Submission #1088308

#	Time	Username	Problem	Language	Result	Execution time	Memory
1088308		rlx0090	Split the sequence (APIO14_sequence)	C++14	71 / 100	2051 ms	93008 KiB

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) {
        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;
    }
};

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);
    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(cur == nullptr) return 0;
    if(nl == nr) return cur->s.f(x);
    int m = (nl + nr) / 2;
    if(x <= m)
        return max(cur->s.f(x), query(cur->left, x, nl, m));
    else
        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 << '\n';
    int s = 0;
    for(int k = K; k >= 1; --k) {
        for(int i = s + 1; i <= N - k; ++i) {
            long long q = (p[N] - p[i]) * (p[i] - p[s]);
            if(ans - q == dp[k - 1][i] ) {
                cout << i << ' ';
                ans -= q;
                s = i;
                break;
            }
        }
    }
 
    return 0;
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29