# 判断是否为树 - Is It A Tree?

## 这个题目，是使用数学方法来解答的

Posted by isheng on July 17, 2016

## 判断是否为树利用数学关系答题

### 原题题目

#### A - Is It A Tree?

Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u

#### Description

A tree is a well-known data structure that is either empty (null, void, nothing) or is a set of one or more nodes connected by directed edges between nodes satisfying the following properties. There is exactly one node, called the root, to which no directed edges point.

Every node except the root has exactly one edge pointing to it. There is a unique sequence of directed edges from the root to each node. For example, consider the illustrations below, in which nodes are represented by circles and edges are represented by lines with arrowheads. The first two of these are trees, but the last is not.

In this problem you will be given several descriptions of collections of nodes connected by directed edges. For each of these you are to determine if the collection satisfies the definition of a tree or not.

#### Input

The input will consist of a sequence of descriptions (test cases) followed by a pair of negative integers. Each test case will consist of a sequence of edge descriptions followed by a pair of zeroes Each edge description will consist of a pair of integers; the first integer identifies the node from which the edge begins, and the second integer identifies the node to which the edge is directed. Node numbers will always be greater than zero.

#### Output

For each test case display the line “Case k is a tree.” or the line “Case k is not a tree.”, where k corresponds to the test case number (they are sequentially numbered starting with 1).

#### Sample Input

6 8 5 3 5 2 6 4
5 6 0 0

8 1 7 3 6 2 8 9 7 5
7 4 7 8 7 6 0 0

3 8 6 8 6 4
5 3 5 6 5 2 0 0
-1 -1

#### Sample Output

Case 1 is a tree.
Case 2 is a tree.
Case 3 is not a tree.

### 调试过程

##### 问题代码
int Week2TextA[10],WeekText5[10];
//建节点统计表。

##### 修正后的代码
#define w2max 20000

int Week2TextA[w2max],WeekText5[w2max];//建节点统计表。


### AC代码

#include <cstdio>
#include <iostream>
using namespace std;
#define w2max 20000

int Week2TextA[w2max],WeekText5[w2max];//建节点统计表。

void w2ta_star(){
for (int i = 0; i < w2max; ++i) {//初始化数据
Week2TextA[i] = 0;
WeekText5[i] = 0;
}
}

int main(){
int a,b,num,map,n = 0;
//    freopen("in.txt", "r", stdin);
while(1){
n ++;
num = 0,map = 0;
int ok = 0;
w2ta_star();
while(scanf("%d %d",&a,&b)){
if(a == 0 || b == 0) break;
if(a == -1 || b == -1) break;
Week2TextA[b] ++;//统计节点数量
WeekText5[a] ++;//统计节点数量
num ++;//统计边的数量
}
if(a == -1 || b == -1) break;
for (int i = 1; i < w2max; ++i) {//处理的数量
if(Week2TextA[i] > 1) {//判断是否每个节点只有一条有向边指向它
ok = 0;
break;
}
else if(WeekText5[i] > 0 || Week2TextA[i] > 0) map ++;
else continue;
}
if(num == map - 1 ){//根据离散数学公式：边数 = 节点数 - 1 判断该图为树
ok = 1;
}
if(num == 0) ok = 1;//排除空树特殊情况
if(ok == 1) printf("Case %d is a tree.\n",n);
else printf("Case %d is not a tree.\n",n);
if(a == -1 || b == -1) break;//程序终止的条件
}
return 0;
}