Submission #922781

#	Time	Username	Problem	Language	Result	Execution time	Memory
922781		thangdz2k7	Split the sequence (APIO14_sequence)	C++17	71 / 100	332 ms	131072 KiB

sequence

#include <bits/stdc++.h>
#define int long long
#define ll long long
#define line pair <ll, ll>
#define Point pair <double, double>
#define A first
#define B second
#define pb push_back
 
using namespace std;
 
const int N = 1e5 + 5;
const ll inf = 1e18;
 
int n, k;
int a[N], best[205][N];
__int128 dp[2][N], pre[N];
 
vector <line> st;
vector <int> idx;
 
Point giao(line l1, line l2){
    Point ans;
    double del = double (l1.A) - double(l2.A);
    ans.A = double (l2.B - l1.B) / del;
    ans.B = double (ans.A) + double(l1.B) / double(l1.A);
    return ans;
}
 
void add(line p, int id){
    if (st.empty()){
        st.pb(p);
        idx.pb(id);
        return;
    }
    while (p.A == st.back().A) return;
 
    while (true){
        int sz = st.size();
        if (sz <= 1) break;
        line l2 = st.back();
        line l3 = st[sz - 2];
        Point k = giao(p, l3);
        if (k.A / double(p.A) > (k.B - double(l2.B) / double(p.A)) / double(l2.A)) break;
        st.pop_back();
        idx.pop_back();
 
    }
    st.pb(p);
    idx.pb(id);
 
}
 
int get(int &cur, int t, int i){
    int sz = st.size();
    cur = min(cur, sz - 1);
    dp[t][i] = st[cur].A * pre[i] + st[cur].B;
    while (cur < sz - 1){
        __int128 val = st[cur + 1].A * pre[i] + st[cur + 1].B;
        if (dp[t][i] < val){
            dp[t][i] = val;
            ++ cur;
        }
        else return idx[cur];
    }
    return idx[cur];
}
 
void solve(){
    cin >> n >> k;
    for (int i = 1; i <= n; ++ i){
        cin >> a[i];
        pre[i] = pre[i - 1] + a[i];
    }
 
    for (int loops = 1; loops <= k; ++ loops){
        st.clear();
        idx.clear();
        int t = loops & 1;
        int cur = 0;
        for (int i = 1; i <= n; ++ i){
            if (i == loops){
                add(line(pre[i], dp[1 ^ t][i] - pre[i] * pre[i]), i);
                best[loops][i] = i;
            }
            if (i > loops){
                dp[t][i] = inf;
                best[loops][i] = get(cur, t, i);
                add(line(pre[i], dp[1 ^ t][i] - pre[i] * pre[i]), i);
                //cout << loops << ' ' << i << ' ' << dp[t][i] << endl;
            }
        }
    }
 
    //cout << inf * inf;
 
    ll ans = dp[k & 1][n];
    cout << ans << '\n';
    int cur = n;
    for (int i = k; i >= 1; -- i){
        cur = best[i][cur];
        cout << cur << ' ';
    }
}
 
signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    solve();
    return 0;
}

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