【HDU5923 2016CCPC东北地区大学生程序设计竞赛 - 重现赛 B】【并查集 暴力 复杂度计算】Prediction 生效若干条链上的所有边条件下的联通块情况
Prediction
Time Limit: 5000/2500 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 356 Accepted Submission(s): 63
Problem Description
There is a graph
G =\left \langle V_G, E_G \right \rangle with
|V_G| = n
and
|E_G| = m, and a magic tree
T =\left \langle V_T, E_T \right \rangle)
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 \subseteq V_T), and you should tell Mr. Frog the number of components in the modified graph G^` = (V_G, 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：
\bullet v \in S.
\bullet 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 \subseteq V_T), and you should tell Mr. Frog the number of components in the modified graph G^` = (V_G, 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：
\bullet v \in S.
\bullet 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 \leq n \leq 500,1 \leq m \leq 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 \leq q \leq 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 k_i followed by k_i integers representing the set S_i.
It is guarenteed that \sum_{i=1}^{q}k_i \leq 300000 .
For each test case, the first line contains two integers n and m( 1 \leq n \leq 500,1 \leq m \leq 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 \leq q \leq 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 k_i followed by k_i integers representing the set S_i.
It is guarenteed that \sum_{i=1}^{q}k_i \leq 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.
Source
2016CCPC东北地区大学生程序设计竞赛 - 重现赛
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