Submission #1326676

#	Time	Username	Problem	Language	Result	Execution time	Memory
1326676		hoangtien69	Split the sequence (APIO14_sequence)	C++20	71 / 100	2099 ms	166300 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MAXN = 1e5 + 1;
const int INF = LLONG_MAX;

int n, k;
int a[MAXN];
int pre[MAXN], suf[MAXN];
int dp[201][MAXN];
vector<int> trace;

struct Line
{
    int a, b;
    mutable int p;
    bool operator<(const Line& o) const
    {
        if (o.a == LLONG_MAX && o.b == LLONG_MAX) return p < o.p;
        return a < o.a;
    }
};
struct LineContainer
{
    multiset<Line> s;

    int divi(int a, int b)
    {
        if (b == 0) return (a > 0 ? INF : -INF);
        int q = a / b;
        if ((a ^ b) < 0 && a % b) --q;
        return q;
    }

    bool isect(multiset<Line>::iterator x, multiset<Line>::iterator y)
    {
        if (y == s.end())
        {
            x->p = INF;
            return false;
        }
        if (x->a == y->a)
            x->p = (x->b > y->b) ? INF : -INF;
        else
            x->p = divi(y->b - x->b, x->a - y->a);
        return x->p >= y->p;
    }
    void add(int a_, int b_)
    {
        auto it = s.insert({a_, b_, 0});
        auto y = next(it);

        while (isect(it, y)) y = s.erase(y);
        if (it != s.begin())
        {
            auto x = it;
            --x;
            if (isect(x, it))
                isect(x, s.erase(it));
        }
        while (true)
        {
            auto y = it;
            if (y == s.begin()) break;
            --y;
            if (y->p < it->p) break;
            isect(y, s.erase(it));
            it = y;
        }
    }
    int query(int x)
    {
        Line q{LLONG_MAX, LLONG_MAX, x};
        auto it = s.lower_bound(q);
        if (it == s.end()) --it;
        return it->a * x + it->b;
    }

    bool empty()
    {
        return s.empty();
    }
};

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    cin >> n >> k;
    for (int i = 1; i <= n; ++i)
    {
         cin >> a[i];
    }

    for (int i = 1; i <= n; ++i)
    {
        pre[i] = pre[i - 1] + a[i];
    }

    for (int i = n; i >= 1; --i)
    {
        suf[i] = suf[i + 1] + a[i];
    }

    for (int t = 0; t <= k; ++t)
    {
        for (int i = 0; i <= n; ++i)
        {
            dp[t][i] = LLONG_MIN;
        }
    }
    for (int i = 1; i <= n-1; ++i)
    {
        dp[1][i] = pre[i] * suf[i + 1];
    }
    if (k == 1)
    {
        int ans = LLONG_MIN;
        int point = 0;
        for (int i = 1; i <= n-1; ++i)
        {
            if (ans < dp[1][i])
            {
                ans = dp[1][i];
                point = i;
            }
        }
        cout << ans << "\n";
        cout << point;
        return 0;
    }
    for (int t = 2; t <= k; ++t)
    {
        LineContainer cht;
        for (int i = t - 1; i <= n - 1; ++i)
        {
            if (dp[t-1][i] != LLONG_MIN)
            {
                cht.add(-pre[i], dp[t-1][i]);
            }
            int nxt = i + 1;
            if (nxt >= t && nxt <= n - 1 && !cht.empty())
            {
                int cur = cht.query(suf[nxt + 1]);
                if (cur != LLONG_MIN)
                {
                     dp[t][nxt] = cur + suf[nxt + 1] * pre[nxt];
                }
            }
        }
    }
    int ans = LLONG_MIN;
    int point = 0;
    for (int i = k; i <= n - 1; ++i)
    {
        if (ans < dp[k][i])
        {
            ans = dp[k][i];
            point = i;
        }
    }
    trace.push_back(point);
    for (int j = k - 1; j >= 1; j--)
    {
        for (int i = 1; i < point; i++)
        {
            if (dp[j + 1][point] == dp[j][i] + (pre[point] - pre[i]) * suf[point + 1])
            {
                point = i;
                trace.push_back(point);
                break;
            }
        }
    }
    reverse(trace.begin(), trace.end());
    cout << ans << "\n";
    for (auto v : trace)
    {
        cout << v << " ";
    }
}

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