【集训DAY16】ALFA【凸壳】【计算几何】

思路：

先同时除以x，然后用凸壳维护，答案二分一下就行了

$code$

#include<iostream>
#include<cstdio>
#include<algorithm>

using namespace std;

const long long MAXN = 5e5 + 10;

long long n, q, tota, totb;
pair<long long, long long> a[MAXN], b[MAXN], ca[MAXN], cb[MAXN];

long long cj(long long x, long long x1, long long y, long long y1) {
    
	return (y - y1) * (x - x1);
}

void doa() {
    
	sort(a + 1, a + 1 + n);
	for(long long i = 1; i <= n; i ++) {
    
		while(tota >= 1 && ca[tota].first == a[i].first 
		|| tota >= 2 && cj(a[i].first, ca[tota - 1].first, ca[tota - 1].second, ca[tota].second) >= 
		cj(ca[tota].first, ca[tota - 1].first, ca[tota - 1].second, a[i].second))
			tota --;
		ca[++ tota] = a[i];
	}
}

void dob() {
    
	sort(b + 1, b + 1 + n);
	for(long long i = 1; i <= n; i ++) {
    
		while(totb >= 1 && cb[totb].first == b[i].first 
		|| totb >= 2 && cj(b[i].first, cb[totb - 1].first, cb[totb - 1].second, cb[totb].second) >= 
		cj(cb[totb].first, cb[totb - 1].first, cb[totb - 1].second, b[i].second))
			totb --;
		cb[++ totb] = b[i];
	}
}


int main() {
    
// freopen("a.in", "r", stdin);
// freopen("a.out", "w", stdout);
	scanf("%lld%lld", &n, &q);
	for(long long i = 1; i <= n; i ++) {
    
		long long x, y;
		scanf("%lld%lld", &x, &y);
		a[i] = make_pair(x, y);
		b[i] = make_pair(-x, -y);
	}
	doa();
	dob();
	while(q --) {
    
		long long x;
		scanf("%lld", &x);
		if(x > 0) {
    
			long long l = 1, r = tota;
			while(l < r) {
    
				long long mid = l + r >> 1;
				if(ca[mid].first * x + ca[mid].second > ca[mid + 1].first * x + ca[mid + 1].second)
					r = mid;
				else l = mid + 1;
			}
			printf("%lld\n", ca[l].first * x * x + ca[l].second * x);
		}
		else if(x < 0) {
    
			long long l = 1, r = totb;
			while(l < r) {
    
				long long mid = l + r >> 1;
				if(cb[mid].first * x + cb[mid].second > cb[mid + 1].first * x + cb[mid + 1].second)
					r = mid;
				else l = mid + 1;
			}
			printf("%lld\n", - cb[l].first * x * x - cb[l].second * x);
		}
		else printf("0\n");
	}
	return 0;
}