CF Round#782 C - Line Empire

C - Line Empire

贪心

1. 每次征服一个国家之后，如果要将首都迁过来，显然之后迁不如现在迁

2. 在征服第 i 个国家后，可利用前缀和 \(O(1)\) 算出 迁或不迁 时征服之后国家的代价，若迁的代价小就迁，否则就不迁

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;
typedef long long ll;
const int N = 2e5 + 10;
ll n, a, b;
ll c[N], s[N];

int main()
{
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	int T;
	cin >> T;
	while(T--)
	{
		cin >> n >> a >> b;
		for (int i = 1; i <= n; i++)
		{
			cin >> c[i];
			s[i] = s[i-1] + c[i];
		}
		int now = 0;
		ll ans = 0;
		for (int i = 1; i <= n; i++)
		{
			ans += b * (c[i] - c[now]);
			int cnt = n - i;
			ll cost1 = a * (c[i] - c[now]) + b * (s[n] - s[i] - cnt * c[i]);
			ll cost2 = b * (s[n] - s[i] - cnt * c[now]);
			if (cost1 <= cost2)
			{
				ans += a * (c[i] - c[now]);
				now = i;
			}
		}
		cout << ans << endl;
	}
	return 0;
}