Submission #66736458

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#include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
using namespace std;
struct Edge {
    int to;
    long long weight;
};
vector<vector<Edge>> adj;
vector<long long> dist;
vector<long long> cycle_basis;
// DFSで基準パスとサイクルを見つける
void find_path_and_cycles(int u) {
    for (const auto& edge : adj[u]) {
        int v = edge.to;
        long long w = edge.weight;
 
 
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#include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>

using namespace std;

struct Edge {
    int to;
    long long weight;
};

vector<vector<Edge>> adj;
vector<long long> dist;
vector<long long> cycle_basis;

// DFSで基準パスとサイクルを見つける
void find_path_and_cycles(int u) {
    for (const auto& edge : adj[u]) {
        int v = edge.to;
        long long w = edge.weight;
        if (dist[v] != -1) {
            // vは訪問済み -> サイクルを発見
            cycle_basis.push_back(dist[u] ^ w ^ dist[v]);
        } else {
            // vは未訪問
            dist[v] = dist[u] ^ w;
            find_path_and_cycles(v);
        }
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int N, M;
    cin >> N >> M;

    adj.resize(N + 1);
    for (int i = 0; i < M; ++i) {
        int u, v;
        long long w;
        cin >> u >> v >> w;
        adj[u].push_back({v, w});
        adj[v].push_back({u, w}); // 問題文は有向グラフだが、サイクルは無向で考えて良いため両方向に追加
    }

    dist.assign(N + 1, -1);
    dist[1] = 0;
    find_path_and_cycles(1);

    if (dist[N] == -1) {
        cout << -1 << endl;
        return 0;
    }

    // XOR基底を構築
    vector<long long> basis;
    for (long long val : cycle_basis) {
        for (long long b : basis) {
            val = min(val, val ^ b);
        }
        if (val > 0) {
            basis.push_back(val);
        }
    }
    
    // 基準パスのXOR和を基底で最小化
    long long result = dist[N];
    for (long long b : basis) {
        result = min(result, result ^ b);
    }

    cout << result << endl;

    return 0;
}

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