Seeking algorithm Closure transfer warshall

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Question: R is a binary relation defined on the set S, R closure request is transmitted.

Input：relation R，set A

Output：t(R),which is the transitive closure of R 

Solution：Warshall algorithm

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Transitive closure (transitive closure) R & lt * = R & lt ^{. 1}  ∪ R & lt ²  ∪ R & lt ^{. 3}  ∪ ∪ R & lt ...... ^n-  

Explain transfer relationship R closure is a relationship that can be represented by R * is represented by t (R).

Warshall algorithm works like this:

First, we represented the R matrix,

Then begins to traverse from the first column by column, for the i-th column, from top to bottom through each element,

If the i-th row j-th column element is 1, corresponds to the i-th row j-th row added.

 

python simulation code:

 

# Assumes that the first two-dimensional array index for the row index R, and the second subscript is the column index. 
Warshall DEF (R & lt): 
　　n-size = (R & lt) 
　　for I in Range (0,. 1-n-): 
　　　　for J in Range (0,. 1-n-): 
　　　　　　IF R & lt [J] [I] ==. 1: 
　　　　　　　　R & lt [ J] [:] = R & lt + [I] [:] 
　　return R & lt