NYOJ-129 树的判定并查集-优快云博客

本文链接：https://blog.youkuaiyun.com/u013299801/article/details/23287553

本文介绍了一种用于判断一组节点和边是否构成树的数据结构算法。通过实现特定的条件检查（如根节点唯一性、无环及每个节点仅有一个父节点），确保了数据集符合树的定义。

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树的判定

时间限制： 1000 ms | 内存限制： 65535 KB

难度： 4

描述

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.

输入

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.

The number of test cases will not more than 20,and the number of the node will not exceed 10000.
The inputs will be ended by a pair of -1.

输出

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).

样例输入

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

样例输出

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

非树的几种情况：

1，根节点多于一个

2，出现环

3，某节点的父节点多于一个。

 
 #include <iostream> 

 
 02. 
 #include <algorithm> 

 
 03. 
 #include <string.h> 

 
 04. 
 using namespace std; 

05.

 
 06. 
 #define maxN 10010 

07.

 
 08. 
 int parent[maxN],vis[maxN]; 

09.

 
 10. 
 int findParent(int x) 

 
 11. 
 { 

 
 12. 
 if(x==parent[x])return x; 

 
 13. 
 else return parent[x]=findParent(parent[x]); 

 
 14. 
 } 

15.

 
 16. 
 int main() 

 
 17. 
 { 

 
 18. 
 int x,y,fx,fy,maxn=0,c=1; 

 
 19. 
 bool flag=true; 

 
 20. 
 memset(vis,0,sizeof(vis)); 

 
 21. 
 for(int i=0;i<maxN;i++) 

 
 22. 
 parent[i]=i; 

 
 23. 
 while(cin>>x>>y) 

 
 24. 
 { 

 
 25. 
 if(x==-1&&y==-1)break; 

 
 26. 
 if(x==0&&y==0) 

 
 27. 
 { 

 
 28. 
 if(flag) 

 
 29. 
 { 

 
 30. 
 int r=0; 

 
 31. 
 for(int i=1;i<=maxn;i++) 

 
 32. 
 if(vis[i]&&i==parent[i]) 

 
 33. 
 r++; 

 
 34. 
 if(r>1)flag=false;//根节点多于1 

 
 35. 
 } 

 
 36. 
 if(flag)cout<<"Case "<<c++<<" is a tree."<<endl; 

 
 37. 
 else cout<<"Case "<<c++<<" is not a tree."<<endl; 

 
 38. 
 flag=true; 

 
 39. 
 maxn=0; 

 
 40. 
 memset(vis,0,sizeof(vis)); 

 
 41. 
 for(int i=0;i<maxN;i++) 

 
 42. 
 parent[i]=i; 

 
 43. 
 } 

 
 44. 
 else 

 
 45. 
 { 

 
 46. 
 maxn=max(maxn,max(x,y)); 

 
 47. 
 vis[x]=1; 

 
 48. 
 vis[y]=1; 

 
 49. 
 if(!flag)continue; 

 
 50. 
 fx=findParent(x); 

 
 51. 
 fy=findParent(y); 

 
 52. 
 if(fx!=fy) 

 
 53. 
 { 

 
 54. 
 if(parent[y]==y) 

 
 55. 
 parent[y]=fx; 

 
 56. 
 else 

 
 57. 
 flag=false; 

 
 58. 
 } 

 
 59. 
 else flag=false;//形成环了 

 
 60. 
 } 

 
 61. 
 } 

 
 62. 
 return 0; 

 
 63. 
 } 

NYOJ-129 树的判定 并查集

树的判定

NYOJ-129 树的判定并查集