Submission #1000679

#	Time	Username	Problem	Language	Result	Execution time	Memory
1000679		vjudge1	Split the sequence (APIO14_sequence)	C++17	49 / 100	2037 ms	89276 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;
    }
};

long double cross(line a,line b){
    return ((a.b - b.b) * 1.0 / ((b.k - a.k) * 1.0));
}
void add(vector<line> &st,line l){
    while((int)st.size() > 1 && cross(l,st[(int)st.size() - 2]) <= cross(l,st.back())){
        st.pop_back();
    }
    st.push_back(l);
}
pair<ll,ll> get(vector<line> &st,ll x){
    int l = -1,r = (int)st.size() - 1;
    while(r - l > 1){
        int mid = (l + r) >> 1;
        if(mid == (int)st.size() - 1 || (st[mid].b - st[mid + 1].b) * 1.0 >= x * 1.0 * (st[mid + 1].k - st[mid].k)){
            r = mid;
        }else{
            l = mid;
        }
    }
    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;
        }
    }
    // cout << x << ' ' << st[0].k << ' ' << st[1].k<< ' ' << r << "x\n";
    return {st[r].get(x),st[r].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';
    int k1 = k;
    while(k){
        f.push_back(ps);
        ps = p[ps][k--];
    }
    reverse(f.begin(),f.end());
    assert((int)f.size() == k1);
    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();
    }
}

Compilation message (stderr)

sequence.cpp: In function 'std::pair<long long int, long long int> get(std::vector<line>&, ll)':
sequence.cpp:40:16: warning: variable 'pos' set but not used [-Wunused-but-set-variable]
   40 |     ll ret =0 ,pos = 0;
      |                ^~~

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