Submission #379590

#	Time	Username	Problem	Language	Result	Execution time	Memory
379590		Aryan_Raina	Split the sequence (APIO14_sequence)	C++14	0 / 100	676 ms	131076 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
 
#define int long long
#define ld long double
#define ar array

const int INF = LLONG_MAX;
const int MOD = 1e9+7;

const int MXN = 1e5+9, MXK = 205;
int dp[2][MXN], par[MXK][MXN]; 

struct CHT {
    struct Line {
        int m, c, index;
        Line(int _m, int _c, int _index) : m(_m), c(_c), index(_index) {}
        ld intersect(Line other) { return (ld) (c - other.c)/(other.m - m); }
        int at(int x) { return m*x + c; }
    };

    deque<Line> dq;

    void add(int m, int c, int index) {
        Line newLine(m, c, index);
        while (dq.size() >= 2 && dq[1].intersect(newLine) >= dq[1].intersect(dq[0])) {
            dq.pop_front();
        }
        dq.push_front(newLine);
    }

    ar<int,2> query(int x) {
        // {m*x + c, index}
        while (dq.size() >= 2 && end(dq)[-1].at(x) <= end(dq)[-2].at(x)) {
            dq.pop_back();
        }
        return {dq.back().at(x), dq.back().index};
    }
};

int32_t main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int n, k; cin>>n>>k;
    vector<int> v(n);
    for (int &i : v) cin>>i;
    vector<int> pf(n);
    partial_sum(v.begin(), v.end(), pf.begin());
    auto sum = [&](int l, int r) {
        return pf[r] - (l-1 >= 0 ? pf[l-1] : 0);
    };
    CHT cht;
    cht.add(0, 0, 0);
    for (int i = 1; i <= k; i++) {
        int I = i&1;
        for (int j = 1; j < n; j++) {
            // for (int a = 0; a < j; a++) {
            //     if (dp[I][j] < dp[I^1][a] + sum(a, j-1)*sum(j, n-1)) {
            //         dp[I][j] = dp[I^1][a] + sum(a, j-1)*sum(j, n-1);
            //         par[i][j] = a;
            //     }
            // }
            ar<int,2> qry = cht.query(sum(j, n-1));
            dp[I][j] = qry[0] + pf[j-1]*sum(j, n-1);
            par[i][j] = qry[1];
            cht.add(-pf[j-1], dp[I^1][j], j);
        }
    }
    int ans = -INF, x = -1;
    for (int j = 1; j < n; j++) {
        if (dp[k&1][j] > ans) {
            ans = dp[k&1][j]; x = j;
        }
    }
    cout<<ans<<"\n";
    vector<int> bruh;
    for (int i = k; i > 0; i--) {
        bruh.push_back(x);
        x = par[i][x];
    }
    for (int i = bruh.size()-1; i >= 0; --i) cout<<bruh[i]<<" ";
}   

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