2115: [Wc2011] Xor(圖上求異或最大值，dfs+線性基)

題目鏈接

題解

 

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 5e4+10,M=1e5+10;
vector<int>G[M];
int a[N];
bool vis[N];
int n,m;
ll ans,dx[N];
vector<ll>num,val[N];
ll p[100];
void dfs(int u,int fa){
	vis[u]=1;
	for(int i=0;i<G[u].size();++i){
		int v = G[u][i];
		ll w1 =val[u][i];
		if(v==fa) continue;
		if(vis[v]){
			num.push_back(dx[u]^dx[v]^w1);
			continue;
		}
		dx[v]=dx[u]^w1;
		dfs(v,u);
	}
}
void insert(ll x){
	for(int i=62;i>=0;--i){
		if((x>>i)&1){
			if(!p[i]){
				p[i]=x;
				break;
			}
			else x^=p[i];
		} 
	}
}
int main()
{
	cin>>n>>m;
	for(int i=1;i<=m;++i){
		int u,v;
		ll w;
		cin>>u>>v>>w;
		G[u].push_back(v);
		G[v].push_back(u);
		val[u].push_back(w);
		val[v].push_back(w);
	}
	dfs(1,0);
	for(int i=0;i<num.size();++i) insert(num[i]);
	ans=dx[n];
	for(int i=62;i>=0;--i){
		if((ans^p[i])>ans)ans^=p[i];
	}
	cout<<ans<<endl;
}