Submission #562754

# Submission time Handle Problem Language Result Execution time Memory
562754 2022-05-15T07:52:16 Z Cyanmond Split the sequence (APIO14_sequence) C++17
100 / 100
842 ms 86460 KB
#include <bits/stdc++.h>

using namespace std;
using i64 = int64_t;

constexpr i64 inf = 1ll << 40;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REP3(i, l, r) for (int i = (l); i < (r); ++i)

template <typename T> bool chmax(T &a, const T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

class CHT {
    deque<pair<i64, i64>> deq;

    int pm(i64 v) { return v == 0 ? 0 : (v > 0 ? 1 : -1); }

    bool check(pair<i64, i64> a, pair<i64, i64> b, pair<i64, i64> c) {
        if (a.second == b.second or b.second == c.second)
            return pm(b.first - a.first) * pm(c.second - b.second) <=
                   pm(c.first - b.first) * pm(b.second - a.second);
        else
            return double(b.first - a.first) * pm(c.second - b.second) /
                       double(abs(b.second - a.second)) <=
                   double(c.first - b.first) * pm(b.second - a.second) /
                       double(abs(c.second - b.second));
    }

  public:
    void add(pair<i64, i64> line) {
        if (deq.empty()) {
            deq.push_back(line);
            return;
        }
        assert(line.first >= deq.back().first);
        if (deq.back().first == line.first) {
            if (deq.back().second > line.second)
                deq.pop_back();
            else
                return;
        }
        while (deq.size() >= 2 and check(deq[deq.size() - 2], deq.back(), line)) deq.pop_back();
        deq.push_back(line);
    }

    pair<i64, i64> query(i64 x) {
        while (deq.size() >= 2 and
               (deq[0].first * x + deq[0].second >= deq[1].first * x + deq[1].second))
            deq.pop_front();
        return {deq[0].first, deq[0].first * x + deq[0].second};
    }
};

int main() {
    int N, K;
    cin >> N >> K;
    ++K;
    vector<i64> A(N);
    for (auto &e : A) cin >> e;
    vector<i64> R(N + 1);
    REP(i, N) R[i + 1] = R[i] + A[i];
    auto calc_sum = [&R](int l, int r) { return R[r] - R[l]; };

    vector<i64> dp(N + 1, -inf);
    dp[0] = 0;
    vector<vector<int>> db(N + 1, vector<int>(K + 1));
    REP(k, K) {
        CHT cht;
        cht.add({calc_sum(0, k), -dp[k]});
        auto ndp = dp;
        REP3(i, k + 1, N + 1) {
            const auto [x, v] = cht.query(calc_sum(i, N));
            ndp[i] = -v + calc_sum(0, i) * calc_sum(i, N);
            db[i][k + 1] = x;
            if (i != N) cht.add({calc_sum(0, i), -dp[i]});
        }
        dp = move(ndp);
    }

    cout << dp[N] << endl;
    int now = N;
    vector<int> data;
    REP(i, K - 1) {
        int nxt = now;
        --nxt;
        while (calc_sum(0, nxt) != db[now][K - i]) --nxt;
        data.push_back(nxt);
        now = nxt;
    }
    reverse(data.begin(), data.end());
    REP(i, K - 1) cout << data[i] << (i == K - 1 ? '\n' : ' ');
}
# Verdict Execution time Memory Grader output
1 Correct 0 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 1 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 0 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 1 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 1 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 0 ms 212 KB contestant found the optimal answer: 999919994 == 999919994
# Verdict Execution time Memory Grader output
1 Correct 0 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 1 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 1 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 1 ms 212 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 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 340 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 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
# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 272 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 7 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 10 ms 1160 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 8 ms 1048 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 7 ms 1164 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 1108 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 468 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 596 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 4 ms 1236 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 4 ms 1236 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 60 ms 8912 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 5 ms 1148 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 45 ms 5800 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 64 ms 6484 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 69 ms 7024 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 43 ms 5844 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 48 ms 6552 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 57 ms 8020 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 41 ms 9532 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 35 ms 9652 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 767 ms 86460 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 46 ms 9660 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 842 ms 86364 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 617 ms 62780 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 604 ms 67760 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 480 ms 56624 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 547 ms 62872 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 709 ms 78588 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845