Submission #1269435

#	Time	Username	Problem	Language	Result	Execution time	Memory
1269435		rayan_bd	Split the sequence (APIO14_sequence)	C++20	71 / 100	255 ms	196608 KiB

sequence

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

struct Line {
    mutable int k, m, p, idx;
    bool operator<(const Line& o) const { return k < o.k; }
    bool operator<(int x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
    static const int inf = LLONG_MAX;
    int div(int a, int b) { return a / b - ((a ^ b) < 0 && a % b); }
    bool isect(iterator x, iterator y) {
        if (y == end()) { x->p = inf; return false; }
        if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
        else x->p = div(y->m - x->m, x->k - y->k);
        return x->p >= y->p;
    }
    void add(int k, int m, int idx) {
        auto z = insert({k, m, 0, idx}), y = z++, x = y;
        while (isect(y, z)) z = erase(z);
        if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
        while ((y = x) != begin() && (--x)->p >= y->p)
            isect(x, erase(y));
    }
    pair<int,int> query(int x) {
        assert(!empty());
        auto l = *lower_bound(x);
        return {l.k * x + l.m, l.idx};
    }
};

const long long NEG_INF = -4e18;

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(nullptr);

    int n, K;
    cin >> n >> K;
    vector<int> ar(n + 1), pref(n + 1);
    for(int i = 1; i <= n; ++i){
        cin >> ar[i];
        pref[i] = pref[i - 1] + ar[i];
    }

    vector<vector<int>> dp(n + 5, vector<int>(K + 5, NEG_INF));
    vector<vector<int>> choice(n + 5, vector<int>(K + 5, -1));

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

    for (int k = 1; k <= K; k++) {
        LineContainer cht;
        for (int j = n; j >= 1; j--) {
            int slope = pref[j];
            int intercept = dp[j+1][k-1] - pref[j] * pref[j];
            cht.add(slope, intercept, j);

            int x = pref[n] + pref[j-1];
            auto [val, idx] = cht.query(x);

            dp[j][k] = -pref[j-1] * pref[n] + val;
            choice[j][k] = idx;
        }
    }

    cout << dp[1][K] << "\n";

    vector<int> cuts;
    int i = 1, k = K;
    while (k > 0 && i <= n) {
        int j = choice[i][k];
        if (j == -1) break;
        cuts.push_back(j);
        i = j + 1;
        k--;
    }
    for (int x : cuts) cout << x << " ";
    cout << "\n";
}

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