A Possible Tree（ICPC2017 Urumqi）
A Possible Tree
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.
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].
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
题意：问从前面开始不冲突的个数
Get 新知识点：带权并查集
这道题就是带权并查集的模本题啊
注意 ^ 的优先级 小于 !=
AC code:
#include <bits/stdc++.h> using namespace std; typedef long long ll; const int N = 1e5 + 10; int pre[N]; ll r[N]; int n; void init() { for(int i = 1;i <= n;i++) pre[i] = i,r[i] = 0; } int find(int x) { if(x == pre[x]) return x; int prex = pre[x]; pre[x] = find(prex); r[x] = r[x]^r[prex]; return pre[x]; } int add(int x,int y,ll val) { int prex = find(x),prey = find(y); if(prex == prey) { if((r[x]^r[y]) != val) return 0; } else { pre[prex] = prey; r[prex] = r[x]^r[y]^val; } return 1; } int main() { int t; scanf("%d",&t); while(t--) { int m,u,v; ll val; scanf("%d%d",&n,&m); init(); for(int i = 1;i < n;i++) scanf("%d%d",&u,&v); int ans = m,flag = 0; for(int i = 0;i < m;i++) { scanf("%d%d%lld",&u,&v,&val); if(!flag&&!add(u,v,val)) ans = i,flag = 1; } printf("%d\n",ans); } return 0; }
