poj1637

maksyuki 发表于 oj 分类，标签:
07 2月 2016
0

Sightseeing tour

The city executive board in Lund wants to construct a sightseeing tour by bus in Lund, so that tourists can see every corner of the beautiful city. They want to construct the tour so that every street in the city is visited exactly once. The bus should also start and end at the same junction. As in any city, the streets are either one-way or two-way, traffic rules that must be obeyed by the tour bus. Help the executive board and determine if it's possible to construct a sightseeing tour under these constraints.

Input

On the first line of the input is a single positive integer n, telling the number of test scenarios to follow. Each scenario begins with a line containing two positive integers m and s, 1 <= m <= 200,1 <= s <= 1000 being the number of junctions and streets, respectively. The following s lines contain the streets. Each street is described with three integers, xi, yi, and di, 1 <= xi,yi <= m, 0 <= di <= 1, where xi and yi are the junctions connected by a street. If di=1, then the street is a one-way street (going from xi to yi), otherwise it's a two-way street. You may assume that there exists a junction from where all other junctions can be reached.

Output

For each scenario, output one line containing the text "possible" or "impossible", whether or not it's possible to construct a sightseeing tour.

Sample Input

4
5 8
2 1 0
1 3 0
4 1 1
1 5 0
5 4 1
3 4 0
4 2 1
2 2 0
4 4
1 2 1
2 3 0
3 4 0
1 4 1
3 3
1 2 0
2 3 0
3 2 0
3 4
1 2 0
2 3 1
1 2 0
3 2 0

Sample Output

possible

impossible

impossible

possible

Source

Northwestern Europe 2003

 

题目类型：混合图欧拉回路

算法分析：给原图中的每个无向边指定一个方向并看作是有向边。然后记录有向边两个端点的出入度并建图。若存在一个顶点的出入度之差是奇数，则一定不可能存在欧拉回路。否则从入度大于出度的顶点向汇点连接一条边，边权为出入度之差的绝对值除以2，从源点向入度小于出度的顶点连接一条边，边权为出入度之差的绝对值除以2。最后跑一个最大流判断是否满流即可。详细内容可以参考： http://www.cnblogs.com/kuangbin/p/3537525.html