Submission #580048

#	Time	Username	Problem	Language	Result	Execution time	Memory
580048		leeh18	Split the sequence (APIO14_sequence)	C++17	100 / 100	1070 ms	95708 KiB

sequence

// #pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define sz(x) (int)size(x)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rep(i, a, b) for(int i = a; i < (b); ++i)
typedef pair<int, int> pii;
typedef vector<int> vi;

// https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
template<class Fun>
class y_combinator_result {
    Fun fun_;
public:
    template<class T>
    explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}

    template<class ...Args>
    decltype(auto) operator()(Args &&...args) {
        return fun_(std::ref(*this), std::forward<Args>(args)...);
    }
};

template<class Fun>
decltype(auto) y_combinator(Fun &&fun) {
    return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun));
}

mt19937 rng((unsigned)chrono::steady_clock::now().time_since_epoch().count());

struct line_container {
    struct line {
        ll a, b, idx;
        line(ll a_, ll b_, int idx_) : a(a_), b(b_), idx(idx_) {}
        line() : a(0LL), b(0LL), idx(0) {}
        ll operator()(ll x) const {
            return a * x + b;
        }
    };
    ll floor_div(ll a, ll b) {
        return a / b - ((a ^ b) < 0 && a % b);
    }
    ll intersect(const line& l1, const line& l2) {
        return floor_div(l2.b - l1.b, l1.a - l2.a);
    }
    deque<line> dq;
    void add(ll a, ll b, int idx) {
        line cur(a, b, idx);
        if (!dq.empty() && dq.back().a == a) {
            if (dq.back().b > b) {
                return;
            } else {
                dq.pop_back();
            }
        }
        while (sz(dq) > 1 && intersect(cur, dq[sz(dq)-1]) <= intersect(dq[sz(dq)-1], dq[sz(dq)-2])) {
            dq.pop_back();
        }
        dq.push_back(cur);
    }
    pair<ll, int> query(ll x) {
        assert((!dq.empty()));
        while (sz(dq) > 1 && dq[0](x) < dq[1](x)) {
            dq.pop_front();
        }
        return {dq[0](x), dq[0].idx};
    }
};

void solve() {
    int n, k;
    cin >> n >> k;
    vector<ll> p(n+1);
    for (int i = 1; i <= n; i++) {
        cin >> p[i];
        p[i] += p[i-1];
    }
    vector<line_container> g(k);
    vector<vector<int>> parent(n+1, vector<int>(k+1));
    vector<ll> dp(k+1);
    for (int i = 1; i <= n; i++) {
        dp[0] = 0;
        for (int j = 1; j < i && j <= k; j++) {
            tie(dp[j], parent[i][j]) = g[j-1].query(p[i]);
        }
        for (int j = 0; j < i && j < k; j++) {
            g[j].add(p[i], -p[i]*p[i] + dp[j], i);
        }
    }
    cout << dp[k] << '\n';
    vector<int> result;
    int idx = n;
    for (int i = k; i >= 1; i--) {
        result.push_back(parent[idx][i]);
        idx = parent[idx][i];
    }
    for (int i = k-1; i >= 0; i--) {
        cout << result[i] << ' ';
    }
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit);
    int t = 1;
    while (t--) {
        solve();
    }
    return 0;
}

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