Submission #976830

#	Time	Username	Problem	Language	Result	Execution time	Memory
976830		tamir1	Split the sequence (APIO14_sequence)	C++17	33 / 100	252 ms	131072 KiB

sequence

#include<bits/stdc++.h>
#define ll long long
using namespace std;
ll n,k,i,j,l,a[100001],sum[100001],ans,idx,dp[201][100001];
int dp2[201][100001];
vector<ll> v;
struct line{
	ll k,d,idx;
};
ll val(line a,ll x){
	return a.k*x+a.d;
}
double intt(line a,line b){
	return double(b.d-a.d)/(a.k-b.k);
}
int main(){
	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin >> n >> k;
	for(i=1;i<=n;i++){
		cin >> a[i];
		sum[i]=sum[i-1]+a[i];
	}
	for(l=1;l<=k;l++){
		deque<line> q;
		q.push_back({sum[l-1],dp[l-1][l-1]-sum[n]*sum[l-1],l-1});
		for(i=l;i<n;i++){
			while(q.size()>=2 && val(q.back(),sum[i])<=val(q[q.size()-2],sum[i])) q.pop_back();
			dp[l][i]=sum[n]*sum[i]-sum[i]*sum[i]+val(q.back(),sum[i]);
			dp2[l][i]=q.back().idx;
			line cur={sum[i],dp[l-1][i]-sum[n]*sum[i],i};
			while(q.size()>=2 && intt(cur,q[0])<=intt(q[0],q[1])) q.pop_front();
			q.push_front(cur);
			/*for(j=l-1;j<i;j++){
				ll x=dp[l-1][j]+(sum[n]-sum[i])*(sum[i]-sum[j]);
				if(x>=dp[l][i]){
					dp[l][i]=x;
					dp2[l][i]=j;
				}
			}*/
			/*dp[l-1][j]-sum[n]*sum[j]
			-sum[i]*sum[i]
			sum[i]*sum[j];*/
		}
	}
	for(i=k;i<n;i++){
		if(dp[k][i]>=ans){
			ans=dp[k][i];
			idx=i;
		}
	}
	for(i=k;i>=1;i--){
		v.push_back(idx);
		idx=dp2[i][idx];
	}
	reverse(v.begin(),v.end());
	cout << ans << "\n";
	for(i=0;i<k;i++) cout << v[i] << " ";
}

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