Submission #1055216

#	Time	Username	Problem	Language	Result	Execution time	Memory
1055216		underwaterkillerwhale	Split the sequence (APIO14_sequence)	C++17	100 / 100	1561 ms	88652 KiB

sequence

#include <bits/stdc++.h>
#define ll long long
#define rep(i,m,n) for(int i=(m); i<=(n); i++)
#define reb(i,m,n) for(int i=(m); i>=(n); i--)
#define pii pair<int,int>
#define pll pair<ll,ll>
#define MP make_pair
#define fs first
#define se second
#define bit(msk, i) ((msk >> i) & 1)
#define iter(id, v) for(auto id : v)
#define pb push_back
#define SZ(v) (int)v.size()
#define ALL(v) v.begin(),v.end()

using namespace std;

mt19937_64 rd(chrono :: steady_clock :: now ().time_since_epoch().count());
ll Rand (ll l, ll r) { return uniform_int_distribution<ll> (l, r) (rd); }

const int N = 1e5 + 7;
const int Mod = 1e9 + 7;
const ll INF = 1e18;
const ll BASE = 137;
const int szBL = 320;

int n, K;
ll a[N];
ll dp[N][2];
int trace[202][N];
ll pre[N];

struct LINE {
    ll a, b, id ;

    LINE (ll a, ll b, ll id ) : a(a), b(b), id(id) {}

    ll operator() (const ll &x) {
        return a * x + b;
    }
};

struct convex_hull_trick {
    vector<LINE> op;
    void init () {
        vector<LINE> ().swap(op);
    }
    bool bad (LINE ln1, LINE ln2, LINE ln3) {
        __int128 hi = 1;
        return hi * (ln3.b - ln1.b) * (ln1.a - ln2.a) <= hi * (ln2.b - ln1.b) * (ln1.a - ln3.a);
    }

    void add (LINE ln) {
        while (SZ(op) >= 2 && bad(op[SZ(op) - 2], op[SZ(op) - 1], ln)) {
            op.pop_back();
        }
        op.push_back(ln);
    }

    pll get (ll x) {
        if (op.empty()) return MP(INF, 0);
        ll lf = 0, rt = SZ(op) - 1;
        while (lf < rt) {
            ll mid = (lf + rt) >> 1;
            if (op[mid](x) <= op[mid + 1](x)) rt = mid;
            else lf = mid + 1;
        }
        return MP(op[lf](x), op[lf].id);

    }
}cht;


void solution () {

    cin >> n >> K;
    rep (i, 1, n) cin >> a[i];
    rep (i, 1, n) pre[i] = pre[i - 1] + a[i];
    rep (i, 1, n) dp[i][1] = 0;
    rep (k, 2, K) {
        cht.init();
        rep (i, 1, n) {
            pll cur = cht.get(pre[i]);
            dp[i][k & 1] = -cur.fs;
            trace[k][i] = cur.se;
//            cout << i <<" "<<k<<" "<<cur.fs<<" "<<cur.se <<"\n";
//            if (dp[i][k & 1] != INF)
            cht.add(LINE(-pre[i], -(dp[i][k & 1 ^ 1] - pre[i] * pre[i]), i));
        }
    }
    ll res = -1;
    int opt = 0;
    rep (i, 1, n) {
        if (res < dp[i][K & 1] + (pre[n] - pre[i]) * pre[i]) {
            res = dp[i][K & 1] + (pre[n] - pre[i]) * pre[i];
            opt = i;
        }
    }
    vector<int> Ans;
    reb (k, K, 1) {
        Ans.push_back(opt);
        opt = trace[k][opt];
    }
    cout << res <<"\n";
    iter (&id, Ans) cout << id<<" ";
}

#define file(name) freopen(name".inp","r",stdin); \
freopen(name".out","w",stdout);
int main () {
//    file("TREEV");
    ios_base :: sync_with_stdio(false); cin.tie(0); cout.tie(0);
    int num_Test = 1;
//    cin >> num_Test;
    while (num_Test--)
        solution();
}
/*
no bug challenge +2
2 + 8 * 2 - 9
7 3
4 1 3 4 0 2 3

*/

Compilation message (stderr)

sequence.cpp: In function 'void solution()':
sequence.cpp:88:45: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
   88 |             cht.add(LINE(-pre[i], -(dp[i][k & 1 ^ 1] - pre[i] * pre[i]), i));
      |                                           ~~^~~

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