Submission #438849

#	Time	Username	Problem	Language	Result	Execution time	Memory
438849		blue	Building Bridges (CEOI17_building)	C++17	30 / 100	3055 ms	4392 KiB

building

#include <iostream>
using namespace std;

/*
dp[1] = 0
Let dp[i] = the minimum cost to connect pillar 1 and pillar i

dp[i] = min{dp[j] + sq(h[i] - h[j]) + w_sum[i-1] - w_sum[j] | j=1..i-1}
      = min{dp[j] + sq(h[i]) - 2*h[i]*h[j] + sq(h[j]) + w_sum[i-1] - w_sum[j]}
      = sq(h[i]) + w_sum[i-1] + min{    (-2*h[j]) * h[i]      +         (dp[j] + sq(h[j]) - w_sum[j]) }
                                              A     *  X       +               B

*/

const long long INF = 1'000'000'000'000'000'000LL;

long long sq(long long x)
{
    return x*x;
}

int main()
{
    int n;
    cin >> n;

    long long h[n+1];
    for(int i = 1; i <= n; i++) cin >> h[i];

    long long w[n+1], w_sum[n+1];
    w_sum[0] = 0;
    for(int i = 1; i <= n; i++)
    {
        cin >> w[i];
        w_sum[i] = w_sum[i-1] + w[i];
    }

    long long dp[n+1];
    dp[1] = 0;
    for(int i = 2; i <= n; i++)
    {
        dp[i] = INF;
        for(int j = 1; j < i; j++)
            dp[i] = min(dp[i], dp[j] + sq(h[i] - h[j]) + w_sum[i-1] - w_sum[j]);
    }

    cout << dp[n] << '\n';
}

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