Submission #537266

#	Time	Username	Problem	Language	Result	Execution time	Memory
537266		Sorting	Split the sequence (APIO14_sequence)	C++17	71 / 100	458 ms	131072 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
template<class T> void check_min(T &a, const T &b){ a = (a < b) ? a : b; }
template<class T> void check_max(T &a, const T &b){ a = (a > b) ? a : b; }
#define a__int128(x) (x).begin(), (x).end()

struct CHT{
    struct Line{
        __int128 first, second;
        int index;

        Line(__int128 first, __int128 second, int index): first(first), second(second), index(index){}
    };

    deque<Line> lines;

    __int128 floor_div3(__int128 a, __int128 b) {
        __int128 d = a / b;
        return d * b == a ? d : d - ((a < 0) ^ (b < 0));
    }

    __int128 ip(Line l1, Line l2){
        __int128 a = l1.second - l2.second;
        __int128 b = l2.first - l1.first;
        return floor_div3(a, b);
    }

    __int128 eval(Line l, __int128 x){
        return l.first * x + l.second;
    }

    void add(__int128 k, __int128 b, __int128 index){
        while(!lines.empty() && k == lines.back().first){
            if(lines.back().second <= b)
                lines.pop_back();
            else
                return;
        }

        while(lines.size() >= 2 && ip(lines[lines.size() - 2], lines.back()) > ip(lines.back(), Line(k, b, 0)))
            lines.pop_back();
        lines.push_back(Line(k, b, index));
    }

    pair<__int128, int> query(__int128 x){
        while(lines.size() >= 2 && eval(lines[0], x) <= eval(lines[1], x))
            lines.pop_front();
        return {eval(lines.front(), x), lines.front().index};
    }
};

const int N = 1e5 + 3;
const int K = 200 + 3;
const __int128 INF = 4e18;

__int128 p[N];
ll a[N], n, k;
__int128 dp[K][N];
int pr[K][N];

int main(){
    ios::sync_with_stdio(false);
    cin.tie(NULL);

    cin >> n >> k;
    ++k;

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

    for(int i = 1; i <= n; ++i)
        p[i] = p[i - 1] + a[i];

    for(int i = 1; i <= n; ++i)
        dp[0][i] = -INF;
    dp[0][n + 1] = 0;

    for(int j = 1; j <= k; ++j){
        CHT cht;
        for(int i = n; i >= 1; --i){
            cht.add(-p[i], -p[i] * p[i] + p[i] * p[n] + dp[j - 1][i + 1], i);

            auto q = cht.query(-p[i - 1]);
            dp[j][i] = q.first - p[i - 1] * p[n];
            pr[j][i] = q.second;
        }
        dp[j][n + 1] = -INF;
    }

    cout << (ll)dp[k][1] << "\n";
    int pos = 1;
    while(k > 1){
        int index = pr[k][pos];
        cout << index << " ";
        pos = index + 1;
        --k;
    }
    cout << "\n";
}
/* 
7 3
4 1 3 4 0 2 3
*/

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