Submission #676587

#	Time	Username	Problem	Language	Result	Execution time	Memory
676587		benjaminkleyn	Split the sequence (APIO14_sequence)	C++17	100 / 100	551 ms	83756 KiB

sequence

#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx,avx2,fma")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;

struct Line
{
    ll m, c;
    int idx;
    Line() : m(0LL), c(0LL), idx(0) {}
    Line(ll _m, ll _c, int _idx) : m(_m), c(_c), idx(_idx) {}
    ll operator()(const ll &x) { return m * x + c; }
    friend ld isect(const Line &a, const Line &b)
    {
        return (ld)(b.c - a.c) / (ld)(a.m - b.m);
    }
};

int N, K, a[100001];
ll pref[100001] = {0};
ll dp[2][100001] = {0};
int last_split[202][100001];

Line cht[100001]; 
int fr = 0, bk = -1;

int main()
{
    cin.tie(0)->sync_with_stdio(0);

    cin >> N >> K;
    for (int i = 1; i <= N; i++)
    {
         cin >> a[i];
         pref[i] = pref[i-1] + a[i];
    }
 
    for (int i = 0; i <= N; i++)
        dp[0][i] = pref[i] * (pref[N] - pref[i]);

    for (int k = 2; k <= K + 1; k++)
    {
        fr = 0, bk = -1;
        for (int i = k; i <= N; i++)
        {
            Line newline(pref[i-1], dp[0][i-1] - pref[i-1] * pref[N], i-1);

            while (fr < bk && isect(cht[bk], newline) <= isect(cht[bk-1], newline))
                bk--;

            cht[++bk] = newline;

            while (fr < bk && cht[fr](pref[i]) <= cht[fr+1](pref[i]))
                fr++;

            dp[1][i] = cht[fr](pref[i]) + pref[i] * (pref[N] - pref[i]);
            last_split[k][i] = cht[fr].idx;
        }
        swap(dp[0], dp[1]);
    }

    cout << dp[0][N] << '\n';
    int i = N;
    do
    {
        i = last_split[K+1][i];
        cout << i << ' ';
    }
    while (--K);
    cout << '\n';
 
    return 0;
}

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