Submission #564298

#	Time	Username	Problem	Language	Result	Execution time	Memory
564298		arayi	Split the sequence (APIO14_sequence)	C++17	71 / 100	148 ms	131072 KiB

sequence

// Arayi
#include <bits/stdc++.h>
#define fr first
#define sc second
#define MP make_pair
#define ad push_back
#define PB push_back
#define fastio                        \
    ios_base::sync_with_stdio(false); \
    cin.tie(0);                       \
    cout.tie(0);
#define lli long long int
#define y1 arayikhalatyan
#define j1 jigglypuff
#define ld long double
#define itn int
#define pir pair<int, int>
#define all(x) (x).begin(), (x).end()
#define str string
#define enl endl
#define en endl
#define cd complex<long double>
#define vcd vector<cd>
#define vii vector<int>
#define vlli vector<lli>
using namespace std;

lli gcd(lli a, lli b) { return (b == 0LL ? a : gcd(b, a % b)); }
ld dist(ld x, ld y1, ld x2, ld y2)
{
    return sqrt((x - x2) * (x - x2) + (y1 - y2) * (y1 - y2));
}
lli S(lli a)
{
    return (a * (a + 1LL)) / 2;
}
mt19937 rnd(363542);
char vow[] = {'a', 'e', 'i', 'o', 'u'};
int dx[] = {0, -1, 0, 1, -1, -1, 1, 1, 0};
int dy[] = {-1, 0, 1, 0, -1, 1, -1, 1, 0};
char dc[] = {'R', 'D', 'L', 'U'};

const int N = 3e5 + 20;
const lli mod = 1e9 + 7;
const ld pi = acos(-1);
const int T = 200;

lli bp(lli a, lli b = mod - 2LL)
{
    lli ret = 1;
    while (b)
    {
        if (b & 1)
            ret *= a, ret %= mod;
        a *= a;
        a %= mod;
        b >>= 1;
    }
    return ret;
}
ostream &operator<<(ostream &c, pir a)
{
    c << a.fr << " " << a.sc;
    return c;
}
template <class T>
void maxi(T &a, T b)
{
    a = max(a, b);
}
template <class T>
void mini(T &a, T b)
{
    a = min(a, b);
}

int n, k;
lli dp[N][220];
lli a[N], pr[N];
ld f(int i, int i1, int x)
{
    ld x1;
    ld a = pr[i1] - pr[i];
    if (a != 0)
        x1 = ((ld)(dp[i1][x] - dp[i][x])) / a;
    else if (dp[i1][x] >= dp[i][x])
        x1 = 1e10;
    else
        x1 = -1;
    return x1;
}
int main()
{
    fastio;
    cin >> n >> k;
    for (int i = 0; i < n; i++)
    {
        cin >> a[i];
        pr[i] = a[i];
        if (i)
            pr[i] += pr[i - 1];
    }
    for (int i = 0; i < n; i++)
        dp[i][1] = pr[i] * (pr[n - 1] - pr[i]); //, cout << dp[i][1] << " ";
    // cout << endl;
    int ii = 0;
    if (k == 1)
    {
        for (int i = 0; i < n; i++)
            if (dp[i][1] > dp[ii][1])
                ii = i;
        cout << dp[ii][1] << endl;
        cout << ii + 1 << endl;
        return 0;
    }
    for (int x = 2; x <= k; x++)
    {
        vector<pair<ld, int>> fp;
        fp.ad(MP(1e10, 0));
        for (int i = 1; i < n; i++)
        {
            while (f(fp.back().sc, i, x - 1) > fp.back().fr)
                fp.pop_back();
            fp.ad(MP(f(fp.back().sc, i, x - 1), i));
        }
        int i1 = 0;
        for (int i = 0; i < n - 1; i++)
        {
            dp[i][x] = pr[i] * (pr[n - 1] - pr[i]);
            ld x1 = pr[n - 1] - pr[i];
            while (i1 + 1 < (int)fp.size() && x1 <= fp[i1 + 1].fr)
                i1++;
            // cout << fp[i1].sc << "-";
            dp[i][x] += dp[fp[i1].sc][x - 1];
            dp[i][x] -= pr[fp[i1].sc] * x1;
            // cout << dp[i][x] << " ";
            if (x == k && dp[i][x] > dp[ii][x])
                ii = i;
        }
    }
    cout << dp[ii][k] << endl;
    vii fp;
    fp.ad(ii);
    for (int i = k - 1; i > 0; i--)
    {
        for (int j = ii - 1; j >= 0; j--)
        {
            if (dp[j][i] + (pr[n - 1] - pr[ii]) * (pr[ii] - pr[j]) == dp[ii][i + 1])
            {
                fp.ad(j);
                ii = j;
                break;
            }
        }
    }
    reverse(all(fp));
    for (auto p : fp)
        cout << p + 1 << " ";
    cout << endl;
    return 0;
}

/*
    __
  *(><)*
    \/ /
    ||/
  --||
    ||
    /\
   /  \
  /    \

*/

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