PT07X  Vertex Cover
You are given an unweighted, undirected tree. Write a program to find a vertex set of minimum size in this tree such that each edge has as least one of its endpoints in that set.
Input
The first line of the input file contains one integer N  number of nodes in the tree (0 < N <= 100000). Next N1 lines contain N1 edges of that tree  Each line contains a pair (u, v) means there is an edge between node u and node v (1 <= u,v <= N).
Output
Print number of nodes in the satisfied vertex set on one line.
Example 1
Input: 3 1 2 1 3 Output: 1 Explanation: The set can be {1}
Example 2
Input: 3 1 2 2 3 Output: 1 Explanation: The set can be {2}
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supriyanta:
20180803 01:51:04
DP on tree 

aman_sachin200:
20180615 12:30:21
Nice One!!DP+DFS!! 

chetan4060:
20180416 14:48:24
simple dp on trees. 

sarwar__05:
20180208 20:37:46
there if no input like:


dunjen_master:
20180120 09:51:35
dp+dfs=ac 

abhi6991:
20170923 05:40:13
In Cpp not passing graph as a reference resulted in 2 WA. 

mamnoonsiam:
20170725 13:07:30
AC in one go :)


d_skyhawk:
20170401 06:45:04
DP+Tree=AC in a go 

rishi_07:
20170331 15:48:01
Finally AC! Nice DP. 

cake_is_a_lie:
20170305 14:44:08
For some reason I understood each vertex needed one neighbour in the output set. That cost me SO many WAs. 
Added by:  ThanhVy Hua 
Date:  20070328 
Time limit:  0.194s1.254s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Coauthor Amber 