Submission #551574

#	Time	Username	Problem	Language	Result	Execution time	Memory
551574		ToroTN	Split the sequence (APIO14_sequence)	C++14	100 / 100	647 ms	87716 KiB

sequence

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define X first
#define Y second
struct line
{
    ll m,c;
};
ll n,m,dp[100005][2],a[100005],qs[100005],u,g;
ll sum[100005],pos,cut;
int back[100005][205];
line t,now,pre;
stack<ll> stk;
vector<pair<line,ll> > v;
ll cal(line node,ll ptr)
{
    return node.m*sum[ptr]+node.c;
}
ll intersect(line l1,line l2,line now)
{
    return (now.c-l1.c)*(l2.m-now.m)-(now.c-l2.c)*(l1.m-now.m)<=0;
}
int main()
{
    scanf("%lld%lld",&n,&m);
    for(int i=1;i<=n;i++)scanf("%lld",&a[i]),sum[i]=sum[i-1]+a[i],qs[i]=qs[i-1]+a[i]*a[i];
    for(int i=0;i<=n;i++)for(int j=0;j<=1;j++)dp[i][j]=2e18;
    dp[0][0]=0;
    memset(back,-1,sizeof back);
    for(int i=1;i<=m+1;i++)
    {
        for(int j=0;j<=n;j++)dp[j][i%2]=2e18;
        for(int j=0;j<=n;j++)
        {
            if(pos>=v.size())pos=v.size()-1;
            while(pos+1<v.size()&&cal(v[pos+1].X,j)<=cal(v[pos].X,j))pos++;
            if(v.size()>0)
            {
                dp[j][i%2]=cal(v[pos].X,j)+sum[j]*sum[j]-qs[j];
                back[j][i]=v[pos].Y;
            }
            if(j<i-1)continue;
            t={-2*sum[j],dp[j][1-(i%2)]+(sum[j]*sum[j]+qs[j])};
            while(v.size()>=1)
            {
                now=v[v.size()-1].X;
                if(now.m==t.m&&t.c<=now.c)
                {
                    v.pop_back();
                }else
                {
                    break;
                }
            }
            while(v.size()>=2)
            {
                now=v[v.size()-1].X;
                pre=v[v.size()-2].X;
                cut=intersect(now,pre,t);
                if(cut)
                {
                    v.pop_back();
                }else
                {
                    break;
                }
            }
            v.pb({t,j});
            //printf("%d %d %lld\n",i,j,dp[j][i%2]);
        }
        while(!v.empty())v.pop_back();
    }
    u=n;
    g=m+1;
    while(1)
    {
        u=back[u][g];
        --g;
        if(u==0)break;
        stk.push(u);
    }
    printf("%lld\n",(sum[n]*sum[n]-qs[n]-dp[n][(m+1)%2])/2);
    while(!stk.empty())
    {
        printf("%lld ",stk.top());
        stk.pop();
    }
    printf("\n");
}
/*
7 3
4 1 3 4 0 2 3
*/

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:37:19: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<line, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   37 |             if(pos>=v.size())pos=v.size()-1;
      |                ~~~^~~~~~~~~~
sequence.cpp:38:24: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<line, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   38 |             while(pos+1<v.size()&&cal(v[pos+1].X,j)<=cal(v[pos].X,j))pos++;
      |                   ~~~~~^~~~~~~~~
sequence.cpp:27:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   27 |     scanf("%lld%lld",&n,&m);
      |     ~~~~~^~~~~~~~~~~~~~~~~~
sequence.cpp:28:31: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   28 |     for(int i=1;i<=n;i++)scanf("%lld",&a[i]),sum[i]=sum[i-1]+a[i],qs[i]=qs[i-1]+a[i]*a[i];
      |                          ~~~~~^~~~~~~~~~~~~~

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