弱省胡策 Round 3 Avalon【可并堆】【计算几何】

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本文深入探讨了一种基于复杂图结构的算法实现细节，通过优先队列和其他数据结构的应用，解决了一个特定问题。该算法涉及图遍历、优先级排序等关键技术，并在实际应用中考虑了性能优化。

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#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <map>
#include <ext/pb_ds/priority_queue.hpp>

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;

const int maxn = 1000010;
const int inf = 0x3f3f3f3f;

inline ll read()
{
	ll x = 0, f = 1; char c = getchar();
	while (c < '0' || c > '9')
		f = (c == '-' ? -1 : 1), c = getchar();
	while (c >= '0' && c <= '9')
		x = x * 10 + c - '0', c = getchar();
	return x * f;
}

__gnu_pbds::priority_queue<pii> Pb[maxn], Pr[maxn];

struct edge
{
	int v, next;
} e[maxn];

struct point
{
	double x, y; int w;
} p[maxn];

struct query
{
	double the; int pr;
}arc[maxn];

int n, k, l, cnt, b[maxn], r[maxn], pr[maxn], 
    head[maxn], fa[maxn], in[maxn], deep[maxn];
ll B[maxn], R[maxn];

void insert(int u, int v)
{
	e[cnt] = (edge) {v, head[u]}, head[u] = cnt++;
}

void dfs(int u)
{
	Pb[u].push(make_pair(deep[u], b[u]));
	Pr[u].push(make_pair(deep[u], r[u]));

	for (int i = head[u]; i != -1; i = e[i].next) {
		int v = e[i].v;
		deep[v] = deep[u] + 1, dfs(v);
		Pb[u].join(Pb[v]), B[u] += B[v];  
		Pr[u].join(Pr[v]), R[u] += R[v];
	}

	while (Pb[u].top().first - k >= deep[u])
		B[u] -= Pb[u].top().second, Pb[u].pop();
	while (Pr[u].top().first - k >= deep[u])
		R[u] -= Pr[u].top().second, Pr[u].pop();
}

double dis(point a, point b)
{
	double x = a.x - b.x, y = a.y - b.y;
	return sqrt(x * x + y * y);
}

bool cmp(query a, query b)
{
	return a.the < b.the || a.the == b.the && a.pr > b.pr;
}

void Max_Circle_Cover()
{
	ll ans = 0;
	
	for (int i = 0; i < cnt; i++) {
		int sum = 0;
		for (int j = 0; j < cnt; j++)
			if (i != j && dis(p[i], p[j]) <= 2.0 * l) {
				double the = atan2((p[i].y - p[j].y), (p[i].x - p[j].x));
				double phi = acos(dis(p[i], p[j]) / (2.0 * l));
				arc[sum++] = (query) {the - phi, p[j].w};
				arc[sum++] = (query) {the + phi, -p[j].w};
			}
		sort(arc, arc + sum, cmp);

		ll tmp = p[i].w;
		for (int j = 0; j < sum; j++) {
		    tmp += arc[j].pr;
			ans = max(ans, tmp);
		}
	}

	cout << ans << endl;
}

int main()
{
	freopen("sample.in", "r", stdin);

	n = read(), k = read(), l = read();

	memset(head, -1, sizeof head);

	for (int i = 1; i <= n; i++) {
		b[i] = B[i] = read();
		r[i] = R[i] = read();
	       	pr[i] = read();
		fa[i] = read();
	       	in[i] = read();
		if (fa[i] != -1)
			insert(fa[i], i);
	}

	dfs(1), cnt = 0;

	for (int i = 1; i <= n; i++)
		if (in[i] == 1)
			p[cnt++] = (point) {B[i], R[i], pr[i]};

	Max_Circle_Cover();

	return 0;
}