In this problem, a tree is an undirected graph that is connected and has no cycles.
The given input is a graph that started as a tree with N nodes (with distinct values 1, 2, …, N), with one additional edge added. The added edge has two different vertices chosen from 1 to N, and was not an edge that already existed.
The resulting graph is given as a 2D-array of edges. Each element of edges is a pair [u, v] with u < v, that represents an undirected edge connecting nodes u and v.
Return an edge that can be removed so that the resulting graph is a tree of N nodes. If there are multiple answers, return the answer that occurs last in the given 2D-array. The answer edge [u, v] should be in the same format, with u < v.
Example 1:Input: [[1,2], [1,3], [2,3]] Output: [2,3] Explanation: The given undirected graph will be like this: 1 / \ 2 - 3
Example 2:Input: [[1,2], [2,3], [3,4], [1,4], [1,5]] Output: [1,4] Explanation: The given undirected graph will be like this: 5 - 1 - 2 | | 4 - 3
Note:The size of the input 2D-array will be between 3 and 1000.Every integer represented in the 2D-array will be between 1 and N, where N is the size of the input array.
这道题用并查集可以很容易地解决。 遍历每一个 edge ，如果第二个顶点所在的树的根结点与第一个结点的根结点不相同，说明在当前构建的树中还不存在路径把两个顶点连接起来，则把当前 edge 的第二个顶点所在的树合并到第一个顶点的树中，使这两个顶点具有相同的根结点，这样就表示找到了一条路径可以连接当前 edge 的两个顶点； 如果第二个顶点所在的树的根结点与第一个结点的根结点相同，说明在前面的构建树的过程中，已经找到路径连接这两个顶点了，因此当前的这个 edge 就是冗余的，可以删掉。把当前的 edge 作为结果返回即可。 （注意一旦找到了冗余的 edge ，则这个 edge 肯定就是 the answer that occurs last in the given 2D-array，用题目的例子细细推导一下就可以知道）