oj.uz

Submission #701688

# Submission time Handle Problem Language Result Execution time Memory
701688 2023-02-22T01:05:31 Z badont Split the sequence (APIO14_sequence) C++17
100 / 100
 1267 ms 84832 KB 
#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

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
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 212 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 212 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 212 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 212 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 212 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 212 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 212 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 212 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 212 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 212 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 212 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 212 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 212 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 212 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 212 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 212 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 212 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 212 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 212 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 212 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 212 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 212 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 212 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 212 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 468 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 212 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 340 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 468 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 468 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 340 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 340 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 340 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 9 ms 1108 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 340 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 12 ms 1180 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 10 ms 980 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 11 ms 1108 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 8 ms 1108 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 468 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 692 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1132 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 1108 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 96 ms 8668 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 980 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 83 ms 5716 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 82 ms 6368 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 88 ms 6740 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 64 ms 5692 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 77 ms 6356 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 98 ms 7892 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 24 ms 7404 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 23 ms 7316 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 902 ms 84832 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 21 ms 7484 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1267 ms 84736 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 836 ms 60888 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 877 ms 65144 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 664 ms 54364 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 751 ms 60996 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 954 ms 76724 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845