hdu 5424 回溯+并查集判断连通性

题意：给定一个n个点n条边的无向图，判断是否存在哈密顿路径。

思路：先用并查集判断图是否连通，然后从度数最小的点开始回溯，看是否能找到一条哈密顿路径。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <set>
using namespace std;

const int INF = 999999;
const int N = 1001;
int f[N];
int d[N];
int head[N];
bool visit[N];
int n, e;

void init()
{
    e = 0;
    memset( d, 0, sizeof(d) );
    memset( head, -1, sizeof(head) );
    memset( visit, 0, sizeof(visit) );
    for ( int i = 1; i < N; i++ ) f[i] = i;
}

struct Edge
{
    int v, next;
} edge[N << 1];

void addEdge( int u, int v )
{
    edge[e].v = v;
    edge[e].next = head[u];
    head[u] = e++;
}

int findf( int x )
{
    if ( f[x] != x ) f[x] = findf( f[x] );
    return f[x];
}

bool union_set( int x, int y )
{
    x = findf(x), y = findf(y);
    if ( x == y )
    {
        return false;
    }
    else
    {
        f[x] = y;
        return true;
    }
}

bool dfs( int u, int cnt )
{
    if ( cnt == n ) return true;
    for ( int i = head[u]; i != -1; i = edge[i].next )
    {
        int v = edge[i].v;
        if ( !visit[v] )
        {
            visit[v] = 1;
            if ( dfs( v, cnt + 1 ) ) return true;
            visit[v] = 0;
        }
    }
    return false;
}

int main ()
{
    while ( scanf("%d", &n) != EOF )
    {
        init();
        int c = 0;
        for ( int i = 1; i <= n; i++ )
        {
            int u, v;
            scanf("%d%d", &u, &v);
            addEdge( u, v );
            addEdge( v, u );
            d[u]++, d[v]++;
            if ( union_set( u, v ) ) c++;
        }
        if ( c != n - 1 )
        {
            puts("NO");
            continue;
        }
        d[0] = INF;       
        int k = 0;
        for ( int i = 1; i <= n; i++ )
        {
            if ( d[i] < d[k] )
            {
                k = i;
            }
        } 
        visit[k] = 1;
        if ( dfs( k, 1 ) )
        {
            puts("YES");
        }
        else
        {
            puts("NO");
        }
    }
    return 0;
}