Submission #982666

#	Time	Username	Problem	Language	Result	Execution time	Memory
982666		Hugo1729	Split the sequence (APIO14_sequence)	C++11	0 / 100	57 ms	131072 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

ll pref[100001]={0};
ll dp[100001][201]={0};
int p[100001][201]={0};

struct line{
    ll m,c;

    line(ll _m, ll _c){m=_m;c=_c;}

    ll intersect(line l){
        return m-l.m==0 ? LLONG_MAX/4 : (l.c-c)/(m-l.m);
    }

    ll value(ll x){
        return m*x+c;
    }
};

deque<pair<line,int>> q;
deque<int> pos;

void insert(ll m, ll c){
    line l(m,c);
    while(!q.empty()&&q.front().second>l.intersect(q.front().first)){
        // cout << "irem" << ' ' << q.front().first.m << ' ' << q.front().first.c << ' ' << q.front().second << '\n';
        q.pop_front();
        pos.pop_front();
    }

    if(q.empty()){
        q.push_front({l,0});
    }else{
        q.push_front({l,l.intersect(q.front().first)});
    }
    // cout << "iadd" << ' ' << q.front().first.m << ' ' << q.front().first.c << ' ' << q.front().second << '\n';
}

ll query(ll x){
    while(q.size()>1&&q[q.size()-2].second<x){
        // cout << "qrem" << ' ' << q.back().first.m << ' ' << q.back().first.c << ' ' << q.back().second << '\n';
        q.pop_back();
        pos.pop_back();
    }

    // cout << "query" << ' ' << q.back().first.m << ' ' << q.back().first.c << ' ' << q.back().second <<  ' ' << q.back().first.value(x) <<'\n';

    return q.back().first.value(x);
}


int main(){
    // cin.tie(0)->sync_with_stdio(0);

    int n,k; cin >> n >> k;

    vector<int> a(n);
    for(int i=0;i<n;i++)cin >> a[i];
    for(int i=0;i<n;i++)pref[i+1]=pref[i]+a[i];

    for(int j=1;j<=k;j++){
        q.clear();
        pos.clear();
        insert(0,0);
        pos.push_front(0);
        for(int i=1;i<=n;i++){

            dp[i][j]=query(pref[i]);
            p[i][j]=pos.back();

            insert(pref[i],dp[i][j-1]-pref[i]*pref[i]);
            pos.push_front(i);
            // cout << '(' << i << j <<')' <<dp[i][j] << ' ' << p[i][j] << ' ';
        }
        // cout << '\n';
    }

    cout << dp[n][k] << '\n';

    int sus=n;
    vector<int> ans;
    while(k>0){
        ans.push_back(p[sus][k--]);
        sus=p[sus][k];
    }

    for(int i=ans.size()-1;i>=0;i--)cout << ans[i] << ' ';

    return 0;
// 7 3
// 4 1 3 4 0 2 3
// (11)0 (21)4 (31)16 (41)35 (51)35 (61)48 (71)72 
// (12)0 (22)4 (32)19 (42)48 (52)48 (62)64 (72)95 
// (13)0 (23)4 (33)19 (43)51 (53)51 (63)72 (73)108 
// 108
}

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