[CF580C]Shortest Cycle(图论，最小环)

Posted 2022-09-15 cnyali-tea

Description:

给 \(n\) 个点的图，点有点权 \(a_i\) ，两点之间有边当且仅当 \(a_i\ \textand\ a_j \not= 0\)，边权为1，求最小环。

Solution:

按每一位考虑若当前这一位为 1 的点超过了 2 个，那么答案就为 3 。

否则只会连一条边，于是最多只有 \(60\) 条边，枚举每条边删掉，求最短路 (边权为1，bfs) 即可。

#include <iostream>
#include <set>
#include <queue>
#include <cstring>
#include <cstdio>
#include <fstream>
 
typedef long long LL;
typedef unsigned long long uLL;
 
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
#define MP(x, y) std::make_pair(x, y)
#define DE(x) cerr << x << endl;
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define GO cerr << "GO" << endl;
 
using namespace std;
 
inline void proc_status()

    ifstream t("/proc/self/status");
    cerr << string(istreambuf_iterator<char>(t), istreambuf_iterator<char>()) << endl;

template<typename T> inline bool chkmin(T &a, T b)  return a > b ? a = b, 1 : 0; 
template<typename T> inline bool chkmax(T &a, T b)  return a < b ? a = b, 1 : 0; 
 
const int maxN = 1e5 + 2;
 
int n;
LL a[maxN];
int dis[maxN];
bool vis[maxN];
int ans(0x3f3f3f3f);
vector<int> g[maxN];
set<pair<int, int> > S;
 
void add(int u, int v)

    g[u].push_back(v);
    g[v].push_back(u);

 
int main()

#ifndef ONLINE_JUDGE
    freopen("xhc.in", "r", stdin);
    freopen("xhc.out", "w", stdout);
#endif
    ios::sync_with_stdio(false);
    cin >> n;
    for (int i = 1; i <= n; ++i)
        cin >> a[i];
    for (int i = 0; i < 62; ++i)
    
        int cnt = 0;
        for (int j = 1; j <= n; ++j)
        
            if (a[j] >> i & 1)
                cnt++;
        
        if (cnt >= 3)
        
            cout << 3 << endl;
            return 0;
        
 
        if (cnt != 2)
            continue;
 
        int first = 0, second = 0;
        for (int j = 1; j <= n; ++j)
            if (a[j] >> i & 1)
            
                if (!first)
                
                    first = j;
                
                else 
                
                    second = j;
                    break;
                
            
        S.insert(MP(first, second));
    
    for (auto p : S)
        add(p.first, p.second);
    for (auto p : S)
    
        int s = p.first, t = p.second;
 
        memset(vis, 0, sizeof vis);
        memset(dis, 0x3f, sizeof dis);
 
        vis[s] = 1;
        queue<int> q;
        q.push(s);
        dis[s] = 0;
 
        while (q.size())
        
            int u = q.front();
            q.pop();
            for (int v : g[u])
            
                if (u == s and v == t) 
                    continue;
                if (!vis[v])
                
                    q.push(v);
                    vis[v] = 1;
                    dis[v] = dis[u] + 1;
                
            
        
        if (dis[t] < 0x3f3f3f3f) chkmin(ans, dis[t] + 1);
    
    if (ans < 0x3f3f3f3f) cout << ans << endl;
    else cout << -1 << endl;
    return 0;