HDU 5379 Mahjong tree （详解，构造+思维）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5379

题面：

Mahjong tree

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1148    Accepted Submission(s): 351

Problem Description

Little sun is an artist. Today he is playing mahjong alone. He suddenly feels that the tree in the yard doesn't look good. So he wants to decorate the tree.（The tree has n vertexs, indexed from 1 to n.）
Thought for a long time, finally he decides to use the mahjong to decorate the tree.
His mahjong is strange because all of the mahjong tiles had a distinct index.（Little sun has only n mahjong tiles, and the mahjong tiles indexed from 1 to n.）
He put the mahjong tiles on the vertexs of the tree.
As is known to all, little sun is an artist. So he want to decorate the tree as beautiful as possible.
His decoration rules are as follows:

(1)Place exact one mahjong tile on each vertex.
(2)The mahjong tiles' index must be continues which are placed on the son vertexs of a vertex.
(3)The mahjong tiles' index must be continues which are placed on the vertexs of any subtrees.

Now he want to know that he can obtain how many different beautiful mahjong tree using these rules, because of the answer can be very large, you need output the answer modulo 1e9 + 7.

 

Input

The first line of the input is a single integer T, indicates the number of test cases.
For each test case, the first line contains an integers n. (1 <= n <= 100000)
And the next n - 1 lines, each line contains two integers ui and vi, which describes an edge of the tree, and vertex 1 is the root of the tree.

 

Output

For each test case, output one line. The output format is "Case #x: ans"(without quotes), x is the case number, starting from 1.

 

Sample Input

292 13 14 35 36 27 48 79 382 13 14 35 16 47 58 4

 

Sample Output

Case #1: 32Case #2: 16

 

Source

2015 Multi-University Training Contest 7

 

解题：

    可以分析一下当每个节点分别有几个叶子和几个继续向下的孩子时的情况，全部累乘就好。详细可以见代码。

总结：

    这题犯了两个致命错误.

    1.天真的以为给定的边都是儿子连向父亲的，本来也觉得不妥，题目没说，可是还是天真的写了下去...不可断章取义啊！！

    2.分析出若某个点有三个可以继续往下的节点，那么这种情况是不合法的，居然，就不管了，当时真是晕了头了，应该输出0才对啊！！

综上，自己实在是太天真了....

代码：

#include <iostream>#include <cstdio>#include <queue>#include <vector>#include <cstring>#define MOD 1000000007using namespace std;long long ans;struct node{    int id;//存真正的孩子    vector <int> child;//存相邻的边vector <int> edge;    int num;}store[100010];queue <int> qe;bool flag;bool vis[100010];void bfs(int x){while(!qe.empty())qe.pop();//先访问的是父亲memset(vis,0,sizeof(vis));    int sz,yezi,qujian;    qe.push(x);    int tmp;    while(!qe.empty())    {//叶子和区间数        yezi=qujian=0;        tmp=qe.front();        qe.pop();//标记为访问过vis[tmp]=1;        sz=store[tmp].num;for(int i=0;i<sz;i++){//如果没访问过，说明是孩子if(!vis[store[tmp].edge[i]]){vis[store[tmp].edge[i]]=1;store[tmp].child.push_back(store[tmp].edge[i]);}}sz=store[tmp].child.size();        for(int i=0;i<sz;i++)        {//不是叶子节点，是还能往下的节点//叶子节点只有其父亲连向它的边，而根节点虽然也是，但不会出现在这里            if(store[store[tmp].child[i]].num>1)            {                qujian++;                qe.push(store[tmp].child[i]);            }            else            {                yezi++;            }        }//开始这里没特判，太理想化了，一个节点有超过三个点还能继续向下，那么答案为0if(qujian>=3){flag=true;return;}//全是叶子节点，全排列        if(yezi==sz)        {            for(int i=1;i<=sz;i++)              ans=ans*i%MOD;        }//一个区间，其他全叶子，只能叶子一边，区间一边//两边互换，叶子全排列        else if(yezi==sz-1)        {            ans=ans*2%MOD;            for(int i=1;i<sz;i++)              ans=ans*i%MOD;        }//两个区间，其他全叶子，只能叶子在中间，区间在两边//叶子全排列，左右俩区间互换        else if(yezi==sz-2)        {            ans=ans*2%MOD;            for(int i=1;i<sz-1;i++)            ans=ans*i%MOD;        }    }}int main(){    int t,n,fa,son;    scanf("%d",&t);    for(int i=1;i<=100000;i++)    {        store[i].id=i;        }    for(int i=1;i<=t;i++)    {//初始化        scanf("%d",&n);        for(int j=1;j<=n;j++)        {            store[j].child.clear();store[j].edge.clear();            store[j].num=0;        }        for(int j=1;j<n;j++)        {            scanf("%d%d",&son,&fa);//连双向边，搜索后才能决定谁是父亲，谁是儿子            store[fa].edge.push_back(son);store[son].edge.push_back(fa);//连边的数量            store[fa].num++;store[son].num++;        }//一个节点特判        if(n==1)ans=1;        else{  flag=false;          ans=2;          bfs(1);  if(flag)  ans=0;}        printf("Case #%d: %lld\n",i,ans);    }    return 0;}