oj.uz

Submission #1088289

# Submission time Handle Problem Language Result Execution time Memory
1088289 2024-09-14T08:01:39 Z rlx0090 Split the sequence (APIO14_sequence) C++14
71 / 100
 2000 ms 93596 KB 
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <limits>
#include <queue>
#include <string.h>
#include <stack>
#include <limits>

using namespace std;
int N, K;
long long p[100005], dp[201][100005];
long long minf = numeric_limits<long long>::min();
struct seg {
    long long k = 0, b = minf;
    seg() {}
    seg(long long _k, long long _b) :k(_k), b(_b) {}
    long long f(long long x) {
        //cout << "k : " << k << " x : " << x << " b : " << b << endl;
        return k * x + b;
    }
};
struct Node {
    Node * left = nullptr;
    Node * right = nullptr;
    seg s;
    ~Node() {
        if(left != nullptr) delete left;
        if(right != nullptr) delete right;
    }
};
// max value
void add(Node* cur, seg ns, int nl, int nr) {
    if(cur->s.b == minf && ns.b == minf) return;
    int m = (nl + nr) / 2;
    bool lef = cur->s.f(nl) < ns.f(nl);
    bool mid = cur->s.f(m) < ns.f(m);
    //cout << "cur : " << cur->s.f(m) << " ns : " << ns.f(m) << " result : " << (cur->s.f(m) < ns.f(m)) <<  endl;
    if(mid) swap(cur->s, ns);
    if(nl == nr) return;
    else if(lef != mid) {
        if(cur->left == nullptr) cur->left = new Node();
        add(cur->left, ns, nl, m);
    }
    else {
        if(cur->right == nullptr) cur->right = new Node();
        add(cur->right, ns, m + 1, nr);
    }
}

long long query(Node* cur, int x, int nl, int nr) {
    if(nl == nr) {return cur->s.f(x);}
    int m = (nl + nr) / 2;
    if(x <= m) {
        if(cur->left == nullptr) {return cur->s.f(x);}
        return max(cur->s.f(x), query(cur->left, x, nl, m));
    } else {
        if(cur->right == nullptr) {return cur->s.f(x);}
        return max(cur->s.f(x), query(cur->right, x, m + 1, nr));
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    cin >> N >> K;
    long long q;
    for(int i = 1; i <= N; ++i) {
        cin >> q;
        p[i] = p[i - 1] + q;
    }
    Node * tree;
    long long ans = 0;
    for(int k = 1; k <= K; ++k) {
        tree = new Node();
        for(int i = N - k - 1;  i >= 0; --i){
            add(tree, seg(p[i + 1], - p[i + 1] * p[i + 1] + p[N] * p[i + 1] + dp[k - 1][i + 1]), 0, 1e9);
            dp[k][i] = query(tree, p[i], 0, 1e9) - p[N] * p[i];
        }
        delete(tree);
    }
    ans = dp[K][0];
    cout << ans << endl;
    int s = 0;
    for(int k = K; k >= 1; --k) {
        for(int i = s + 1; i <= N - k; ++i) {
            if(ans - ( (p[N] - p[i]) * (p[i] - p[s]) ) == dp[k - 1][i] ) {
                cout << i << " ";
                ans -= (p[N] - p[i]) * (p[i] - p[s]);
                s = i;
                break;
            }
        }
    }

    return 0;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 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 348 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 348 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 460 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 1 ms 348 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 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 1 ms 348 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 348 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 1 ms 604 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 348 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 348 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 348 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 604 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 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 348 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 468 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 1784 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 348 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 4 ms 1372 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 5 ms 1628 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 4 ms 1628 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 720 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 604 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 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 344 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 344 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 28 ms 2836 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 348 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 43 ms 2876 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 35 ms 2644 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 30 ms 2880 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 32 ms 2828 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 8 ms 856 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 15 ms 1372 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 860 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 9 ms 1372 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 349 ms 17804 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 7 ms 1372 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 322 ms 11040 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 356 ms 12860 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 277 ms 13648 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 249 ms 11404 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 270 ms 12880 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 336 ms 16172 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 85 ms 8120 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 83 ms 9292 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2066 ms 93596 KB Time limit exceeded
4 Halted 0 ms 0 KB -