Rikka with Tree

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

For a tree T, let F(T,i) be the distance between vertice 1 and vertice i.(The length of each edge is 1).

Two trees A and B are similiar if and only if the have same number of vertices and for each i meet F(A,i)=F(B,i).

Two trees A and B are different if and only if they have different numbers of vertices or there exist an numberi which vertice i have different fathers in tree A and tree B when vertice 1 is root.

Tree A is special if and only if there doesn‘t exist an tree B which A and B are different and A and B are similiar.

Now he wants to know if a tree is special.

It is too difficult for Rikka. Can you help her?

There are no more than 100 testcases.

For each testcase, the first line contains a number n(1≤n≤1000).

Then n?1 lines follow. Each line contains two numbers u,v(1≤u,v≤n) , which means there is an edge between u and v.

3
1 2
2 3
4
1 2
2 3
1 4

YES
NO

Hint
For the second testcase, this tree is similiar with the given tree:
4
1 2
1 4
3 4
 

只要，每层结点数是1  1 1 .... x的结构的树，就一定是唯一的。

#define N 1005
#define M 100005
#define maxn 205
#define MOD 1000000000000000007
int n,a,b,num[N],depth;
vector<int> p[N];
queue<int> q;
bool vis[N];
void DFS(int top,int step){
    num[step]++;
    vis[top] = true;
    depth = max(depth,step);
    FI(p[top].size()){
        int goal = p[top][i];
        if(!vis[goal]){
            DFS(goal,step+1);
        }
    }
}
bool BFS(){
    fill(vis,false);
    fill(num,0);
    depth = 0;
    DFS(1,0);
    FI(depth+1){
        if(num[i] >= 2 && i != depth) return false;
    }
    return true;
}
int main()
{
    //freopen("in.txt", "r", stdin);
    //freopen("out.txt", "w", stdout);
     while(S(n)!=EOF)
    {
        FI(n+1)   p[i].clear();
        FI(n-1){
            S2(a,b);
            p[a].push_back(b);
            p[b].push_back(a);
        }
        if(BFS())
            printf("YES\n");
        else
            printf("NO\n");
    }
    //fclose(stdin);
    //fclose(stdout);
    return 0;
}

hdu 5423 Rikka with Tree 树的性质

原文：http://blog.csdn.net/mengzhengnan/article/details/48094099