A Possible Tree（裸带权并查集）
问题 I: A Possible Tree
时间限制: 2 Sec 内存限制: 128 MB
提交: 61 解决: 20
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题目描述
Alice knows that Bob has a secret tree (in terms of graph theory) with n nodes with n − 1 weighted edges with integer values in [0, 260 −1]. She knows its structure but does not know the specific information about edge weights.
Thanks to the awakening of Bob’s conscience, Alice gets m conclusions related to his tree. Each conclusion provides three integers u, v and val saying that the exclusive OR (XOR) sum of edge weights in the unique shortest path between u and v is equal to val.
Some conclusions provided might be wrong and Alice wants to find the maximum number W such that the first W given conclusions are compatible. That is say that at least one allocation of edge weights satisfies the first W conclusions all together but no way satisfies all the first W + 1 conclusions (or there are only W conclusions provided in total).
Help Alice find the exact value of W.
输入
The input has several test cases and the first line contains an integer t (1 ≤ t ≤ 30) which is the number of test cases.
For each case, the first line contains two integers n (1 ≤ n ≤ 100000) and c (1 ≤ c ≤ 100000) which are the number of nodes in the tree and the number of conclusions provided. Each of the following n−1 lines contains two integers u and v (1 ≤ u, v ≤ n) indicating an edge in the tree between the u-th node and the v-th node. Each of the following c lines provides a conclusion with three integers u, v and val where 1 ≤ u, v ≤ n and val ∈ [0, 260 − 1].
输出
For each test case, output the integer W in a single line.
样例输入
2
7 5
1 2
2 3
3 4
4 5
5 6
6 7
1 3 1
3 5 0
5 7 1
1 7 1
2 3 2
7 5
1 2
1 3
1 4
3 5
3 6
3 7
2 6 6
4 7 7
6 7 3
5 4 5
2 5 6
样例输出
3
4
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题意：有一棵树，已知树的结构，不知道树的权值，给m次询问，每次询问代表节点a到节点b的权值是否为c，求最多能满足多少组这样的询问。
分析：很明显的并查集，当时太长没做，超级简单超级水。一开始给的n个关于树的结构，是一点用也没有，但是总觉得不放心，打开题解小看一眼，真的是卵用都没有。直接对m次操作搞就行了，一个裸的带权并查集。
1、对于每次询问，并查集逐渐完善这棵树。
2、用sum[i]表示i到根节点所有边权的异或和。
3、并查集维护这个异或和。
4、每次询问都进行判断，如果a,b根节点相同，看一下sum[a]^sum[b]是否等于c。如果不相同，就他们并起来，更新sum[fx]。
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