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   Problem Statement  

 Problem Statement for Permatchd2

Problem Statement

    

Hero has a simple undirected graph. (Simple means that each edge connects two different vertices, and each pair of vertices is connected by at most one edge.)

A graph is considered pretty if it is a simple undirected graph in which each connected component contains an even number of edges.

You are given the adjacency matrix of Hero's graph as a String[] graph. ('Y' means that the two vertices are connected by an edge, 'N' means that they aren't.)

Change Hero's graph into a pretty graph by adding as few edges as possible. Return the minimum number of edges you have to add, or -1 if Hero's graph cannot be changed into a pretty graph.
 

Definition

    
Class:Permatchd2
Method:fix
Parameters:String[]
Returns:int
Method signature:int fix(String[] graph)
(be sure your method is public)
    
 

Notes

-Don't forget that the graph you'll obtain after adding the edges must still be simple.
 

Constraints

-n will be between 1 and 50, inclusive.
-graph will contain exactly n elements.
-Each element in graph will contain exactly n characters.
-Each character in graph will be either 'N' or 'Y'.
-For all valid i graph[i][i] will be equal to 'N'.
-For all valid i, j graph[i][j] will be equal to graph[j][i].
 

Examples

0)
    
{"NYN",
 "YNN",
 "NNN"}
Returns: 1
This is the adjacency matrix of a simple graph on three vertices. Two of the three vertices are connected by an edge. Here, an optimal solution is to add one edge that will connect the remaining vertex to one of the other two. The resulting graph is a simple graph with a single connected component. The connected component contains two edges, which is an even number.
1)
    
{"NYY",
 "YNN",
 "YNN"}
Returns: 0
2)
    
{"NYY",
 "YNY",
 "YYN"}
Returns: -1
3)
    
{"NYYY",
 "YNYY",
 "YYNN",
 "YYNN"}
Returns: 1
4)
    
{"NYNNNN",
 "YNNNNN",
 "NNNYNN",
 "NNYNNN",
 "NNNNNY",
 "NNNNYN"}
Returns: 3
5)
    
{"N"}
Returns: 0

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This problem was used for:
       Single Round Match 709 Round 1 - Division II, Level Two
       Humblefool Cup Round 1 - Division I, Level Two