Submission #1259053

#	Time	Username	Problem	Language	Result	Execution time	Memory
1259053		paulcode	Building Bridges (CEOI17_building)	C++20	0 / 100	57 ms	66120 KiB

building

#include <bits/stdc++.h>
using namespace std;
#define ll long long
const ll dx[4] = {-1,0,1,0}, dy[4] = {0,1,0,-1};
const ll N = 1e6;
const ll INF = 1e18;
ll a[N];
ll h[N] , w[N] , dp[N] , pre[N];
struct line{
   ll a , b = INF;
   ll operator()(ll x)
   {
       return a * x + b;
   }
}st[4 * N];
void up(ll id , ll l , ll r , line cur)
{
    ll mid = (l + r) / 2;
    bool L = cur(l) < st[id](l);
    bool R = cur(mid) < st[id](mid);
    if(l + 1== r) return;
    if(R) swap(cur , st[id]);
    if(L != R)
    {
        up(id * 2 , l , mid , cur);
    }
    else up(id * 2 + 1 , mid , r ,cur);
}
ll get(ll id , ll l, ll r , ll x)
{
    if(l + 1 == r) return st[id](x);
    ll mid = (l + r) / 2;
    if(x < mid) return min(st[id](x) , get(id * 2 , l ,mid , x));
    else return min(st[id](x) , get(id * 2 + 1 , mid , r , x));
}
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    ll n;
    cin >> n;
    for(int i = 1; i <= n ; i++)
    {
        cin >> h[i];
        dp[i] = 1e18;
    }
    for(int i = 1;  i <= n ; i++)
    {
        cin >> w[i];
        pre[i] = pre[i-1] + w[i];
    }
    /*
     dp[i] = dp[j] + (hi - hj)^2 + pre[i] - pre[j-1]
     => đưa về dạng y = a*x + b;
        dp[j] + h[i] * h[i] - 2*h[i] *h[j] + h[i] * h[i] + pre[i-1] - pre[j-1];
        ta thấy với vị trí hiện tại mà i thì dp[i] =  [MIN(-2 * h[j] * h[i] + h[j] * h[j] - pre[j-1] + dp[j])] + h[i] * h[i] + pre[i];
        với vai trò là j thì up(a = -2 * h[j] * h[j] , b = dp[i] + h[j] * h[j] - pre[i];
    */

    dp[1] = 0;
    up(1 , 0 , N , {-2 * h[1] , dp[1] + h[1] * h[1] - pre[1]});
    for(int i = 1 ; i <= n ; i++)
    {
        dp[i] = get(1 , 0 , N , h[i]) + h[i] * h[i] + pre[i-1];
        up(1 , 0 , N ,{ -2 * h[i] , dp[i] + h[i] * h[i] - pre[i]});
    }
    cout<<dp[n]<<'\n';
    return 0;
}
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/

• Subtask 1: 0 / 30
• Subtask 2: 0 / 30
• Subtask 3: 0 / 40