Submission #1239255

#	Time	Username	Problem	Language	Result	Execution time	Memory
1239255		Aiperiii	Building Bridges (CEOI17_building)	C++17	100 / 100	54 ms	35572 KiB

building

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define all(x) x.begin(),x.end()
#define pb push_back
#define ff first
#define ss second
const int N=1e6+5; //max h value
pair <int,int> t[N*4];
void build(int v,int tl,int tr){
    t[v]={1e9,1e18};
    if(tl!=tr){
        int tm=(tl+tr)/2;
        build(v*2,tl,tm);
        build(v*2+1,tm+1,tr);
    }
}
int f(int m,int x,int c){
    return m*x+c;
}
int get(int v,int tl,int tr,int x){
    if(tl==tr){
        return f(t[v].ff,x,t[v].ss);
    }
    else{
        int tm=(tl+tr)/2;
        if(x<=tm)return min(f(t[v].ff,x,t[v].ss),get(v*2,tl,tm,x));
        else return min(f(t[v].ff,x,t[v].ss),get(v*2+1,tm+1,tr,x));
    }
}

void insert(int v,int tl,int tr,int m,int c){
    if(tl==tr){
        if(f(t[v].ff,tl,t[v].ss)>=f(m,tl,c)){
            t[v]={m,c};
        }
    }
    else{
        if(t[v].ff>m){
            swap(t[v].ff,m);
            swap(t[v].ss,c);
        }
        int tm=(tl+tr)/2;
        if(f(t[v].ff,tm,t[v].ss)<=f(m,tm,c)){
            insert(v*2,tl,tm,m,c);
        }
        else{
            insert(v*2+1,tm+1,tr,t[v].ff,t[v].ss);
            t[v]={m,c};
        }
    }
}
signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    int n;
    cin>>n;
    vector <int> h(n+1),w(n+1),dp(n+1);
    for(int i=1;i<=n;i++){
        cin>>h[i];
    }
    int sum=0;
    for(int i=1;i<=n;i++){
        cin>>w[i];
        sum+=w[i];
    }
    build(1,1,1e6);
    dp[1]=-w[1];
    insert(1,1,1e6,-2*h[1],dp[1]+h[1]*h[1]);
    for(int i=2;i<=n;i++){
        dp[i]=h[i]*h[i]-w[i]+get(1,1,1e6,h[i]);
        insert(1,1,1e6,-2*h[i],dp[i]+h[i]*h[i]);
    }
    cout<<dp[n]+sum<<"\n";
}

/*
dp[i]=dp[j]+(h[j]-h[i])^2-w[i];
dp[i]=(h[i])^2-w[i];

dp[j]+h[j]^2-2*h[i]*h[j]
 
 y=mx+c
 m=-2*h[j]
 x=h[i]
 c=dp[j]+h[j]^2
 y=-2*h[j]*h[i]+dp[j]+h[j]^2
*/

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