Submission #701688

#	Time	Username	Problem	Language	Result	Execution time	Memory
701688		badont	Split the sequence (APIO14_sequence)	C++17	100 / 100	1267 ms	84832 KiB

sequence

#include<iostream>
#include<algorithm>
#include<vector>
#include<set>
#include<cassert>
#include<climits>
#include<deque>
using namespace std;



using ll = long long;
#define all(x) x.begin(),x.end()

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

    ll get(ll x) { return k * x + m; }
};

struct LineContainer : multiset<Line, less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) return x->p = inf, 0;
		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(ll k, ll 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<ll, int> query(ll x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return {l.k * x + l.m, l.idx};
	}
};

int better(const Line& a, const Line& b, const Line& c) {
  // (a1-a2) * x = b2-b1
  // x = (b2 - b1) / (a1 - a2)
  return (__int128)(a.m - b.m) * (a.k - c.k) >= (__int128)(a.m - c.m) * (a.k - b.k);
}

void solve() {
    ll n, k;
    cin >> n >> k;

    vector<ll> a(n);
    for (auto& u : a)
        cin >> u;

    const ll INF = 1e18;

    auto solve = [&](vector<ll> a) -> pair<ll, vector<ll>> {
        vector<ll> p = a;
        
        for (int i = 1; i < n; i++)
            p[i] += p[i - 1];

        auto prefix = [&p](ll g) -> ll {
            g--;
            return (g < 0 ? 0LL : p[g]);
        };

        vector parent(k + 1, vector<int>(n + 1, 0));
        vector<ll> dp(n + 1, -INF);
        dp[0] = 0;

        for (int i = 1; i <= k; i++) {
            vector<ll> ndp(n + 1, -INF);
            LineContainer lc;

            deque<Line> q;

            auto slope = [&](const Line& a, const Line& b) -> double {
                return (double)(a.m - b.m) / (a.k - b.k);
            };

            for (int j = i; j <= n; j++) {
                //cout << j - 1 << ' ' << dp[j - 1] << '\n';
                if (dp[j - 1] != -INF) {
                    //cout << "adding line at: " << i << ' ' << j - 1 << " " << prefix(j - 1) << ' ' << dp[j - 1] - prefix(j - 1) * prefix(n) << '\n';
                    //lc.add(prefix(j - 1), dp[j - 1] - prefix(j - 1) * prefix(n), j - 1);
                    Line here {prefix(j - 1), dp[j - 1] - prefix(j - 1) * prefix(n), 69, j - 1};
                    while(q.size() > 1 and better(here, q.back(), q[q.size() - 2]))
                        q.pop_back();
                    q.push_back(here);
                }
                assert(!q.empty());
                
                ll x = prefix(j);
                while (q.size() > 1 and q[0].get(x) <= q[1].get(x)) {
                    q.pop_front();
                }

                auto [slope, intercept, __, transition] = q.front();
                ll value = q.front().get(x);
                //auto [value, transition] = lc.query(prefix(j));
                //cout << j << ' ' << prefix(j) << " " << prefix(n) << '\n';
                ndp[j] = value + prefix(j) * prefix(n) - prefix(j) * prefix(j);
                //cout << i << ' ' << j << ' ' << ndp[j] << ' ' << transition << '\n';
                parent[i][j] = transition;
            }

            swap(ndp, dp);
            ndp.clear();
        }

        ll cur_idx = 0, max_dp = -INF;
        for (int i = 1; i <= n; i++) {
            if (dp[i] > max_dp) {
                max_dp = dp[i];
                cur_idx = i;
            }
        }

        vector<ll> ret_seq;
        for (int i = k; i > 0; i--) {
            assert(cur_idx > 0);
            //cout << cur_idx << '\n';
            ret_seq.emplace_back(cur_idx);
            cur_idx = parent[i][cur_idx];
        }

        reverse(all(ret_seq));
        return {max_dp, ret_seq};
    };

    auto [ans1, seq1] = solve(a);
    reverse(all(a));
    auto [ans2, seq2] = solve(a);
    if (ans2 > ans1) {
        ans1 = ans2;
        swap(seq1, seq2);
        for (auto& u : seq1) {
            u = n - u;
        }
    }

    cout << ans1 << '\n';
    for (auto u : seq1)
        cout << u << ' ';
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    solve();
    return 0;
}

Compilation message (stderr)

sequence.cpp: In lambda function:
sequence.cpp:86:18: warning: variable 'slope' set but not used [-Wunused-but-set-variable]
   86 |             auto slope = [&](const Line& a, const Line& b) -> double {
      |                  ^~~~~

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