标签：
Ba Gua Zhen
Time Limit: 1 Sec
Memory Limit: 256 MB
无
2
3 3
1 2 1
1 3 2
2 3 0
6 7
1 2 1
1 3 1
2 3 1
3 4 4
4 5 2
4 6 2
5 6 2
Sample Output
Case #1: 3
Case #2: 3
A XOR takes two bit patterns of equal length and performs the logical exclusive OR operation on each pair of corresponding bits. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1. In this we perform the comparison of two bits, being 1 if the two bits are different, and 0 if they are the same.
题意
有一个n(<=50000)个顶点m(<=100000)条边的无向图，每条边有一个边权(0<=边权<2^60)，求所有回路中边权xor和的最大值。
题解：
首先dfs，跑出所有环的xor值，比如里面有k个环
然后我们就可以转化为，给你k个数，让你选择任意多的数，使得异或值最大
这个要用高斯消元做:http://wenku.baidu.com/link?url=BFic5zoh7tkGkLTgrRta5OtFliMsghlACqlx-XyjMFPgLh14ujAo33SDtLbFhHYN6JoGt2b1d9XsxMP97Degfpb8QzUs_eZJNEwgbhPVScO
代码：
#include<iostream> #include<math.h> #include<vector> #include<stdio.h> #include<cstring> using namespace std; #define maxn 50005 vector<pair<int,long long> >G[maxn]; vector<long long> ans; long long Xor[maxn]; int vis[maxn]; void dfs(int x,int pre,long long Ans) { if(vis[x]) { long long p = Ans ^ Xor[x]; ans.push_back(p); return; } vis[x]=1; for(int i=0;i<G[x].size();i++) { int v = G[x][i].first; if(pre == v)continue; if(!vis[v])Xor[v]=Ans^G[x][i].second; dfs(v,x,Ans ^ G[x][i].second); } } int main() { int t;scanf("%d",&t); for(int cas=1;cas<=t;cas++) { ans.clear(); memset(vis,0,sizeof(vis)); memset(Xor,0,sizeof(Xor)); int n,m;scanf("%d%d",&n,&m); for(int i=1;i<=n;i++) G[i].clear(); for(int i=1;i<=m;i++) { int x,y;long long z; scanf("%d%d%lld",&x,&y,&z); G[x].push_back(make_pair(y,z)); G[y].push_back(make_pair(x,z)); } dfs(1,-1,0); int k=0; for(int i=60;i>=0;i--) { int j; for(j=k;j<ans.size();j++) if((ans[j]&(1LL<<i))!=0) { break; } if (j==ans.size()) continue; if (j!=k) swap(ans[k],ans[j]); //cout<<d[j]<<endl; for (j=k+1;j<ans.size();j++) if ((ans[j]&(1LL<<i))!=0) ans[j]^=ans[k]; k++; } long long Ans = 0; for(int i=0;i<k;i++) Ans = max(Ans,Ans ^ ans[i]); printf("Case #%d: %lld\n",cas,Ans); } }
2015南阳CCPC E - Ba Gua Zhen 高斯消元 xor最大
标签：
原文地址：http://www.cnblogs.com/qscqesze/p/4902518.html
