Submission #655288

#	Time	Username	Problem	Language	Result	Execution time	Memory
655288		benjaminkleyn	Split the sequence (APIO14_sequence)	C++17	0 / 100	2084 ms	10848 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
 
struct Line {
    mutable ll k, m, p, idx;
    bool operator<(const Line& o) const { return k < o.k; }
    bool operator<(ll x) const { return p < x; }
};
 
struct LineContainer : multiset<Line, less<>> {
    static const ll inf = LLONG_MAX;
    ll div(ll a, ll b) {
        return a / b - ((a ^ b) < 0 && a % b); }
    bool isect(iterator x, iterator y) {
        if (y == end()) return x->p = inf, 0;
        if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
        else x->p = div(y->m - x->m, x->k - y->k);
        return x->p >= y->p;
    }
    void add(ll k, ll m, int idx) {
        auto z = insert({k, m, 0, idx}), y = z++, x = y;
        while (isect(y, z)) z = erase(z);
        if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
        while ((y = x) != begin() && (--x)->p >= y->p)
            isect(x, erase(y));
    }
    pair<ll,int> query(ll x) {
        assert(!empty());
        auto l = *lower_bound(x);
        return {l.k * x + l.m, l.idx};
    }
};
 
int N, K, a[100001];
ll pref[100001] = {0};
ll dp[100001] = {0};
int last_split[100001];
int cnt[100001];
 
LineContainer cht;
int calc(ll cost)
{
    cht.clear();
    cnt[0] = 0;
    for (int i = 1; i <= N; i++)
    {
        dp[i] = 0;
        cht.add(pref[i-1], dp[i-1] - pref[i-1] * pref[i-1], i-1);
        auto [val, idx] = cht.query(pref[i]);
        dp[i] = val - cost;
        last_split[i] = idx;
        cnt[i] = cnt[idx] + 1;
    }
    return cnt[N];
}
 
int main()
{
    cin >> N >> K;
    for (int i = 1; i <= N; i++)
    {
         cin >> a[i];
         pref[i] = pref[i-1] + a[i];
    }
 
    ll lo = -1e12, hi = 1e12;
    while (lo < hi)
    {
        ll mid = (lo + hi) / 2;
 
        if (calc(mid) > K + 1)
            lo = mid + 1;
        else
            hi = mid;
    }
 
    calc(lo);
    cout << dp[N] + lo * cnt[N] << '\n';
 
    int i = N;
    do
    {
        i = last_split[i];
        cout << i << ' ';
    } while (--K);
    cout << '\n';
 
    return 0;
}

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