【拓扑】【堆】【DFS】我的世界

$Link$

$luoguT145121$

$Description$

$Sample$ $Input$

4 
3 1
1 2 
4 2

$Sample$ $Output$

3 2 4 1

$Hint$

$Solution$

其实很好发现，肯定是点之间两两配对才行，那么我们从叶子节点出发，与它父亲配对，然后将这两个点标记，然后继续弄
然后再将配对的点与其他点连边啥的，得到一个图，再搞一下拓扑排序，用堆维护，每次取最小编号就好了

$Code$

#include 
#include
#include
#include

using namespace std;
priority_queue< int,vector<int>,greater<int> >d;

int t, n, e, tt;
int ans[500005], ru[500005];
int hh[500005], h[500005], link[500005];

int read() 
{
	int x = 0, flag = 1; char ch = getchar();
	while (ch < '0' || ch > '9') {if (ch == '-') flag = -1; ch = getchar();}
	while (ch >= '0' && ch <= '9'){x = x * 10 + ch - '0'; ch = getchar();}
	return x * flag;
}

void write(int x)
{
    if (x < 0) { 
		x = -x; 
		putchar('-');
	}
	if (x > 9) write(x / 10);
	putchar(x % 10 + 48);
	return;
}

struct node
{
	int to, next;
}w[1000005];

struct nodex
{
	int to, next;
}p[1000005];

void addx(int x, int y)
{p[++e] = (nodex){y, hh[x]}; hh[x] = e;}

void add(int x, int y)
{
	w[++t] = (node){y, h[x]}; h[x] = t;
	w[++t] = (node){x, h[y]}; h[y] = t;
}

void build(int x, int fath)
{
	for (int i = h[x]; i; i = w[i].next)
		if (w[i].to != fath) build(w[i].to, x);
	if (link[fath] || link[x]) return;
	link[x] = fath; link[fath] = x;
	for (int i = h[fath]; i; i = w[i].next)
		if (w[i].to != x) 
			ru[w[i].to]++, addx(x, w[i].to);
	for (int i = h[x]; i; i = w[i].next)
		if (w[i].to != fath)
			ru[w[i].to]++, addx(fath, w[i].to);
}

int main()
{
	n = read();
	if (n % 2) {printf("-1"); return 0;}
	for (int i = 1; i < n; ++i)
	{
		int u, v;
		u = read(); v = read();
		add(u, v);
	}
	build(1, 0);
	for (int i = 1; i <= n; ++i)
		if (!link[i]) {
			putchar('-');
			putchar('1');
			return 0;
		}
	for (int i = 1; i <= n; ++i)
		if (!ru[i]) d.push(i);
	for (int i = 1; i <= n; ++i)
	{
		ans[i] = d.top();
		d.pop();
		for (int k = hh[ans[i]]; k; k = p[k].next)
		{
			ru[p[k].to]--;
			if (!ru[p[k].to]) 
				d.push(p[k].to);
		}
	}
	for (int i = 1; i <= n; ++i)
		write(ans[i]), putchar(' ');
	return 0;
}