Submission #46981

#	Time	Username	Problem	Language	Result	Execution time	Memory
46981		dqhungdl	Building Bridges (CEOI17_building)	C++17	100 / 100	119 ms	78036 KiB

building

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

typedef pair<int64_t,int64_t> ii;
int64_t n,a[100005],b[100005],F[100005];
ii tree[4000005];

int64_t f(ii line,int64_t x)
{
    return line.first*x+line.second;
}

void Update(int64_t k,int64_t l,int64_t r,ii line)
{
    int64_t mid=(l+r)/2;
    bool cleft=(f(line,l)<f(tree[k],l));
    bool cmid=(f(line,mid)<f(tree[k],mid));
    if(cmid==true)
        swap(tree[k],line);
    if(r-l==1)
        return;
    if(cleft!=cmid)
        Update(2*k,l,mid,line);
    else
        Update(2*k+1,mid,r,line);
}

int64_t Query(int64_t k,int64_t l,int64_t r,int64_t x)
{
    int64_t mid=(l+r)/2;
    if(r-l==1)
        return f(tree[k],x);
    if(x<=mid)
        return min(Query(2*k,l,mid,x),f(tree[k],x));
    return min(Query(2*k+1,mid,r,x),f(tree[k],x));
}

void Naive()
{
    for(int64_t i=2;i<=n;i++)
    {
        F[i]=1e15;
        for(int64_t j=1;j<i;j++)
            F[i]=min(F[i],F[j]+(a[i]-a[j])*(a[i]-a[j])+b[i-1]-b[j]);
    }
    for(int64_t i=1;i<=n;i++)
        cout<<F[i]<<' ';
    exit(0);
}

int main()
{
    ios_base::sync_with_stdio(false);
    //freopen("TEST.INP","r",stdin);
    cin>>n;
    for(int64_t i=1;i<=n;i++)
        cin>>a[i];
    for(int64_t i=1;i<=n;i++)
    {
        cin>>b[i];
        b[i]+=b[i-1];
    }
    //Naive();
    for(int64_t i=1;i<=4e6;i++)
        tree[i]=ii(0,1e15);
    Update(1,0,1e6,ii(-2*a[1],F[1]+a[1]*a[1]-b[1]));
    for(int64_t i=2;i<=n;i++)
    {
        F[i]=Query(1,0,1e6,a[i])+a[i]*a[i]+b[i-1];
        Update(1,0,1e6,ii(-2*a[i],F[i]+a[i]*a[i]-b[i]));
    }
    cout<<F[n];
}

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40