Submission #973396

# Submission time Handle Problem Language Result Execution time Memory
973396 2024-05-01T22:15:42 Z avighna Split the sequence (APIO14_sequence) C++17
71 / 100
444 ms 131072 KB
#include <bits/stdc++.h>

typedef long long ll;

template <typename T> class Vector : public std::vector<T> {
public:
    using std::vector<T>::vector;
    std::vector<ll> psum;

    void calculate_prefix_sum() {
        psum.resize(this->size());
        std::partial_sum(this->begin(), this->end(), psum.begin());
    }

    T sum(ll a, ll b) {
        if (a > b) {
            return 0;
        }
        T ans = psum[b];
        if (a - 1 >= 0) {
            ans -= psum[a - 1];
        }
        return ans;
    }
};

const ll N = 1e5 + 1, K = 201;
const ll inf = 1e15;

ll dp[K][N];

struct Line {
    int m;
    ll b;

    ll eval(ll x) {
        return m * x + b;
    }
};

class CHT {
private:
    bool parallel(const Line &a, const Line &b) {
        return a.m == b.m;
    }
    long double x_intersection(const Line &a, const Line &b) {
        return (a.b - b.b) / ((long double) (b.m - a.m));
    }

public:
    std::deque<Line> dq;

    void insert(Line l) {
        if (dq.size() >= 1 && parallel(l, dq.back()) && l.b <= dq.back().b) {
            return;
        }
        while (dq.size() >= 2) {
            if (parallel(l, dq.back())) {
                if (l.b > dq.front().b) {
                    dq.pop_front();
                    continue;
                } else {
                    return;
                }
            }
            if (x_intersection(l, dq.back()) <= x_intersection(dq.back(), dq[dq.size() - 2])) {
                dq.pop_back();
            } else {
                break;
            }
        }
        if (dq.size() == 1 && parallel(l, dq.back()) && l.b > dq.back().b) {
            dq.pop_back();
        }
        dq.push_back(l);
    }

    ll query(ll x) {
        while (dq.size() >= 2 && dq[0].eval(x) <= dq[1].eval(x)) {
            dq.pop_front();
        }
        return dq[0].eval(x);
    }
};

int main() {
    ll n, k;
    std::cin >> n >> k;
    Vector<ll> a(n);
    for (auto &i : a) {
        std::cin >> i;
    }
    a.calculate_prefix_sum();

    if (n == 2) {
        std::cout << a[0] * a[1] << "\n1\n";
        return 0;
    }

    for (ll i = 0; i <= k; ++ i) {
        CHT hull;
        for (ll j = n - 1; j >= 0; -- j) {
            if (j == n - 1) {
                dp[i][j] = -inf * (i != 0);
                continue;
            }
            if (i == 0) {
                dp[i][j] = 0;
                continue;
            }

            int m = a.sum(j + 1, n - 1);
            ll b = dp[i - 1][j + 1] + a.sum(0, j) * a.sum(j + 1, n - 1);
            hull.insert({m, b});
            ll ans = hull.query(-a.sum(0, j - 1));
            dp[i][j] = std::max(0LL, ans);
        }
    }

    std::cout << dp[k][0] << "\n";
    ll i = 0;
    ll ops = k;
    for (ll c = i; c < n - 1 && ops > 0; c++) {
        if (dp[ops][i] == a.sum(i, c) * a.sum(c + 1, n - 1) + dp[ops - 1][c + 1]) {
            std::cout << c + 1 << " ";
            ops--;
            i = c + 1;
        }
    }
}
# Verdict Execution time Memory Grader output
1 Correct 1 ms 4444 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 2396 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 348 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 4440 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 8540 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 2396 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 2396 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 4444 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 4444 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 4440 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 4440 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 4444 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 4444 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 4444 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 4440 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 4452 KB contestant found the optimal answer: 999919994 == 999919994
# Verdict Execution time Memory Grader output
1 Correct 1 ms 4444 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 4444 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 5 ms 39260 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 4548 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 8540 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 6488 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 20828 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 10584 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 6492 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 12716 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 1 ms 4440 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 4440 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 11 ms 95324 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 4440 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 11 ms 98908 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 13 ms 97112 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 11 ms 93276 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 5 ms 35164 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 22872 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 6 ms 45404 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 1 ms 4452 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 4444 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 15 ms 93788 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 4444 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 15 ms 99932 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 15 ms 99420 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 16 ms 97884 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 15 ms 93788 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 5 ms 33368 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 9 ms 63836 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 2 ms 4696 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 4 ms 4700 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 63 ms 107280 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 4700 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 43 ms 95060 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 45 ms 100420 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 61 ms 101204 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 48 ms 97324 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 51 ms 98392 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 52 ms 101720 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 19 ms 6752 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 19 ms 6540 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Runtime error 444 ms 131072 KB Execution killed with signal 9
4 Halted 0 ms 0 KB -