# | Time | Username | Problem | Language | Result | Execution time | Memory |
---|---|---|---|---|---|---|---|
308034 | avengers | Split the sequence (APIO14_sequence) | C++14 | 0 ms | 0 KiB |
This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
using ll=long long int;
typedef struct Line{
ll p, q;
}line;
int n, k;
ll a[100005];
ll s[100005]={};
ll dp[2][100005]={};
int track[205][100005];
line cht[100005];
ll sz=0;
ll now=0;
double cx(line a, line b)
{
return 1.0*(double)(b.q-a.q)/(a.p-b.p);
}
void insert(line v)
{
cht[sz]=v;
while(sz>1&&cx(cht[sz-2], cht[sz-1])>cx(cht[sz], cht[sz-1]))
{
cht[sz-1]=cht[sz];
sz--;
}
sz++;
}
pair <ll, ll> sol(ll x)
{
ll lo=0;
ll hi=sz-1;
while(lo<hi)
{
ll mid=(lo+hi)/2;
if(cx(cht[mid], cht[mid+1])<=x) lo=mid+1;
else hi=mid;
}
return cht[lo].p*x+cht[lo].q;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin>>n>>k;
ll t;
for(int i=1; i<=n; i++)
{
cin>>a[i];
s[i]=s[i-1]+a[i];
}
line l;
for(int i=1; i<=k; i++)
{
l.p=0;
l.q=0;
insert(l);
for(int j=1; j<=n; j++)
{
pair <ll, ll> p=sol(s[j]);
dp[i%2][j]=p.first;
track[i][j]=p.second;
l.p=s[j];
l.q=dp[(i+1)%2][j]-s[j]*s[j];
insert(l);
}
sz=0;
now=0;
}
cout<<dp[k%2][n]<<'\n';
vector <int> ans;
ll cur=n;
for(int i=k; i>=1; i--)
{
ans.push_back(track[i][cur]);
cur=track[i][cur];
}
reverse(ans.begin(), ans.end());
for(auto i:ans) cout<<i<<' ';
}