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Submission #1027074

# Submission time Handle Problem Language Result Execution time Memory
1027074 2024-07-18T20:26:35 Z borisAngelov Split the sequence (APIO14_sequence) C++17
71 / 100
 133 ms 76384 KB 
#include <bits/stdc++.h>

using namespace std;

const int maxn = 10005;
const int maxk = 205;
const long long inf = 1e18;

int n, k;
long long a[maxn];
long long pref[maxn];

long long dp[maxk];
int prvState[maxn][maxk];

long long sum(int from, int to)
{
    return pref[to] - pref[from - 1];
}

struct Line
{
    long long a;
    long long b;
    int idx;

    long long calc(long long x)
    {
        return a * x + b;
    }
};

struct ConvexHullTrickMAX
{
    vector<pair<Line, double>> upperEnvelope;

    double cross(const Line& l1, const Line& l2)
    {
        return (1.0 * (l1.b - l2.b)) / (1.0 * (l2.a - l1.a));
    }

    bool toRemove(const Line& newLine, pair<Line, double> last)
    {
        if (newLine.a == last.first.a)
        {
            return newLine.b >= last.first.b;
        }

        return cross(newLine, last.first) <= last.second;
    }

    void addLine(Line newLine)
    {
        while (upperEnvelope.size() >= 1 && toRemove(newLine, upperEnvelope.back()) == true)
        {
            upperEnvelope.pop_back();
        }

        if (upperEnvelope.empty())
        {
            upperEnvelope.push_back({newLine, -inf});
        }
        else
        {
            upperEnvelope.push_back({newLine, cross(newLine, upperEnvelope.back().first)});
        }
    }

    Line query(long long x)
    {
        /*cout << "now query " << x << endl;

        for (auto [line, point] : upperEnvelope)
        {
            cout << line.idx << " " << point << endl;
        }*/

        int l = 0;
        int r = upperEnvelope.size() - 1;

        while (l <= r)
        {
            int mid = (l + r) / 2;

            if (upperEnvelope[mid].second <= 1.0 * x)
            {
                l = mid + 1;
            }
            else
            {
                r = mid - 1;
            }
        }

        return upperEnvelope[r].first;
    }
};

ConvexHullTrickMAX cht[maxk];

void fastIO()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
}

int main()
{
    fastIO();

    cin >> n >> k;

    for (int i = 1; i <= n; ++i)
    {
        cin >> a[i];
        pref[i] = pref[i - 1] + a[i];
    }

    for (int i = 1; i <= n; ++i)
    {
        for (int j = 0; j <= min(i - 1, k); ++j)
        {
            if (j != 0)
            {
                Line curr = cht[j - 1].query(pref[i]);
                dp[j] = curr.calc(pref[i]);
                prvState[i][j] = curr.idx;
            }
            else
            {
                dp[j] = 0;
            }

            //cout << i << " " << j << " :: " << dp[i][j] << endl;
        }

        for (int j = 0; j <= min(i - 1, k); ++j)
        {
            //cout << "add " << j << " " << pref[i] << " :: " << dp[i][j] - pref[i] * pref[i] << endl;;
            cht[j].addLine({pref[i], dp[j] - pref[i] * pref[i], i});
        }

        //cout << "end of " << i << endl;
        //cout << "------------------------------" << endl;
    }

    long long ans = dp[k];
    int pos = n;
    stack<int> splits;

    while (k > 0)
    {
        splits.push(prvState[pos][k]);
        pos = splits.top();
        --k;
    }

    cout << ans << endl;

    while (!splits.empty())
    {
        cout << splits.top() << " ";
        splits.pop();
    }

    cout << endl;

    return 0;
}

/*
6 1
0 0 0 0 1 1

7 3
4 1 3 4 0 2 3

2 1 4
3 1 16
3 2 19
4 1 35
4 2 48
4 3 51
5 1 35
5 2 48
5 3 51
6 1 48
6 2 64
6 3 72
7 1 72
7 2 95
7 3 108
*/

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 348 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 348 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 348 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 348 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 344 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 344 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 348 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 348 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 348 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 348 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 348 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 348 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 348 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 348 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 344 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 348 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 348 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 348 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 348 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 344 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 344 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 348 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 348 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 348 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 348 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 604 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 604 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 1480 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 604 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 1116 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 1116 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 1372 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 860 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 856 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 860 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2648 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2652 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 9052 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 2908 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 7 ms 8796 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 6 ms 7772 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 7 ms 9308 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 7 ms 9052 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 3932 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 5468 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 9684 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 9408 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 133 ms 76384 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 4 ms 9920 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 64 ms 38808 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 80 ms 35776 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 100 ms 58300 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 77 ms 49280 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 90 ms 52728 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 108 ms 64580 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Incorrect 1 ms 604 KB Integer 0 violates the range [1, 99999]
2 Halted 0 ms 0 KB -