HDU5923——Prediction（数据结构，并查集）
Prediction
Time Limit: 5000/2500 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 476 Accepted Submission(s): 109
Problem Description
There is a graph
G=⟨VG,EG⟩ with
|VG|=n and
|EG|=m, and a magic tree
T=⟨VT,ET⟩) rooted at 1, which contains m vertices.
Each vertex of the magic tree corresponds to an edge in the original graph G and each edge occurs in the magic tree exactly once.
Each query includes a set S(S⊆VT), and you should tell Mr. Frog the number of components in the modified graph G‘=(VG,E‘G), where E‘G is a set of edges in which every edge corresponds to a vertex v in magic tree T satisfying at least one of the following two conditions：
∙v∈S.
∙v is an ancestor of some vertices in S.
Note that the queries are independent, and namely one query will not influence another.
Each vertex of the magic tree corresponds to an edge in the original graph G and each edge occurs in the magic tree exactly once.
Each query includes a set S(S⊆VT), and you should tell Mr. Frog the number of components in the modified graph G‘=(VG,E‘G), where E‘G is a set of edges in which every edge corresponds to a vertex v in magic tree T satisfying at least one of the following two conditions：
∙v∈S.
∙v is an ancestor of some vertices in S.
Note that the queries are independent, and namely one query will not influence another.
Input
The input contains several test cases and the first line of the input data is an integer T, denoting the number of test cases.
For each test case, the first line contains two integers n and m( 1≤n≤500,1≤m≤10000), where n is the number of vertices and m is the number of edges.
The second line contains m - 1 integers describing the magic tree, i-th integer represents the parent of the (i + 1)-th vertex.
Then the following m lines describe the edges of the graph G. Each line contains two integers u and v indicating the two ends of the edge.
The next line contains only one integer q( 1≤q≤50000), indicating the number of queries.
Then the following q lines represent queries, i-th line represents the i-th query, which contains an integer ki followed by ki integers representing the set Si.
It is guarenteed that ∑qi=1ki≤300000.
For each test case, the first line contains two integers n and m( 1≤n≤500,1≤m≤10000), where n is the number of vertices and m is the number of edges.
The second line contains m - 1 integers describing the magic tree, i-th integer represents the parent of the (i + 1)-th vertex.
Then the following m lines describe the edges of the graph G. Each line contains two integers u and v indicating the two ends of the edge.
The next line contains only one integer q( 1≤q≤50000), indicating the number of queries.
Then the following q lines represent queries, i-th line represents the i-th query, which contains an integer ki followed by ki integers representing the set Si.
It is guarenteed that ∑qi=1ki≤300000.
Output
For each case, print a line "Case #x:", where x is the case number (starting from 1).
For each query, output a single line containing only one integer representing the answer, namely the number of components.
For each query, output a single line containing only one integer representing the answer, namely the number of components.
Sample Input
1 5 4 1 1 3 1 2 2 3 3 4 4 5 3 1 2 2 2 3 2 2 4
Sample Output
Case #1: 3 2 1
In the first query, S = {2} and the modified graph G' = {{1, 2, 3, 4}, {(1, 2), (2, 3)}}, thus the number of the components in the modified graph is 3. In the second query, S = {1, 2, 3}, where 1 is the ancestor of 2 (and 3) in the magic tree, and the modified graph G'' = {{1, 2, 3,4}, {(1, 2), (2, 3), (3, 4)}}, therefore the number of the components in the modified graph is 2. In the third query, S = {1, 2, 3, 4}, where 1 is the ancestor of 2 (and 4), 3 is the ancestor of 4, and the modified graph G' = {{1, 2, 3,4}, {(1, 2), (2, 3), (3,4), (4, 5)}}, therefore the answer equals to 1.
Hint
magic tree and the original graph in the sample are:
In the first query, S = {2} and the modified graph G' = {{1, 2, 3, 4}, {(1, 2), (2, 3)}}, thus the number of the components in the modified graph is 3. In the second query, S = {1, 2, 3}, where 1 is the ancestor of 2 (and 3) in the magic tree, and the modified graph G'' = {{1, 2, 3,4}, {(1, 2), (2, 3), (3, 4)}}, therefore the number of the components in the modified graph is 2. In the third query, S = {1, 2, 3, 4}, where 1 is the ancestor of 2 (and 4), 3 is the ancestor of 4, and the modified graph G' = {{1, 2, 3,4}, {(1, 2), (2, 3), (3,4), (4, 5)}}, therefore the answer equals to 1.
题意：分别给你一个有根树还有一个图，有根树得每个节点代表图的一条边。每次询问给你一个集合，把集合里所有的点以及所有点的祖先节点代表得边连起来。问连接后的图中有多少个连通分量
思路：很容易发现，用DFS遍历一棵树的时候。是从祖先遍历到儿子的。那么可以建立m个并查集，在遍历的时候预处理出每一个节点及其祖先节点的并查集。然后查询的时候只需要把这些并查集合并即可。
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