北大考研复试上机——Is It A Tree?

A tree is a well-known data structure that is either empty (null, void, nothing) or is a set of one or more nodes connected by directed edges between nodes satisfying the following properties.There is exactly one node, called the root, to which no directed edges point. Every node except the root has exactly one edge pointing to it. There is a unique sequence of directed edges from the root to each node. For example, consider the illustrations below, in which nodes are represented by circles and edges are represented by lines with arrowheads. The first two of these are trees, but the last is not. In this problem you will be given several descriptions of collections of nodes connected by directed edges. For each of these you are to determine if the collection satisfies the definition of a tree or not.

输入描述:

The input will consist of a sequence of descriptions (test cases) followed by a pair of negative integers. Each test case will consist of a sequence of edge descriptions followed by a pair of zeroes Each edge description will consist of a pair of integers; the first integer identifies the node from which the edge begins, and the second integer identifies the node to which the edge is directed. Node numbers will always be greater than zero and less than 10000.

输出描述:

For each test case display the line "Case k is a tree." or the line "Case k is not a tree.", where k corresponds to the test case number (they are sequentially numbered starting with 1).

示例1

输入

6 8  5 3  5 2  6 4
5 6  0 0

8 1  7 3  6 2  8 9  7 5
7 4  7 8  7 6  0 0

3 8  6 8  6 4
5 3  5 6  5 2  0 0
-1 -1

输出

Case 1 is a tree.
Case 2 is a tree.
Case 3 is not a tree.

    思路：看了一些别人的代码，似乎都是用出度入度解决的，但是这种解决方法并不能处理有环的情况。比如对于数据：

 

  1 2 2 3 3 4 4 5 5 1 6 7 0 0

    这组数据。

    因此我的思路不是这样的。我的方法是

    ①先判断是不是空树，如果是空树（直接输入两个0），就直接判断是树；

    ②然后找这棵树的根节点，如果有一个节点它的入度为0而出度不为0，那它就是根节点，如果没有找到这样的结点就判断它不是树；

    ③在找到一个根节点之后，用广度优先遍历的方法，通过根节点遍历一遍这棵树，如果两次遍历到同一个结点，那就说明这个结点的入度不是1，这就不是树；

    ④广度优先遍历结束之后，如果所有的结点都被访问过了，那就说明这是树，否则就不是树（不是连通的）。

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