Submission #1197704

#	Time	Username	Problem	Language	Result	Execution time	Memory
1197704		TahirAliyev	Split the sequence (APIO14_sequence)	C++20	71 / 100	464 ms	161312 KiB

sequence

#include <bits/stdc++.h>

// #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define int long long
#define ld long double
#define ll long long
#define pii pair<int, int>
#define all(v) v.begin(), v.end()
using namespace std;
const int oo = 1e18 + 9;
const int MAX = 4000 + 5, LOGMAX = 20, B = 441, MOD = 998244353;

struct line{
    int k, b;
    int f(int x){
        return x * k + b;
    }
    ld inter(line a){
        return (ld)(a.b - b) / (ld)(k - a.k);
    }
};

void solve(){
    int n, k; cin >> n >> k;
    k++;
    int arr[n + 1];
    int pre[n + 1];
    pre[0] = 0;
    for(int i = 1; i <= n; i++){
        cin >> arr[i];
        pre[i] = pre[i - 1] + arr[i];
    }
    vector<int> dp(n + 1, -oo);
    dp[0] = 0;
    //dp[i] = (dp[j] - pre[j] * pre[j]) + pre[i] * pre[j];
    vector<int> par[k + 1];
    for(int j = 1; j <= k; j++){
        vector<int> ndp(n + 1, -oo);
        par[j].resize(n + 1, 0);
        deque<line> dq;
        deque<int> id;
        dq.push_back({pre[j - 1], (dp[j - 1] - pre[j - 1] * pre[j - 1])});
        id.push_back(j - 1);
        for(int i = j; i <= n; i++){
            while(dq.size() >= 2 && dq[0].f(pre[i]) < dq[1].f(pre[i])){
                dq.pop_front();
                id.pop_front();
            }
            ndp[i] = dq[0].f(pre[i]);
            par[j][i] = id[0];
            if(dp[i] < 0) continue;
            line a = {pre[i], dp[i] - pre[i] * pre[i]};
            while(dq.size() >= 2 && a.k != dq.back().k && a.inter(dq[dq.size()-2]) <= dq.back().inter(dq[dq.size()-2])){
                dq.pop_back();
                id.pop_back();
            } 
            while(dq.size() && a.k == dq.back().k && a.b >= dq.back().b){  
                dq.pop_back();
                id.pop_back();
            }
            if(!dq.size() || dq.back().k != a.k){
                dq.push_back(a);
                id.push_back(i);
            }
        }
        swap(ndp, dp);
    }
    cout << dp[n] << '\n';
    vector<int> v;
    int i = n;
    while(k){
        if(i != n) v.push_back(i);
        i = par[k][i];
        k--;
    }
    reverse(all(v));
    if(!v.size()) v.push_back(1);
    for(int a : v) cout << a << ' ';
    cout << '\n';
}   

signed main(){
    // ios::sync_with_stdio(0);
    // cin.tie(0);
    // cout.tie(0);
    int t = 1;
    // cin >> t;
    while(t--) solve();
}

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