Submission #1088286

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
1088286	2024-09-14T07:59:06 Z	rlx0090	Split the sequence (APIO14_sequence)	C++14	0 / 100	56 ms	6900 KB

sequence

#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, 1000 * N) - p[N] * p[i];
            if(k == K) ans = max(ans, dp[k][i]);
        }
        delete(tree);
    }
    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
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	1 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	1 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	348 KB	contestant found the optimal answer: 100400096 == 100400096
10	Incorrect	0 ms	348 KB	contestant didn't find the optimal answer: 600320019 < 900320000
11	Halted	0 ms	0 KB	-

Subtask #2
0 / 11.0

#	Verdict	Execution time	Memory	Grader output
1	Incorrect	0 ms	348 KB	contestant didn't find the optimal answer: 1093426 < 1093956
2	Halted	0 ms	0 KB	-

Subtask #3
0 / 11.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	348 KB	contestant found the optimal answer: 610590000 == 610590000
2	Incorrect	1 ms	348 KB	contestant didn't find the optimal answer: 207933467 < 311760000
3	Halted	0 ms	0 KB	-