BZOJ2753【最小树形图】

最新推荐文章于 2018-12-05 21:02:00 发布

原创最新推荐文章于 2018-12-05 21:02:00 发布 · 687 阅读

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该博客主要介绍了如何解决BZOJ2753问题，涉及最小树形图的构建。文章通过使用Kruskal算法进行边的排序，并通过广度优先搜索确定树的节点数，最后输出最小树形图的权值总和。

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/* I will wait for you*/

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <ctime>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <string>
#define make make_pair
#define fi first
#define se second

using namespace std;

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

const int maxn = 1000010;
const int maxm = 1010;
const int maxs = 26;
const int inf = 0x3f3f3f3f;
const int P = 1000000007;
const double error = 1e-9;

inline int read()
{
	int x = 0, f = 1;
	char ch = getchar();
	while (ch <= 47 || ch >= 58)
		f = (ch == 45 ? -1 : 1), ch = getchar();
	while (ch >= 48 && ch <= 57)
		x = x * 10 + ch - 48, ch = getchar();
	return x * f;
}

struct edge
{
	int u, v, w, next;
} e[2 * maxn];

int n, m, cnt, tmp, head[maxn], vis[maxn], hi[maxn], fa[maxn];
ll ans;

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

void bfs()
{
	queue<int> q; 
	q.push(1), vis[1] = 1;

	while (!q.empty()) {
		int u = q.front(); 
		tmp++, q.pop();

		for (int i = head[u]; i != -1; i = e[i].next) {
			int v = e[i].v;
			if (!vis[v]) 
				vis[v] = 1, q.push(v);
		}
	}
	
	printf("%d ", tmp);
}

bool cmp(edge a, edge b)
{
	return hi[a.v] > hi[b.v] || hi[a.v] == hi[b.v] && a.w < b.w;
}

int find(int u)
{
	return u == fa[u] ? u : fa[u] = find(fa[u]);
}

void kruskal()
{
	sort(e, e + cnt, cmp);

	for (int i = 1; i <= n; i++)
		fa[i] = i;

	for (int i = 0; i < cnt; i++) {
		int u = e[i].u, v = e[i].v;
		if (vis[u] && vis[v]) {
			int fu = find(u), fv = find(v);
			if (fu != fv)
				ans += e[i].w, fa[fu] = fv;
		}
	}

	printf("%lld\n", ans);
}

int main()
{
	n = read(), m = read();
	
	for (int i = 1; i <= n; i++)
		hi[i] = read();

	memset(head, -1, sizeof head);	
	for (int i = 1; i <= m; i++) {
		int u = read(), v = read(), w = read();
		if (hi[u] >= hi[v])
			insert(u, v, w);
		if (hi[v] >= hi[u])
			insert(v, u, w);
	}

	bfs(), kruskal();

	return 0;
}