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Submission #849590

# Submission time Handle Problem Language Result Execution time Memory
849590 2023-09-15T03:52:33 Z TCLMinh Split the sequence (APIO14_sequence) C++17
89 / 100
 1699 ms 88420 KB 
#include <iostream>
#include <deque>
#include <algorithm>
#include <utility>
#include <vector>
#define int long long
using namespace std;
 
struct Line
{
    int a = 0, b = 0;
    Line(int a, int b) :a(a), b(b) {}
    Line() {}
 
    const inline int operator()(int x) const
    {
        return a * x + b - x * x;
    }
 
    const bool operator<(const Line& other) const
    {
        return a == other.a ? b < other.b : a < other.a;
    }
 
    const inline int intersect(const Line& other) const
    {
        return (other.b - b) / (a - other.a) + ((other.b - b) % (a - other.a) != 0);
    }
};
 
struct Node
{
    int idx = 0;
    int itsPos = 0;
    Line line = Line();
    Node(int itsPos, const Line& line, int idx) :itsPos(itsPos), line(line), idx(idx) {}
    Node(int itsPos) {}
    Node() {}
    const bool operator<(const Node& other) const
    {
        return itsPos < other.itsPos;
    }
};
 
std::deque<Node> dq;
 
void addLine(const Line& line, int idx)
{
    while (!dq.empty())
    {
        if (dq.back().line.a == line.a)
        {
            if (dq.back().line.b < line.b) dq.pop_back();
            return;
        }
        if (dq.back().line.intersect(line) <= dq.back().itsPos) dq.pop_back();
        else break;
    }
    if (dq.empty()) dq.push_back({ -99999999999999999LL,line,idx });
    else dq.push_back({ dq.back().line.intersect(line),line, idx });
}
 
void clearDeque()
{
    while (!dq.empty()) dq.pop_back();
}
 
pair<int, int> query(int x)
{
    int l = 0, r = dq.size() - 1;
    int result = 0;
    int idx = 0;
    while (l <= r)
    {
        int mid = (l + r) / 2;
        if (result < dq[mid].line(x))
        {
            result = dq[mid].line(x);
            idx = dq[mid].idx;
        }
        if (dq[mid].itsPos <= x)
        {
            l = mid + 1;
        }
        else
        {
            r = mid - 1;
        }
    }
    return{ result,idx };
}
 
int n, k;
signed trace[201][100001];
int dp[2][100001];
Line pre[2][100001];
int a[100001];
int prx[100001];
 
 
void debug()
{
    for (int i = 0; i <= k; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            cerr << trace[i][j] << " ";
        }
        cerr << "\n";
    }
    cerr << "\n";
 
}
 
int sum(int l, int r)
{
    return prx[r] - prx[l - 1];
}
 
 
signed main()
{
    cin >> n >> k;
    //k++;
    k--;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i];
        prx[i] = prx[i - 1] + a[i];
    }
 
    //maximize this dp: dp[t][i] = max(dp[t][i],dp[t - 1][j - 1] + sum(j,i) * sum(i + 1,n));
 
    for (int i = 2; i <= n; i++)
    {
        dp[0][i] = prx[i - 1] * (prx[n] + prx[0]) - prx[i - 1] * prx[i - 1] - prx[0] * prx[n];
        pre[0][i] = Line((prx[n] + prx[i - 1]), dp[0][i] - prx[i - 1] * prx[n]);
    }
 
 
    for (signed t = 1; t <= k; t++)
    {
        //cerr << t << "\n";
        clearDeque();
        for (signed i = t + 1; i <= n; i++)
        {
            //add previous one
            addLine(pre[(t-1)&1][i - 1], i - 1);
            //get
            pair<int,int> x = query(prx[i - 1]);
            int val = x.first;
            int idx = x.second;
            dp[t&1][i] = val;
            trace[t][i] = idx;
            //apply
            if (i < n)
            {
                pre[t&1][i] = Line(prx[n] + prx[i - 1], val - prx[i - 1] * prx[n]);
            }
        }
        /*
        for (auto x : dq)
        {
            cerr << x.itsPos << " " << x.line.a << "x " << x.line.b << " -x^2 \n";
        }
        */
    }
    vector<int> res;
    int result = 0, idx = 0;
    for (int i = n; i >= 1; i--)
    {
        if (result < dp[k&1][i])
        {
            result = dp[k&1][i];
            idx = i;
        }
    }
    res.push_back(idx-1);
    for (int i = k; i >= 1; i--)
    {
        res.push_back(trace[i][idx] - 1);
        idx = trace[i][idx];
    }
 
    //debug();
    cout << result << '\n';
    sort(res.begin(), res.end());
 
    int id = 1;
    for (auto x : res)
    {
        if (x < 0 || x < id)
        {
            cout << id++ << " ";
        }else
        cout << x << " ";
    }
    return 0;
}

Compilation message

sequence.cpp: In constructor 'Node::Node(long long int, const Line&, long long int)':
sequence.cpp:35:10: warning: 'Node::line' will be initialized after [-Wreorder]
   35 |     Line line = Line();
      |          ^~~~
sequence.cpp:33:9: warning:   'long long int Node::idx' [-Wreorder]
   33 |     int idx = 0;
      |         ^~~
sequence.cpp:36:5: warning:   when initialized here [-Wreorder]
   36 |     Node(int itsPos, const Line& line, int idx) :itsPos(itsPos), line(line), idx(idx) {}
      |     ^~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 8536 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 8540 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 6488 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 8536 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 10588 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 6488 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 6688 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 6488 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 8536 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 8536 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 8536 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 8540 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 8536 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 8536 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 8536 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 8536 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 8536 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 8540 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 8536 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 3 ms 26968 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 8792 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 10584 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 10584 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 16732 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 10588 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 10584 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 12632 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 8536 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 8536 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 10 ms 84460 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 8540 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 7 ms 61784 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Incorrect 9 ms 78424 KB declared answer doesn't correspond to the split scheme: declared = 103780000, real = 107630184
7 Halted 0 ms 0 KB -

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 8540 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 8536 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 18 ms 84568 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 8536 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 18 ms 84568 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 16 ms 74328 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 20 ms 84568 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 18 ms 84568 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 5 ms 22872 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 9 ms 39260 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 8792 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 8796 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 132 ms 84816 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 4 ms 9048 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 89 ms 54096 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 114 ms 62292 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 119 ms 66384 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 100 ms 56144 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 108 ms 62300 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 136 ms 78676 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 31 ms 11600 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 30 ms 11352 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1544 ms 88420 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 34 ms 11860 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1699 ms 87380 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1342 ms 64124 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1386 ms 69376 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 1179 ms 58924 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 1233 ms 65052 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1567 ms 81776 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845