Submission #1088372

#	Time	Username	Problem	Language	Result	Execution time	Memory
1088372		rlx0090	Split the sequence (APIO14_sequence)	C++14	71 / 100	2043 ms	30032 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;
int cache[205][100005];
long long p[100005], dp[2][100005];
long long minf = numeric_limits<long long>::min();
struct seg {
    long long k = 0, b = minf;
    int label = -1;
    seg() {}
    seg(long long _k, long long _b, int _label) :k(_k), b(_b), label(_label) {}
    long long f(long long x) {
        return k * x + b;
    }
};
bool which_is_big(seg a, seg b, int x) {
    if(a.f(x) == b.f(x)) return a.label < b.label;
    return a.f(x) > b.f(x);
}
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(ns.b == minf) return;
    int m = (nl + nr) / 2;
    bool lef = which_is_big(ns, cur->s, nl);
    bool mid = which_is_big(ns, cur->s, 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);
    }
}
 
seg query(Node* cur, int x, int nl, int nr) {
    if(cur == nullptr || cur->s.b == minf) return seg();
    if(nl == nr) return cur->s;
    int m = (nl + nr) / 2;
    if(x <= m){
        seg c = query(cur->left, x, nl, m);
        if(which_is_big(c, cur->s, x)) return c;
        return cur->s;
    }
    else {
        seg c = query(cur->right, x, m + 1, nr);
        if(which_is_big(c, cur->s, x)) return c;
        return cur->s;
    }
}
 
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;
    int before = 0, cur = 0;
    for(int k = 1; k <= K; ++k) {
        before = k % 2; cur = (k + 1) % 2;
        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[before][i + 1], i + 1), 0, 1e9);
            seg c = query(tree, p[i], 0, 1e9);
            dp[cur][i] = c.f(p[i]) - p[N] * p[i];
            cache[k][i] = c.label;
        }
        delete(tree);
    }
    cout << dp[cur][0] << '\n';
    int s = 0;

    for(int k = K; k >= 1; --k) {
        cout << cache[k][s] << ' ';
        s = cache[k][s];
    }
 
    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