Submission #248468

#	Time	Username	Problem	Language	Result	Execution time	Memory
248468		Autoratch	Split the sequence (APIO14_sequence)	C++14	71 / 100	2101 ms	89872 KiB

sequence

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

const int N = 1e5 + 1;
const int K = 201;

int n,k;
long long s[N];
pair<long long,int> dp[N][K];
vector<long long> m[K],b[K],id[K];

bool bad(vector<long long> &m,vector<long long> &b,int l1,int l2,int l3)
{
    return (double)(b[l2]-b[l3])*(m[l2]-m[l1])<(double)(b[l1]-b[l2])*(m[l3]-m[l2]);
}

void add(vector<long long> &m,vector<long long> &b,vector<long long> &id,long long mx,long long bx,long long idx)
{
    if(!m.empty() and m.back()==mx and b.back()==bx) return;
    m.push_back(mx),b.push_back(bx),id.push_back(idx);
    while(m.size()>2 and bad(m,b,m.size()-3,m.size()-2,m.size()-1))
        m.erase(m.end()-2),b.erase(b.end()-2),id.erase(id.end()-2);
}

int ptr[K];

pair<long long,int> query(int &ptr,vector<long long> &m,vector<long long> &b,vector<long long> &id,long long x)
{
    if(m.empty()) return {0,0};
    while(m.size()>1 and m[1]*x+b[1]>=m[0]*x+b[0]) m.erase(m.begin()),b.erase(b.begin()),id.erase(id.begin());
    return {m[0]*x+b[0],id[0]};
}

int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0);

    cin >> n >> k; 
    for(int i = 1;i <= n;i++) cin >> s[i],s[i]+=s[i-1];
    for(int i = 1;i <= n;i++) 
    {
        for(int j = 1;j <= k;j++) dp[i][j] = query(ptr[j-1],m[j-1],b[j-1],id[j-1],s[i]);
        for(int j = 0;j <= k;j++) if(!(j>1 and !dp[i][j].second) and j<i) add(m[j],b[j],id[j],s[i],dp[i][j].first-s[i]*s[i],i);
    }
    cout << dp[n][k].first << '\n';
    vector<int> ans;
    int l = k;
    for(int x = dp[n][k].second;x;x = dp[x][--l].second) ans.push_back(x);
    assert(l==0);
    reverse(ans.begin(),ans.end());
    for(int x : ans) cout << x << ' ';
}

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