Submission #444762

#	Time	Username	Problem	Language	Result	Execution time	Memory
444762		impri	Split the sequence (APIO14_sequence)	C++14	0 / 100	1235 ms	89712 KiB

sequence

#include<bits/stdc++.h>
using namespace std;
int n,k;
int arr[100001];
long long psum[100001];
long long dp[100001][2];
int res[100001][202];
struct line{
long long a,b;
double s;
int p;
};
int main(void){
    cin.tie(0);
    ios_base::sync_with_stdio(false);
cin >> n >> k;
k++;
for(int i=1;i<=n;i++)
    cin >> arr[i];
for(int i=1;i<=n;i++)
    psum[i]=psum[i-1]+arr[i];
for(int i=1;i<n;i++)
    dp[i][1]=psum[i]*(psum[n]-psum[i]);
for(int i=2;i<=k;i++){
    vector<line>lines;
    lines.push_back({-psum[i-1],dp[i-1][(i+1)%2],10e12,i-1});

    int cur=0;
    for(int j=i;j<=n;j++){
        while(1){
            if(cur+1==lines.size())break;
            if(lines[cur+1].s<(psum[n]-psum[j]))break;
            cur++;
        }
        dp[j][i%2]=lines[cur].a*(psum[n]-psum[j])+lines[cur].b+psum[j]*psum[n]-psum[j]*psum[j];
        res[j][i]=lines[cur].p;
    
        line nxt;
        nxt.a=-psum[j];
        nxt.b=dp[j][(i+1)%2];
        nxt.p=j;
        bool ok=true;
        while(!lines.empty()){
            if(lines.back().a==nxt.a){
                if(lines.back().b>nxt.b){
                ok=false;break;}
                else{
                    lines.pop_back();
                }
            }
            else{
            double point=1.0*(lines.back().b-nxt.b)/(nxt.a-lines.back().a);
            if(point>lines.back().s)
               {

                lines.pop_back();
                if(cur==lines.size())
                    cur--;
               }
            else{
                nxt.s=point;
                break;
            }
        }
        }
        if(ok)
        lines.push_back(nxt);
    }
}
cout << dp[n][k%2] <<'\n';
int cur=n;
vector<int>r;
for(int i=k;i>1;i--){
    r.push_back(res[cur][i]);
    cur=res[cur][i];
}
for(int i=k-2;i>=0;i--)
    cout << r[i] << ' ';
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:31:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   31 |             if(cur+1==lines.size())break;
      |                ~~~~~^~~~~~~~~~~~~~
sequence.cpp:57:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   57 |                 if(cur==lines.size())
      |                    ~~~^~~~~~~~~~~~~~

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