HDU 5424 Rikka with Graph II

题目大意: 在 N 个点 N 条边组成的图中判断是否存在汉密尔顿路径。

思路:忽略重边与自回路，先判断是否连通，否则输出“NO”，DFS搜索是否存在汉密尔顿路径。

include

include

include

include

include

include

include

include

include

using namespace std;
#define INF 0x7fffffff
int n,ans,vis[1010],f[1010],cnt;
vector adj[1010];
#define pii pair<int,int>
map<pii,int> MAP;

int find(int x){
return f[x] == x ? x : f[x] = find(f[x]);
}

void init(){
int i;
for(i=0;i<=n;i++){
adj[i].clear();
f[i] = i;
}
}

void judge(int u) {
vis[u] = 1;
cnt ++;
int d = adj[u].size();
for(int i = 0; i < d; i ++) {
int v = adj[u][i];
if(!vis[v]) {
judge(v);
}
}
}

bool DFS(int u, int cnt) {
vis[u] = 1;
if(cnt == n) return true;
int d = adj[u].size();
for(int i = 0; i < d; i ++) {
int v = adj[u][i];
if(!vis[v]) {
if(DFS(v, cnt + 1)) return true;
vis[v] = 0;
}
}
return false;
}

int main(){
int i,j,a,b,x,y,degree[1010];
while(scanf("%d",&n) == 1){
memset(degree,0,sizeof(degree));
MAP.clear();
init();
for(i=1;i<=n;i++){
scanf("%d%d",&a,&b);
if(MAP.find(make_pair(a,b)) == MAP.end() && MAP.find(make_pair(b,a)) == MAP.end() && a != b){
degree[a] ++;
degree[b] ++;
MAP[make_pair(a,b)] = 1;
MAP[make_pair(b,a)] = 1;
adj[a].push_back(b);
adj[b].push_back(a);
x = find(a);
y = find(b);
if(x != y)
f[x] = y;
}
}
int k,MIN = INF;
for(i=1;i<=n;i++)
if(degree[i] < MIN){
k = i;
MIN = degree[i];
}
int num2 = 0;
for(i=1;i<=n;i++){
if(degree[i] == 1)
num2 ++;
}
if(num2 > 2){
printf("NO\n");
continue ;
}

cnt = 0;
memset(vis,0,sizeof(vis));
judge(1);
if(cnt != n){
printf("NO\n");
continue;
}
memset(vis,0,sizeof(vis));
if(DFS(k,1))
printf("YES\n");
else
printf("NO\n");
}
return 0;
}