Time	Username	Problem	Language	Result	Execution time	Memory
154923		srvlt	Split the sequence (APIO14_sequence)	C++14	100 / 100	1309 ms	84700 KiB

sequence

//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse2,avx")
#include <bits/stdc++.h>
#define ll long long
#define db long double
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define fi first
#define se second
#define mp make_pair
#define endl "\n"
using namespace std;

void dout() {
    cerr << endl;
}

template <typename Head, typename... Tail>
void dout(Head H, Tail... T) {
    cerr << H << ' ';
    dout(T...);
}

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef pair <ll, int> pii;
const int N = 1e5 + 3, K = 203;
const ll inf = 1e18;
int n, k, a[N], p[N], last[K][N];
ll dp[2][N];

struct line {
    int k = 0;
    ll b = 0;
    line(int k, ll b) {
        this -> k = k;
        this -> b = b;
    }
    ll val(int x) {
        return (ll)k * x + b;
    }
    db intrsc(const line & l) {
        return (db)(l.b - b) / (db)(k - l.k);
    }
    bool del(line & l1, line & l2) {
        if (k == l1.k) {
            return b >= l1.b;
        }
        return intrsc(l2) < l1.intrsc(l2);
    }
};

vector <line> h;
vector <int> ind, ans;
vector <ll> pnt;

void upd(int x, ll y, int pos) {
    line tmp = line(x, y);
    while (h.size() > 1 && tmp.del(h[h.size() - 1], h[h.size() - 2])) {
        h.ppb();
        pnt.ppb();
        ind.ppb();
    }
    if (h.size() > 0) {
        pnt.pb((int)(tmp.intrsc(h.back())));
    }
    h.pb(tmp);
    ind.pb(pos);
}

pii getmax(int x) {
    if (h.empty()) {
        return {0, 0};
    }
    int tmp = upper_bound(pnt.begin(), pnt.end(), x) - pnt.begin() - 1;
    return {h[tmp].val(x), ind[tmp]};
}

void getans(int x, int y) {
    if (!y) {
        return;
    }
    ans.pb(y);
    getans(x - 1, last[x][y]);
}

void solve(int tc) {
    cin >> n >> k;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        p[i] = p[i - 1] + a[i];
    }
    for (int i = 1; i <= k; i++) {
        h = {}, pnt = {-inf}, ind = {};
        for (int j = 1; j < i; j++) {
            dp[i & 1][j] = 0;
        }
        for (int j = 1; j < i; j++) {
            if (i > 1) {
                upd(p[j], dp[(i - 1) & 1][j], j);
            }
        }
        for (int j = i; j < n; j++) {
            int x = p[n] - p[j];
            pii z = getmax(-x);
            dp[i & 1][j] = (ll)p[j] * x + z.fi;
            last[i][j] = z.se;
            if (i > 1) {
                upd(p[j], dp[(i - 1) & 1][j], j);
            }
        }
    }
    int res = -1;
    for (int i = 1; i < n; i++) {
        if (res == -1 || dp[k & 1][res] < dp[k & 1][i]) {
            res = i;
        }
    }
    getans(k, res);
    cout << dp[k & 1][res] << endl;
    reverse(ans.begin(), ans.end());
    for (auto i : ans) {
        cout << i << " ";
    }
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);
    int tc = 1;
//    cin >> tc;
    for (int i = 0; i < tc; i++) {
        solve(i);
//        cleanup();
    }
}

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