Submission #1269450

#	Time	Username	Problem	Language	Result	Execution time	Memory
1269450		rayan_bd	Split the sequence (APIO14_sequence)	C++20	0 / 100	1 ms	324 KiB

sequence

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

const int INF_NEG = LLONG_MIN / 4;

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 long long INF = LLONG_MAX;
    // safe division using __int128 to avoid overflow
    long long div(long long a, long long b) {
        if (b == 0) return (a >= 0 ? LLONG_MAX : LLONG_MIN);
        __int128 A = a, B = b;
        __int128 q = A / B;
        if ((A ^ B) < 0 && (A % B)) q -= 1; // floor for negatives
        if (q > LLONG_MAX) return LLONG_MAX;
        if (q < LLONG_MIN) return LLONG_MIN;
        return (long long) q;
    }
    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 it = lower_bound(x);       // finds line with p >= x
        Line l = *it;
        return { l.k * x + l.m, l.idx };
    }
};

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

    int n, K;
    cin >> n >> K;
    vector<int> ar(n+1), pref(n+1,0);
    for (int i = 1; i <= n; ++i) {
        cin >> ar[i];
        pref[i] = pref[i-1] + ar[i];
    }

    auto qsum = [&](int l, int r)->long long{
        if (r < l) return 0;
        return pref[r] - pref[l-1];
    };

    // dp[j] = pair{value, chosen_j} for the previous layer (k-1)
    vector<pair<int,int>> dp(n+2, {INF_NEG, -1});
    // base layer (k = 0)
    for (int i = 1; i <= n+1; ++i) dp[i] = {0, -1};

    LineContainer cht;

    for (int k = 1; k <= K; ++k) {
        cht.clear();
        vector<pair<int,int>> ndp(n+2, {INF_NEG, -1}); // new layer (k)
        // iterate j from n down to 1
        for (int j = n; j >= 1; --j) {
            // slope = pref[j]
            long long slope = pref[j];
            // intercept uses dp[j+1] from previous layer
            long long intercept = dp[j+1].first - pref[j]*pref[j];
            cht.add((int)slope, (int)intercept, j);

            long long x = pref[n] + pref[j-1];
            auto pr = cht.query((int)x);
            long long val = -pref[j-1] * pref[n] + pr.first;
            ndp[j] = {(int)val, pr.second};
        }
        dp.swap(ndp); // dp now holds current layer k
    }

    cout << dp[1].first << "\n";

    // reconstruct splits from final dp (each dp[j].second is the chosen j)
    int i = 1, k = K;
    while (k > 0 && i <= n) {
        int j = dp[i].second;
        if (j <= 0) break;
        cout << j << " ";
        i = j + 1;
        --k;
    }
    cout << "\n";
    return 0;
}

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