oj.uz

Submission #1011998

# Submission time Handle Problem Language Result Execution time Memory
1011998 2024-07-01T13:49:37 Z vjudge1 Split the sequence (APIO14_sequence) C++17
71 / 100
 55 ms 131072 KB 
#include <bits/stdc++.h>
using namespace std;
#define endl "\n"
#define ll long long
template <bool kGetMin = false>
struct LineDeque
{
    using T = long long;

    struct Line
    {
        mutable T a, b, p;
        bool operator<(const Line &other) const { return a < other.a; }
        bool operator<(T x) const { return p < x; }
        T eval(T x) const { return a * x + b; }
    };

    using Set = std::deque<pair<Line, int>>;
    using Iterator = typename Set::iterator;
    Set s;

    static const T inf = std::numeric_limits<T>::max();

    // doubles: inf = 1/.0, div(a, b) = a / b
    T div(T a, T b)
    { // floored division
        return a / b - ((a ^ b) < 0 && a % b);
    }

    bool intersect(Line &x, Line &y)
    {
        if (x.a == y.a)
        {
            x.p = x.b > y.b ? inf : -inf;
        }
        else
        {
            x.p = div(y.b - x.b, x.a - y.a);
        }
        return x.p >= y.p;
    }

    void _add_line1(T a, T b, int id)
    { // increasing slope
        Line to_add = {a, b, inf};
        if (s.size())
        {
            intersect(s.back().first, to_add);
        }
        while (s.size() >= 2 && intersect(s.at(s.size() - 2).first, s.at(s.size() - 1).first))
        {
            s.pop_back();
            intersect(s.back().first, to_add);
        }
        s.push_back({to_add, id});
    }

    void _add_line2(T a, T b, int id)
    { // decreasing slope
        Line to_add = {a, b, 0};
        while (s.size() && intersect(to_add, s.front()))
        {
            s.pop_front();
        }
        s.push_front({to_add, id});
    }

    void add_line_increasing_slope(T a, T b, int id)
    {
        if constexpr (kGetMin)
        {
            _add_line2(-a, -b, id);
        }
        else
        {
            _add_line1(a, b, id);
        }
    }

    void add_line_decreasing_slope(T a, T b, int id)
    {
        if constexpr (kGetMin)
        {
            _add_line1(-a, -b, id);
        }
        else
        {
            _add_line2(a, b, id);
        }
    }

    T query(T x)
    { // arbitrary
        assert(!s.empty());
        auto l = *std::lower_bound(s.begin(), s.end());
        // To get min
        if constexpr (kGetMin)
        {
            return -l.eval(x);
        }
        else
        {
            return l.eval(x);
        }
    }

    pair<T, int> query_increasing(T x)
    {
        while (s.size() >= 2 && s[0].first.eval(x) <= s[1].first.eval(x))
        {
            s.pop_front();
        }
        if constexpr (kGetMin)
        {
            return {-s[0].first.eval(x), s[0].second};
        }
        else
        {
            return {s[0].first.eval(x), s[0].second};
        }
    }

    pair<T, int> query_decreasing(T x)
    {
        while (s.size() >= 2 && s.at(s.size() - 1).first.eval(x) <= s.at(s.size() - 2).first.eval(x))
        {
            s.pop_back();
        }
        if constexpr (kGetMin)
        {
            return {-s[0].first.eval(x), s[0].second};
        }
        else
        {
            return {s[0].first.eval(x), s[0].second};
        }
    }
};
ll n, k, a[100005];
ll s[100005];
pair<ll, int> dp[100005][250];
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin >> n >> k;
    vector<int> res;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i];
        s[i] = s[i - 1] + a[i];
    }
    LineDeque<false> d[250];
    // res.push_back(1);
    for (int i = 1; i <= k; i++)
    {
        d[i - 1]._add_line1(0LL, 0LL, 0);
        for (int j = 1; j <= n; j++)
        {
            dp[j][i] = d[i - 1].query_increasing(s[j]);
            d[i - 1].add_line_increasing_slope(s[j], dp[j][i - 1].first - s[j] * s[j], j);
        }
    }
    int x = n;
    int the = k;
    for (int i = k; i >= 1; i--)
    {
        res.push_back(dp[x][i].second);
        x = dp[x][i].second;
    }
    reverse(res.begin(), res.end());
    cout << dp[n][k].first << endl;
    for (int i : res)
    {
        cout << i << " ";
    }
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:165:9: warning: unused variable 'the' [-Wunused-variable]
  165 |     int the = k;
      |         ^~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 600 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 604 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 604 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 604 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 604 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 600 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 604 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 604 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 476 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 604 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 604 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 600 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 604 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 604 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 480 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 604 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 604 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 2652 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 2648 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 2652 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 2936 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 2652 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 2652 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 2652 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 2652 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 2652 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2648 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 2652 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 2652 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 2652 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 2648 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 2908 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 2908 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 2652 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 2876 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 2648 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4700 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 4444 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 5 ms 4956 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 4952 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 5 ms 5000 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 5 ms 4956 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 5068 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 5 ms 5464 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 4956 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 4444 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 40028 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 14 ms 40504 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 54 ms 41468 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 14 ms 40164 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 45 ms 40284 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 48 ms 40792 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 54 ms 41364 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 43 ms 41552 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 46 ms 41044 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 55 ms 41404 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Runtime error 50 ms 131072 KB Execution killed with signal 9
2 Halted 0 ms 0 KB -