Submission #1085076

#	Time	Username	Problem	Language	Result	Execution time	Memory
1085076		ZeroCool	Split the sequence (APIO14_sequence)	C++14	0 / 100	32 ms	12396 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ld long double
#define ar array

const int LOG = 20;
const int MOD = 1e9 + 7;
const int INF = 1e18;

const int N = 3005;
struct LINE {
    int a, b, id ;
 
    LINE (int a, int b, int id ) : a(a), b(b), id(id) {}
 
    int operator() (const int &x) {
        return a * x + b;
    }
};
 
struct convex_hull_trick {
    vector<LINE> op;
    void init () {
        vector<LINE> ().swap(op);
    }
    bool bad (LINE ln1, LINE ln2, LINE ln3) {
        __int128 hi = 1;
        return hi * (ln3.b - ln1.b) * (ln1.a - ln2.a) <= hi * (ln2.b - ln1.b) * (ln1.a - ln3.a);
    }
 
    void add (LINE ln) {
        while (op.size() >= 2 && bad(op[op.size() - 2], op[op.size() - 1], ln)) {
            op.pop_back();
        }
        op.push_back(ln);
    }
 
    ar<int,2> get (int x) {
        if (op.empty()) return ar<int,2>{INF, -1l};
        int lf = 0, rt = op.size() - 1;
        while (lf < rt) {
            int mid = (lf + rt) >> 1;
            if (op[mid](x) <= op[mid + 1](x)) rt = mid;
            else lf = mid + 1;
        }
        return ar<int,2>{op[lf](x), op[lf].id};
 
    }
}CHT;
signed main() {
    int n, k;
    cin>>n>>k;
    int A[n];
    for(int i = 0;i < n;i++)cin>>A[i];
    int pref[n];
    int prv[n][k];
    pref[0] = A[0];
    for(int i= 1;i < n;i++)pref[i] = pref[i - 1] + A[i];
    int dp[n][k + 1];
    for(int i = 0;i < n;i++)dp[i][0] = 0;

    for(int j = 1;j < k;j++){
        CHT.init();
        for(int i = 0;i < n;i++){
            ar<int, 2> c = CHT.get(pref[i]);
            dp[i][j] = -c[0];
            prv[j][i] = c[1]; 
            CHT.add(LINE{-pref[i], -(dp[i][j - 1] - pref[i] * pref[i]), i});
        }
    }
    for(int j = 1;j < k;j++){
        for(int i = 1;i < n;i++){
            //cout<<prv[j][i]<<" ";
        }
            //cout<<'\n';
    }
    int res = -1;
    int opt = -1;
    for(int i = 0;i < n;i++){
        if(res < dp[i][k - 1] + (pref[n - 1] - pref[i]) * pref[i]){
            res = dp[i][k - 1] + (pref[n - 1] - pref[i]) * pref[i];
            opt = i;

        }
    }
    cout<<res<<'\n';
    vector<int> ans;
    for(int j = k - 1;j >= 0;j--){
        ans.push_back(opt);
        opt = prv[j][opt];
    }
    for(auto u:ans)cout<<u + 1<<" ";
}

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