Submission #676584

#	Time	Username	Problem	Language	Result	Execution time	Memory
676584		benjaminkleyn	Split the sequence (APIO14_sequence)	C++17	100 / 100	649 ms	82124 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;

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

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

#define m(j) (pref[j])
#define c(j) (dp[0][j]-pref[j]*pref[N])

inline ld isect(const int &a, const int &b)
{
    return (ld)(c(b) - c(a)) / (ld)(m(a) - m(b));
}

inline bool bad(const int &x, const int &y, const int &z)
{
    return isect(z, y) <= isect(z, x);
}

inline ll eval(const int &i, const ll &x)
{
    return m(i) * x + c(i);
}
 
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++)
        {
            while (fr < bk && bad(cht[bk-1], cht[bk], i-1))
                bk--;

            cht[++bk] = i-1;

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

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