Submission #1000672

#	Time	Username	Problem	Language	Result	Execution time	Memory
1000672		dimashhh	Split the sequence (APIO14_sequence)	C++17	0 / 100	2055 ms	64296 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int  N = 1e5 + 30, MOD = 1e9 + 7;
int n,k;
ll a[N];
ll pref[N],sf[N];
int p[N][201];
ll dp[N],tdp[N];
struct line{
    ll k,b;
    int pos = 0;
    ll get(ll x){
        return k * x + b;
    }
};

void add(vector<line> &st,line l){
    st.push_back(l);
}
pair<ll,ll> get(vector<line> &st,ll x){
    ll ret =0 ,pos = 0;
    for(int i = 0;i < (int)st.size();i++){
        if(st[i].get(x) >= ret){
            ret = st[i].get(x);
            pos = st[i].pos;
        }
    }
    return {ret,pos};
}
void test(){
    cin >> n >> k;
    for(int i = 1;i <= n;i++){
        cin >> a[i];
    }
    for(int i = 1;i <= n;i++){
        pref[i] = pref[i - 1] + a[i];
    }
    for(int i = n;i >= 1;i--){
        sf[i] = sf[i + 1] + a[i];
    }
    for(int i = 1;i <= k;i++){
        vector<line> st;
        add(st,{0,0});
        for(int j = 1;j <= n;j++){
            pair<ll,ll> G = get(st,sf[j + 1]);
            dp[j] = G.first+ pref[j] * sf[j + 1];
            p[j][i] = G.second;
            line nv = {-pref[j],tdp[j],j};
            add(st,nv);
            // for(int prev = 0;prev < j;prev++){
            //     dp[j] = max(dp[j],tdp[prev] + pref[j] * sf[j + 1] - pref[prev] * sf[j + 1]);
            // }
        }
        for(int j = 1;j <= n;j++){
            tdp[j] = dp[j];
            dp[j] =0 ;
        }
    }
    ll res = 0;
    int ps = 0;
    for(int i = 1;i <= n;i++){
        if(tdp[i] > res){
            res = tdp[i];
            ps = i;
        }
    }
    vector<int> f;
    cout << res << '\n';
    while(k){
        f.push_back(ps);
        ps = p[ps][k--];
    }
    reverse(f.begin(),f.end());
    assert((int)f.size() == k);
    for(int j:f){
        cout << j << ' ';
    }
}
int main() {
    ios_base::sync_with_stdio(false);cin.tie(0);
    int t = 1;
    // cin >> t;
    while(t--){
        test();
    }
}

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