Submission #855432

#TimeUsernameProblemLanguageResultExecution timeMemory
855432vjudge1Split the sequence (APIO14_sequence)C++17
0 / 100
21 ms131072 KiB
#include<bits/stdc++.h>
#pragma GCC target( "sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
#pragma GCC optimize("Ofast,unroll-loops,fast-math,O3")
using namespace std;
#define int long long
#define y1 cheza
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int N=2e5+100;
const int B=700;
const int M=1e7+10;
const int mod=1e9+7;
const int INF=1e18;
const long double eps=1e-8;
const int dx[]={1,-1,0,0};
const int dy[]={0,0,-1,1};
const int debug=0;
int n,k;
int a[N];
int dp[N][220];
int pr[N][220];
int pref[N];
struct point{
    int k,b,id;
};
deque<point>v;
int prec(point x,int y){
    return x.k*y+x.b;
}
bool calc(point x,point y,int z){
    return prec(x,z)<prec(y,z);
}
bool right(point x,point y,point z){
    return (y.k-x.k)*(pref[y.id]-pref[z.id])<=(y.k-z.k)*(pref[z.id]-pref[x.id]);
}
pair<int,int> get(int z){
    while(v.size()>=2&&calc(v[0],v[1],z)){
        v.pop_front();
    }   
    return {v.front().k*z+v.front().b,v.front().id};
}
void add(point x){
    while(v.size()>=2&&right(v[v.size()-1],v[v.size()-2],x)){
        v.pop_back();
    }
    v.push_back(x);
}



void test(){
    cin>>n>>k;
    for(int i=1;i<=n;i++){
        cin>>a[i];
        pref[i]=pref[i-1]+a[i];
    }
    for(int kk=1;kk<=k;kk++){
        // cout<<kk<<" <<<<<<<\n";
        add({0,0,0});
        for(int i=1;i<=n;i++){
            // for(int j=0;j<i;j++){
            //     int y=dp[j][kk-1]+(pref[i]-pref[j])*(pref[n]-pref[i]);
            //     if(y>=dp[i][kk]){
            //         dp[i][kk]=y;
            //         pr[i][kk]=j;
            //     }
            // }

            dp[i][kk]=pref[i]*pref[n]-pref[i]*pref[i];
            auto res=get(pref[n]-pref[i]);
            dp[i][kk]+=res.first;
            pr[i][kk]=res.second;
            add({-pref[i],dp[i][kk-1],i});
        }
        v.clear();


        // cout<<'\n';
    }
    // A B C
    // k1=AC+BC
    // k1=AB+BC
    // k1=AB+AC
    // k2=AC+BC+AB
    // k2=AB+AC+BC
    // for(int i=1;i<=k;i++){
    //     for(int j=1;j<=n;j++){
    //         cout<<dp[j][i]<<' ';
    //     }
    //     cout<<'\n';
    // }
    // for(int i=1;i<=k;i++){
    //     for(int j=1;j<=n;j++){
    //         cout<<pr[j][i]<<' ';
    //     }
    //     cout<<'\n';
    // }
    // return;
    int mx=0;
    int cur=0;
    for(int i=1;i<=n;i++){
        if(mx<=dp[i][k]){
            mx=dp[i][k];
            cur=i;
        }
    }
    vector<int>ans;
    ans.push_back(cur);
    for(int i=k;i>=2;i--){
        cur=pr[cur][i];
        ans.push_back(cur);
    }
    cout<<mx<<'\n';
    // reverse(ans.begin(),ans.end());
    sort(ans.begin(),ans.end());
    for(auto i:ans){
        cout<<i<<' ';
    }
    cout<<'\n';
}
/*
int y=dp[j][kk-1]+(pref[i]-pref[j])*(pref[n]-pref[i]);
i ,j
dp[i][kk]=min dp[j][kk-1] + (pref[i]-pref[j])*(pref[n]-pref[i]);
dp[i][kk]=pref[i]*pref[n]-pref[i]*pref[i];
-pref[j]*(pref[n]-pref[i])+dp[j][kk-1];
*/
signed main(){
    // cout<<"HEllo\n";
    // freopen("INPUT.TXT","r",stdin);
    // freopen("OUTPUT.TXT","w",stdout);
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    // cout.tie(nullptr);
    long long t2=1;
    //  cin>>t2;
    // scanf("%lld",&t2);
    for(int i=1;i<=t2;i++){
        // cout<<"Case "<<i<<": ";
        test();
    }
    
    return 0;

}
/*
temmie luck

*/
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