Submission #543586

#	Time	Username	Problem	Language	Result	Execution time	Memory
543586		Olympia	Split the sequence (APIO14_sequence)	C++17	0 / 100	17 ms	4956 KiB

sequence

#include <vector>
#include <algorithm>
#include <iostream>
#include <set>
#include <cmath>
#include <map>
#include <random>
#include <cassert>
#include <ctime>
#include <cstdlib>
#include <queue>
#include <limits.h>
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")

using namespace std;
long long dv(long long a, long long b) { return a / b /*- ((a^b)<0 && a%b)*/; }

struct Line {
    long long a, b; int id;
    Line(long long _a, long long _b, int _id) : a(_a), b(_b), id(_id) {}
    long long intersect(Line L) { return dv(L.b-b, a-L.a); }
    // double intersect(const Line& L) const { return (double)(L.b-b) / (a-L.a); }
    long long eval(long long x) { return a*x + b; }
};


struct CHT {
    deque<Line> cht;
    void add(Line L) {
        if(cht.size() && cht.front().a == L.a) {
            if(cht.front().b > L.b) return;
            cht.pop_front();
        }
        while(cht.size() >= 2 && L.intersect(cht[1]) < L.intersect(cht[0]))
            cht.pop_front();
        cht.push_front(L);
    }
    Line query(int64_t x) {
        /* Line ans(-1, -1, -1);
        for(Line l : cht)
            if(l.eval(x) > ans.eval(x)) ans = l;
        return ans; */
        while(cht.size() >= 2 && cht[ cht.size() - 2 ].eval(x) >= cht.back().eval(x))
            cht.pop_back();
        return cht.back();
    }
};
int main () {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int n, k;
    cin >> n >> k;
    int64_t arr[n]; int64_t pref[n + 1]; pref[0] = 0;
    for (int i = 0; i < n; i++) {
        cin >> arr[i];
        pref[i + 1] = pref[i] + arr[i];
    }
    vector<int64_t> dp_cur(n - 1), dp_prev(n - 1);
    int prev[n - 1][k + 1];
    for (int i = 0; i < n - 1; i++) {
        dp_prev[i] = (pref[i + 1]) * (pref[n] - pref[i + 1]);
        prev[i][1] = -1;
    }
    for (int j = 2; j <= k; j++) {
        CHT cht;
        dp_cur[0] = 0;
        for (int i = 1; i < n - 1; i++) {
            cht.add(Line(pref[i], dp_prev[i - 1], i));
            Line b = cht.query(pref[i + 1] - pref[n]);
            dp_cur[i] = max(b.eval(pref[i + 1] - pref[n]), 0ll) + pref[i + 1] * pref[n] - pref[i + 1] * pref[i + 1];
            prev[i][j] = b.id - 1;
        }
        dp_prev = dp_cur;
    }
    int64_t myMax = 0;
    for (int i = 0; i < n - 1; i++) {
        myMax = max(myMax, dp_prev[i]);
    }
    cout << myMax << '\n';
    for (int i = 0; i < n - 1; i++) {
        if (myMax == dp_prev[i]) {
            int mid = i;
            int cntr = 0;
            while (cntr != k) {
                cout << mid + 1 << ' ';
                mid = prev[mid][k - cntr];
                cntr++;
            }
            return 0;
        }
    }
}

Compilation message (stderr)

sequence.cpp:14: warning: ignoring '#pragma GCC optimization' [-Wunknown-pragmas]
   14 | #pragma GCC optimization ("O3")
      | 
sequence.cpp:15: warning: ignoring '#pragma GCC optimization' [-Wunknown-pragmas]
   15 | #pragma GCC optimization ("unroll-loops")
      |

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