POJ3687 Labeling Balls【优先队列+反向拓扑排序】

Description

Windy has N balls of distinct weights from 1 unit to N units. Now he tries to label them with 1 to N in such a way that:

1. No two balls share the same label.
2. The labeling satisfies several constrains like "The ball labeled with a is lighter than the one labeled with b".

Can you help windy to find a solution?

Input

The first line of input is the number of test case. The first line of each test case contains two integers, N (1 ≤ N ≤ 200) and M (0 ≤ M ≤ 40,000). The next M line each contain two integers a and b indicating the ball labeled with a must be lighter than the one labeled with b. (1 ≤ a, b ≤ N) There is a blank line before each test case.

Output

For each test case output on a single line the balls' weights from label 1 to label N. If several solutions exist, you should output the one with the smallest weight for label 1, then with the smallest weight for label 2, then with the smallest weight for label 3 and so on... If no solution exists, output -1 instead.

Sample Input

5

4 0

4 1
1 1

4 2
1 2
2 1

4 1
2 1

4 1
3 2

Sample Output

1 2 3 4
-1
-1
2 1 3 4
1 3 2 4

解题思路

题目大意：这道题目的意思比较难理解，在基本的拓扑排序的基础上又增加了一个要求：编号最小的节点要尽量排在前面；在满足上一个条件的基础上，编号第二小的节点要尽量排在前面；在满足前两个条件的基础上，编号第三小的节点要尽量排在前面……依此类推。（注意，这和字典序是两回事，不可以混淆。）参考博文：博文

思路：如上面参考博文提到的一样，我们这里得采用反向拓扑排序，然后使用优先队列，保证编号大的点先出队列。（这里的反向拓扑排序指的是，我们先挑出出度为0的点）。这里要注意，输入的边可能会有重边，即一条边出现两次，此时不能再去增加一遍出度。

代码

#include
#include
#include
using namespace std;
#define MAXN 210

int t, n, m;
int map[MAXN][MAXN], outdegree[MAXN], ans[MAXN];

int topoSort()
{
	priority_queue q;
	int num = n;
	for (int i = 1; i <= n; i++)
	{
		if (outdegree[i] == 0)
			q.push(i);
	}
	while (!q.empty())
	{
		int u = q.top();
		ans[num--] = u;
		q.pop();
		for (int j = 1; j <= n; j++)
		{
			if (map[j][u])
			{
				outdegree[j]--;
				if (outdegree[j] == 0)
					q.push(j);
			}
		}
	}
	if (num != 0)
		return 0;
	else return 1;
}

int main()
{
	scanf("%d", &t);
	while (t--)
	{
		scanf("%d%d", &n, &m);
		memset(map, 0, sizeof(map));
		memset(outdegree, 0, sizeof(outdegree));
		memset(ans, 0, sizeof(ans));
		for (int i = 1; i <= m; i++)
		{
			int a, b;
			scanf("%d%d", &a, &b);
			if (!map[a][b])
			{
				map[a][b] = 1;
				outdegree[a]++;
			}
		}
		if (!topoSort())
		{
			printf("-1\n");
		}
		else
		{
			int tmp[MAXN];
			for (int i = 1; i <= n; i++)
				tmp[ans[i]] = i;
			for (int i = 1; i <= n; i++)
			{
				if (i != n)
					printf("%d ", tmp[i]);
				else printf("%d\n", tmp[i]);
			}
		}
	}
	return 0;
}